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Cut to the point: What IS a deep network, anyway? It's a network with multiple hidden layers. Also site krizhevsky to counter the "rebranding" claim and added link to that reference.
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{{Short description|Branch of machine learning}}
{{Overly detailed|date=May 2017|details=at 300+ citations – a lot of which spammy – this article should be trimmed, and replaced with a short summary and link to ''survey literature'' instead of pretending to list every single incremental paper ever written on this topic... this is too much, get to the point.}}
{{For|the TV series episode|Deep Learning (South Park)}}
{{condense|date=May 2017}}<!-- section 5.18.8, do I need to say more? -->
[[File:Deep Learning.jpg|alt=Representing images on multiple layers of abstraction in deep learning|thumb|upright=1.35|Representing images on multiple layers of abstraction in deep learning<ref>{{Cite journal|last1=Schulz|first1=Hannes|last2=Behnke|first2=Sven|date=1 November 2012|title=Deep Learning|journal=KI - Künstliche Intelligenz|language=en|volume=26|issue=4|pages=357–363|doi=10.1007/s13218-012-0198-z|s2cid=220523562|issn=1610-1987|url=https://www.semanticscholar.org/paper/51a80649d16a38d41dbd20472deb3bc9b61b59a0}}</ref>]]
{{For|deep versus shallow learning in educational psychology|Student approaches to learning}}
{{Artificial intelligence|Approaches}}
{{machine learning bar}}
 
In [[machine learning]], '''deep learning''' focuses on utilizing multilayered [[neural network (machine learning)|neural network]]s to perform tasks such as [[Statistical classification|classification]], [[Regression analysis|regression]], and [[representation learning]]. The field takes inspiration from [[Neuroscience|biological neuroscience]] and is centered around stacking [[artificial neuron]]s into layers and "training" them to process data. The adjective "deep" refers to the use of multiple layers (ranging from three to several hundred or thousands) in the network. Methods used can be [[Supervised learning|supervised]], [[Semi-supervised learning|semi-supervised]] or [[Unsupervised learning|unsupervised]].<ref name="NatureBengio">{{cite journal |last1=LeCun |first1= Yann|last2=Bengio |first2=Yoshua | last3=Hinton | first3= Geoffrey|s2cid=3074096 |year=2015 |title=Deep Learning |journal=Nature |volume=521 |issue=7553 |pages=436–444 |doi=10.1038/nature14539 |pmid=26017442|bibcode=2015Natur.521..436L |url= https://hal.science/hal-04206682/file/Lecun2015.pdf}}</ref>
'''Deep learning''' (also known as '''deep structured learning''', '''hierarchical learning''' or '''deep machine learning''') is the study of [[artificial neural networks]] and related [[machine learning]] [[algorithm]] that contain more than one [[Multilayer_perceptron#Layers|hidden layer]]. These deep nets:<ref name="BOOK2014.1">{{cite journal |last1=Deng |first1=L. |last2=Yu |first2=D. |year=2014 |title=Deep Learning: Methods and Applications |url=http://research.microsoft.com/pubs/209355/DeepLearning-NowPublishing-Vol7-SIG-039.pdf |journal=Foundations and Trends in Signal Processing |volume=7 |issue=3–4 |pages=199–200 |doi=10.1561/2000000039}}</ref>
* use a cascade of many layers of [[Nonlinear filter|nonlinear processing]] units for [[feature extraction]] and transformation. Each successive layer uses the output from the previous layer as input. The algorithms may be [[Supervised learning|supervised]] or [[Unsupervised learning|unsupervised]] and applications include pattern analysis (unsupervised) and classification (supervised).
* are based on the (unsupervised) learning of multiple levels of features or representations of the data. Higher level features are derived from lower level features to form a hierarchical representation.
* are part of the broader machine learning field of learning representations of data.
* learn multiple levels of representations that correspond to different levels of abstraction; the levels form a hierarchy of concepts.
 
Some common deep learning network architectures include [[fully connected network]]s, [[deep belief network]]s, [[recurrent neural networks]], [[convolutional neural networks]], [[generative adversarial network]]s, [[Transformer (machine learning model)|transformers]], and [[neural radiance field]]s. These architectures have been applied to fields including [[computer vision]], [[speech recognition]], [[natural language processing]], [[machine translation]], [[bioinformatics]], [[drug design]], [[medical image analysis]], [[Climatology|climate science]], material inspection and [[board game]] programs, where they have produced results comparable to and in some cases surpassing human expert performance.<ref name=":9">{{Cite book |doi=10.1109/cvpr.2012.6248110 |isbn=978-1-4673-1228-8|arxiv=1202.2745|chapter=Multi-column deep neural networks for image classification|title=2012 IEEE Conference on Computer Vision and Pattern Recognition|pages=3642–3649|year=2012|last1=Ciresan|first1=D.|last2=Meier|first2=U.|last3=Schmidhuber|first3=J.|s2cid=2161592}}</ref><ref name="krizhevsky2012">{{cite journal|last1=Krizhevsky|first1=Alex|last2=Sutskever|first2=Ilya|last3=Hinton|first3=Geoffrey|date=2012|title=ImageNet Classification with Deep Convolutional Neural Networks|url=https://www.cs.toronto.edu/~kriz/imagenet_classification_with_deep_convolutional.pdf|journal=NIPS 2012: Neural Information Processing Systems, Lake Tahoe, Nevada|access-date=2017-05-24|archive-date=2017-01-10|archive-url=https://web.archive.org/web/20170110123024/http://www.cs.toronto.edu/~kriz/imagenet_classification_with_deep_convolutional.pdf|url-status=live}}</ref><ref>{{cite web |title=Google's AlphaGo AI wins three-match series against the world's best Go player |url=https://techcrunch.com/2017/05/24/alphago-beats-planets-best-human-go-player-ke-jie/ |website=TechCrunch |date=25 May 2017 |access-date=17 June 2018 |archive-date=17 June 2018 |archive-url=https://web.archive.org/web/20180617065807/https://techcrunch.com/2017/05/24/alphago-beats-planets-best-human-go-player-ke-jie/amp/ |url-status=live }}</ref>
In a simple case, there might be two sets of [[Artificial neuron|neurons]]: one set that receives an input signal and one that sends an output signal. When the input layer receives an input it passes on a modified version of the input to the next layer. In a deep network, there are many layers between the input and the output (and the layers are not made of neurons but it can help to think of it that way), allowing the algorithm to use multiple processing layers, composed of multiple linear and non-[[linear transformation]]s.<ref name="goodfellow2016">Ian Goodfellow, Yoshua Bengio, and Aaron Courville (2016). Deep Learning. MIT Press. [http://www.deeplearningbook.org Online]</ref><ref name="BOOK2014">{{cite journal |last1=Deng |first1=L. |last2=Yu |first2=D. |year=2014 |title=Deep Learning: Methods and Applications |url=http://research.microsoft.com/pubs/209355/DeepLearning-NowPublishing-Vol7-SIG-039.pdf |journal=Foundations and Trends in Signal Processing |volume=7 |issue=3–4 |pages=1–199 |doi=10.1561/2000000039}}</ref><ref name="BENGIODEEP">{{cite journal |first=Yoshua |last=Bengio |year=2009 |title=Learning Deep Architectures for AI |url=http://sanghv.com/download/soft/machine%20learning,%20artificial%20intelligence,%20mathematics%20ebooks/ML/learning%20deep%20architectures%20for%20AI%20%282009%29.pdf |journal=Foundations and Trends in Machine Learning |volume=2 |issue=1 |pages=1–127 |doi=10.1561/2200000006}}</ref><ref name="BENGIO2012">{{cite journal |last1=Bengio |first1=Y. |last2=Courville |first2=A. |last3=Vincent |first3=P. |year=2013 |title=Representation Learning: A Review and New Perspectives |journal=IEEE Transactions on Pattern Analysis and Machine Intelligence |volume=35 |issue=8 |pages=1798–1828 |arxiv=1206.5538 |doi=10.1109/tpami.2013.50}}</ref><ref name="SCHIDHUB">{{cite journal |last=Schmidhuber |first=J. |year=2015 |title=Deep Learning in Neural Networks: An Overview |journal=Neural Networks |volume=61 |pages=85–117 |arxiv=1404.7828 |doi=10.1016/j.neunet.2014.09.003}}</ref><ref name="NatureBengio">{{cite journal |last1=Bengio |first1=Yoshua |last2=LeCun |first2= Yann| last3=Hinton | first3= Geoffrey|year=2015 |title=Deep Learning |journal=Nature |volume=521 |pages=436–444 |doi=10.1038/nature14539 |pmid=26017442}}</ref><ref>Deep Machine Learning – A New Frontier in Artificial Intelligence Research – a survey paper by Itamar Arel, Derek C. Rose, and Thomas P. Karnowski. IEEE Computational Intelligence Magazine, 2013</ref><ref name="scholarpedia">{{cite journal | last1 = Schmidhuber | first1 = Jürgen | authorlink = Jürgen Schmidhuber | year = 2015 | title = Deep Learning | url = http://www.scholarpedia.org/article/Deep_Learning | journal = Scholarpedia | volume = 10 | issue = 11| page = 32832 | doi=10.4249/scholarpedia.32832}}</ref><ref name="DLPATTERNS">{{Cite web | title=A Pattern Language for Deep Learning| author=Carlos E. Perez| url=http://www.deeplearningpatterns.com}}</ref>
 
Early forms of neural networks were inspired by information processing and distributed communication nodes in [[biological system]]s, particularly the [[human brain]]. However, current neural networks do not intend to model the brain function of organisms, and are generally seen as low-quality models for that purpose.<ref>{{Cite web |date=2022-11-02 |title=Study urges caution when comparing neural networks to the brain |url=https://news.mit.edu/2022/neural-networks-brain-function-1102 |access-date=2023-12-06 |website=MIT News {{!}} Massachusetts Institute of Technology |language=en}}</ref>
Deep learning is part of a broader family of machine learning methods based on [[learning representation]]s of data. An observation (e.g., an image) can be represented in many ways such as a [[Vector space|vector]] of intensity values per pixel, or in a more abstract way as a set of edges, regions of particular shape, etc. Some representations are better than others at simplifying the learning task (e.g., face recognition or facial expression recognition<ref>{{cite thesis |last=Glauner |first=P. |year=2015 |title=Deep Convolutional Neural Networks for Smile Recognition |arxiv=1508.06535 |type=MSc Thesis |publisher=[[Imperial College London]], Department of Computing}}</ref>). One of the promises of deep learning is replacing handcrafted [[Feature (machine learning)|features]] with efficient algorithms for [[Unsupervised learning|unsupervised]] or [[Semi-supervised learning|semi-supervised]] [[feature learning]] and hierarchical [[feature extraction]].<ref>{{cite book |last1=Song |first1=H.A. |last2=Lee |first2=S. Y. |year=2013 |chapter=Hierarchical Representation Using NMF |title=Neural Information Processing |series=Lectures Notes in Computer Sciences |volume=8226 |issue= |pages=466–473 |publisher=[[Springer Berlin Heidelberg]] |isbn=978-3-642-42053-5 |doi=10.1007/978-3-642-42054-2_58}}</ref>
Research in this area attempts to make better representations and create models to learn these representations from large-scale unlabeled data. Some of the representations are inspired by advances in [[neuroscience]] and are loosely based on interpretation of information processing and communication patterns in a [[nervous system]], such as [[neural coding]] which attempts to define a relationship between various stimuli and associated neuronal responses in the [[brain]].<ref>{{cite journal |last1=Olshausen |first1=B. A. |year=1996 |title=Emergence of simple-cell receptive field properties by learning a sparse code for natural images |journal=Nature |volume=381 |issue=6583 |pages=607–609 |doi=10.1038/381607a0 |pmid=8637596}}</ref>
 
Various deep learning architectures such as [[#Deep_neural_network_architectures|deep neural network]]s, [[convolutional neural network|convolutional deep neural networks]], [[deep belief network]]s and [[recurrent neural network]]s have been applied to fields like [[computer vision]], [[automatic speech recognition]], [[natural language processing]], audio recognition and [[bioinformatics]] where they have been shown to produce state-of-the-art results on various tasks.
 
Although ''Deep learning'' has been characterized as a [[buzzword]], or a rebranding of [[neural network]]s<ref>{{cite video |last=Collobert |first=R. |date=April 2011 |title=Deep Learning for Efficient Discriminative Parsing |url=http://videolectures.net/aistats2011_collobert_deep/ |website=VideoLectures.net |time=7min 45s}}</ref><ref>{{cite web |last=Gomes |first=L. |date=20 October 2014 |title=Machine-Learning Maestro Michael Jordan on the Delusions of Big Data and Other Huge Engineering Efforts |url=http://spectrum.ieee.org/robotics/artificial-intelligence/machinelearning-maestro-michael-jordan-on-the-delusions-of-big-data-and-other-huge-engineering-efforts |work=[[IEEE Spectrum]]}}</ref>, deep neural nets have demonstrated an ability to out-perform other machine learning algorithms on tasks such as object recognition in the field of [[computer vision]].
<ref name="krizhevsky2012"></ref>
== Introduction ==
 
=== Definitions ===
 
{{toclimit|3}}
Deep learning is a class
of [[machine learning]] [[algorithm]]s that<ref name="BOOK2014" />{{rp|pages=199–200}}
* use a cascade of many layers of [[Nonlinear filter|nonlinear processing]] units for [[feature extraction]] and transformation. Each successive layer uses the output from the previous layer as input. The algorithms may be [[Supervised learning|supervised]] or [[Unsupervised learning|unsupervised]] and applications include pattern analysis (unsupervised) and classification (supervised).
* are based on the (unsupervised) learning of multiple levels of features or representations of the data. Higher level features are derived from lower level features to form a hierarchical representation.
* are part of the broader machine learning field of learning representations of data.
* learn multiple levels of representations that correspond to different levels of abstraction; the levels form a hierarchy of concepts.
 
== Overview ==
These definitions have in common (1) multiple layers of nonlinear processing units and (2) the supervised or unsupervised learning of feature representations in each layer, with the layers forming a hierarchy from low-level to high-level features.<ref name="BOOK2014" />{{rp|page=200}} The composition of a layer of nonlinear processing units used in a deep learning algorithm depends on the problem to be solved. Layers that have been used in deep learning include hidden layers of an [[artificial neural network]] and sets of complicated [[propositional formula]]s.<ref name="BENGIODEEP" /> They may also include latent variables organized layer-wise in deep generative models such as the nodes in Deep Belief Networks and Deep Boltzmann Machines.
Most modern deep learning models are based on multi-layered [[neural network (machine learning)|neural network]]s such as [[convolutional neural network]]s and [[transformer (neural network)|transformer]]s, although they can also include [[propositional formula]]s or latent variables organized layer-wise in deep [[generative model]]s such as the nodes in [[deep belief network]]s and deep [[Boltzmann machine]]s.<ref name="BENGIODEEP">{{cite journal|last=Bengio|first=Yoshua|year=2009|title=Learning Deep Architectures for AI|url=http://sanghv.com/download/soft/machine%20learning,%20artificial%20intelligence,%20mathematics%20ebooks/ML/learning%20deep%20architectures%20for%20AI%20%282009%29.pdf|journal=Foundations and Trends in Machine Learning|volume=2|issue=1|pages=1–127|doi=10.1561/2200000006|citeseerx=10.1.1.701.9550|s2cid=207178999 |access-date=3 September 2015|archive-url=https://web.archive.org/web/20160304084250/http://sanghv.com/download/soft/machine%20learning,%20artificial%20intelligence,%20mathematics%20ebooks/ML/learning%20deep%20architectures%20for%20AI%20(2009).pdf|archive-date=4 March 2016|url-status=dead}}</ref>
 
Fundamentally, deep learning refers to a class of [[machine learning]] [[algorithm]]s in which a hierarchy of layers is used to transform input data into a progressively more abstract and composite representation. For example, in an [[image recognition]] model, the raw input may be an [[image]] (represented as a [[Tensor (machine learning)|tensor]] of [[pixel]]s). The first representational layer may attempt to identify basic shapes such as lines and circles, the second layer may compose and encode arrangements of edges, the third layer may encode a nose and eyes, and the fourth layer may recognize that the image contains a face.
Deep learning algorithms transform their inputs through more layers than shallow learning algorithms. At each layer, the signal is transformed by a processing unit, like an artificial neuron, whose parameters are 'learned' through training.<ref name="SCHIDHUB" />{{rp|page=6}} A chain of transformations from input to output is a ''credit assignment path'' (CAP). CAPs describe potentially causal connections between input and output and may vary in length – for a feedforward neural network, the depth of the CAPs (thus of the network) is the number of hidden layers plus one (as the output layer is also parameterized), but for [[recurrent neural network]]s, in which a signal may propagate through a layer more than once, the CAP is potentially unlimited in length. There is no universally agreed upon threshold of depth dividing shallow learning from deep learning, but most researchers in the field agree that deep learning has multiple nonlinear layers (CAP > 2) and [[Juergen Schmidhuber]] considers CAP > 10 to be very deep learning.<ref name="SCHIDHUB" />{{rp|page=7}}
 
Importantly, a deep learning process can learn which features to optimally place at which level ''on its own''. Prior to deep learning, machine learning techniques often involved hand-crafted [[feature engineering]] to transform the data into a more suitable representation for a classification algorithm to operate on. In the deep learning approach, features are not hand-crafted and the model [[representation learning|discovers]] useful feature representations from the data automatically. This does not eliminate the need for hand-tuning; for example, varying numbers of layers and layer sizes can provide different degrees of abstraction.<ref name="BENGIO2012">{{cite journal|last2=Courville|first2=A.|last3=Vincent|first3=P.|year=2013|title=Representation Learning: A Review and New Perspectives|journal=IEEE Transactions on Pattern Analysis and Machine Intelligence|volume=35|issue=8|pages=1798–1828|arxiv=1206.5538|doi=10.1109/tpami.2013.50|pmid=23787338|last1=Bengio|first1=Y.|bibcode=2013ITPAM..35.1798B |s2cid=393948}}</ref><ref name="NatureBengio" />
=== Fundamental concepts ===
 
The word "deep" in "deep learning" refers to the number of layers through which the data is transformed. More precisely, deep learning systems have a substantial ''credit assignment path'' (CAP) depth. The CAP is the chain of transformations from input to output. CAPs describe potentially causal connections between input and output. For a [[feedforward neural network]], the depth of the CAPs is that of the network and is the number of hidden layers plus one (as the output layer is also parameterized). For [[recurrent neural network]]s, in which a signal may propagate through a layer more than once, the CAP depth is potentially unlimited.<ref name="SCHIDHUB" /> No universally agreed-upon threshold of depth divides shallow learning from deep learning, but most researchers agree that deep learning involves CAP depth higher than two. CAP of depth two has been shown to be a universal approximator in the sense that it can emulate any function.<ref>{{Cite book|url=https://books.google.com/books?id=9CqQDwAAQBAJ&pg=PA15|title=Human Behavior and Another Kind in Consciousness: Emerging Research and Opportunities: Emerging Research and Opportunities|last=Shigeki|first=Sugiyama|date=12 April 2019|publisher=IGI Global|isbn=978-1-5225-8218-2|language=en}}</ref> Beyond that, more layers do not add to the function approximator ability of the network. Deep models (CAP > two) are able to extract better features than shallow models and hence, extra layers help in learning the features effectively.
Deep learning algorithms are based on distributed representations. The underlying assumption behind distributed representations is that observed data are generated by the interactions of factors organized in layers. Deep learning adds the assumption that these layers of factors correspond to levels of abstraction or composition. Varying numbers of layers and layer sizes can be used to provide different amounts of abstraction.<ref name="BENGIO2012"/>
 
Deep learning architectures can be constructed with a [[greedy algorithm|greedy]] layer-by-layer method.<ref name=BENGIO2007>{{cite conference | first1=Yoshua | last1=Bengio | first2=Pascal | last2=Lamblin | first3=Dan | last3=Popovici | first4=Hugo | last4=Larochelle | title=Greedy layer-wise training of deep networks | year=2007 | url=http://papers.nips.cc/paper/3048-greedy-layer-wise-training-of-deep-networks.pdf | conference=Advances in neural information processing systems | pages=153–160 | access-date=2019-10-06 | archive-date=2019-10-20 | archive-url=https://web.archive.org/web/20191020195638/http://papers.nips.cc/paper/3048-greedy-layer-wise-training-of-deep-networks.pdf | url-status=live }}</ref> Deep learning helps to disentangle these abstractions and pick out which features improve performance.<ref name="BENGIO2012" />
Deep learning exploits this idea of hierarchical explanatory factors where higher level, more abstract concepts are learned from the lower level ones. These architectures are often constructed with a [[greedy algorithm|greedy]] layer-by-layer method. Deep learning helps to disentangle these abstractions and pick out which features are useful for learning.<ref name="BENGIO2012"/>
 
Deep learning algorithms can be applied to unsupervised learning tasks. This is an important benefit because unlabeled data is more abundant than the labeled data. Examples of deep structures that can be trained in an unsupervised manner are [[deep belief network]]s.<ref name="BENGIO2012" /><ref name="SCHOLARDBNS">{{cite journal | last1 = Hinton | first1 = G.E. | year = 2009| title = Deep belief networks | journal = Scholarpedia | volume = 4 | issue = 5| page = 5947 | doi=10.4249/scholarpedia.5947| bibcode = 2009SchpJ...4.5947H| doi-access = free }}</ref>
For [[supervised learning]] tasks, deep learning methods obviate [[feature engineering]], by translating the data into compact intermediate representations akin to [[Principal Component Analysis|principal components]], and derive layered structures which remove redundancy in representation.<ref name="BOOK2014"/>
 
The term ''deep learning'' was introduced to the machine learning community by [[Rina Dechter]] in 1986,<ref name="dechter1986">[[Rina Dechter]] (1986). Learning while searching in constraint-satisfaction problems. University of California, Computer Science Department, Cognitive Systems Laboratory.[https://www.researchgate.net/publication/221605378_Learning_While_Searching_in_Constraint-Satisfaction-Problems Online] {{Webarchive|url=https://web.archive.org/web/20160419054654/https://www.researchgate.net/publication/221605378_Learning_While_Searching_in_Constraint-Satisfaction-Problems|date=2016-04-19}}</ref> and to artificial neural networks by Igor Aizenberg and colleagues in 2000, in the context of [[Boolean network|Boolean]] threshold neurons.<ref name="MV_1">{{cite book |author1=Aizenberg, I.N. |url=https://link.springer.com/book/10.1007/978-1-4757-3115-6 |title=Multi-Valued and Universal Binary Neurons |author2=Aizenberg, N.N. |author3=Vandewalle, J. |date=2000 |publisher=Science & Business Media |isbn=978-0-7923-7824-2 |doi=10.1007/978-1-4757-3115-6 |access-date=27 December 2023}}</ref><ref>Co-evolving recurrent neurons learn deep memory POMDPs. Proc. GECCO, Washington, D. C., pp. 1795–1802, ACM Press, New York, NY, USA, 2005.</ref> Although the history of its appearance is apparently more complicated.<ref>{{Cite journal |last=Fradkov |first=Alexander L. |date=2020-01-01 |title=Early History of Machine Learning |journal=IFAC-PapersOnLine |series=21st IFAC World Congress |volume=53 |issue=2 |pages=1385–1390 |doi=10.1016/j.ifacol.2020.12.1888 |issn=2405-8963 |s2cid=235081987 |doi-access=free}}</ref>
Many deep learning algorithms are applied to [[unsupervised learning]] tasks. This is an important benefit because unlabeled data are usually more abundant than labeled data. Examples of deep structures that can be trained in an unsupervised manner are neural history compressors<ref name="SCHMID1992"/> and deep belief networks.<ref name="BENGIO2012"/><ref name="SCHOLARDBNS">{{cite journal | last1 = Hinton | first1 = G.E. | year = | title = Deep belief networks | url = | journal = Scholarpedia | volume = 4 | issue = 5| page = 5947 | doi=10.4249/scholarpedia.5947}}</ref>
 
== Interpretations ==
Deep neural networks are generally interpreted in terms of the [[universal approximation theorem]]<ref name=cyb>{{cite journal | last1 = Cybenko | year = 1989 | title = Approximations by superpositions of sigmoidal functions | url = http://deeplearning.cs.cmu.edu/pdfs/Cybenko.pdf | journal = [[Mathematics of Control, Signals, and Systems]] | volume = 2 | issue = 4 | pages = 303–314 | doi = 10.1007/bf02551274 | bibcode = 1989MCSS....2..303C | s2cid = 3958369 | url-status = dead | archive-url = https://web.archive.org/web/20151010204407/http://deeplearning.cs.cmu.edu/pdfs/Cybenko.pdf | archive-date = 10 October 2015 }}</ref><ref name=horn>{{cite journal | last1 = Hornik | first1 = Kurt | year = 1991 | title = Approximation Capabilities of Multilayer Feedforward Networks | journal = Neural Networks | volume = 4 | issue = 2| pages = 251–257 | doi=10.1016/0893-6080(91)90009-t| s2cid = 7343126 }}</ref><ref name="Haykin, Simon 1998">{{cite book|first=Simon S. |last=Haykin|title=Neural Networks: A Comprehensive Foundation|url={{google books |plainurl=y |id=bX4pAQAAMAAJ}}|year=1999|publisher=Prentice Hall|isbn=978-0-13-273350-2}}</ref><ref name="Hassoun, M. 1995 p. 48">{{cite book|first=Mohamad H. |last=Hassoun|title=Fundamentals of Artificial Neural Networks|url={{google books |plainurl=y |id=Otk32Y3QkxQC|page=48}}|year=1995|publisher=MIT Press|isbn=978-0-262-08239-6|page=48}}</ref><ref name=ZhouLu>Lu, Z., Pu, H., Wang, F., Hu, Z., & Wang, L. (2017). [http://papers.nips.cc/paper/7203-the-expressive-power-of-neural-networks-a-view-from-the-width The Expressive Power of Neural Networks: A View from the Width] {{Webarchive|url=https://web.archive.org/web/20190213005539/http://papers.nips.cc/paper/7203-the-expressive-power-of-neural-networks-a-view-from-the-width |date=2019-02-13 }}. Neural Information Processing Systems, 6231-6239.</ref> or [[Bayesian inference|probabilistic inference]].<ref>{{cite journal |last1=Orhan |first1=A. E. |last2=Ma |first2=W. J. |date=2017 |title=Efficient probabilistic inference in generic neural networks trained with non-probabilistic feedback |journal=Nature Communications |volume=8 |issue=1 |pages=138 | pmid=28743932 | doi=10.1038/s41467-017-00181-8|pmc=5527101 |bibcode=2017NatCo...8..138O | doi-access=free}}</ref><ref name="BOOK2014">{{cite journal |last1=Deng |first1=L. |last2=Yu |first2=D. |year=2014 |title=Deep Learning: Methods and Applications |url=http://research.microsoft.com/pubs/209355/DeepLearning-NowPublishing-Vol7-SIG-039.pdf |url-status=live |journal=Foundations and Trends in Signal Processing |volume=7 |issue=3–4 |pages=1–199 |doi=10.1561/2000000039 |archive-url=https://web.archive.org/web/20160314152112/http://research.microsoft.com/pubs/209355/DeepLearning-NowPublishing-Vol7-SIG-039.pdf |archive-date=2016-03-14 |access-date=2014-10-18}}</ref><ref name="BENGIO2012" /><ref name="SCHIDHUB">{{cite journal|last=Schmidhuber|first=J.|s2cid=11715509|year=2015|title=Deep Learning in Neural Networks: An Overview|journal=Neural Networks|volume=61|pages=85–117|arxiv=1404.7828|doi=10.1016/j.neunet.2014.09.003|pmid=25462637}}</ref><ref name = MURPHY>{{cite book|first=Kevin P. |last=Murphy|title=Machine Learning: A Probabilistic Perspective|url={{google books |plainurl=y |id=NZP6AQAAQBAJ}}|date=24 August 2012|publisher=MIT Press|isbn=978-0-262-01802-9}}</ref>
 
The classic universal approximation theorem concerns the capacity of [[feedforward neural networks]] with a single hidden layer of finite size to approximate [[continuous functions]].<ref name="cyb"/><ref name="horn"/><ref name="Haykin, Simon 1998"/><ref name="Hassoun, M. 1995 p. 48"/> In 1989, the first proof was published by [[George Cybenko]] for [[sigmoid function|sigmoid]] activation functions<ref name="cyb" /> and was generalised to feed-forward multi-layer architectures in 1991 by Kurt Hornik.<ref name="horn" /> Recent work also showed that universal approximation also holds for non-bounded activation functions such as [[Kunihiko Fukushima]]'s [[rectified linear unit]].<ref name="Fukushima1969">{{cite journal |last1=Fukushima |first1=K. |date=1969 |title=Visual feature extraction by a multilayered network of analog threshold elements |journal=IEEE Transactions on Systems Science and Cybernetics |volume=5 |issue=4 |pages=322–333 |doi=10.1109/TSSC.1969.300225}}</ref><ref name=sonoda17>{{cite journal | last1 = Sonoda | first1 = Sho | last2=Murata | first2=Noboru | s2cid = 12149203 | year = 2017 | title = Neural network with unbounded activation functions is universal approximator | journal = Applied and Computational Harmonic Analysis | volume = 43 | issue = 2 | pages = 233–268 | doi = 10.1016/j.acha.2015.12.005| arxiv = 1505.03654 }}</ref>
Deep neural networks are generally interpreted in terms of: [[Universal approximation theorem]]<ref name="ReferenceB">Balázs Csanád Csáji (2001). Approximation with Artificial Neural Networks; Faculty of Sciences; Eötvös Loránd University, Hungary</ref><ref name=cyb>{{cite journal | last1 = Cybenko | year = 1989 | title = Approximations by superpositions of sigmoidal functions | url = http://deeplearning.cs.cmu.edu/pdfs/Cybenko.pdf | format = PDF | journal = [[Mathematics of Control, Signals, and Systems]] | volume = 2 | issue = 4| pages = 303–314 | doi=10.1007/bf02551274}}</ref><ref name=horn>{{cite journal | last1 = Hornik | first1 = Kurt | year = 1991 | title = Approximation Capabilities of Multilayer Feedforward Networks | url = | journal = Neural Networks | volume = 4 | issue = 2| pages = 251–257 | doi=10.1016/0893-6080(91)90009-t}}</ref><ref name="Haykin, Simon 1998">Haykin, Simon (1998). ''Neural Networks: A Comprehensive Foundation'', Volume 2, Prentice Hall. ISBN 0-13-273350-1.</ref><ref name="Hassoun, M. 1995 p. 48">Hassoun, M. (1995) ''Fundamentals of Artificial Neural Networks'' MIT Press, p.&nbsp;48</ref> or [[Bayesian inference|Probabilistic inference]].<ref name="BOOK2014" /><ref name="BENGIODEEP" /><ref name="BENGIO2012" /><ref name="SCHIDHUB" /><ref name="SCHOLARDBNS" /><ref name = MURPHY>Murphy, K.P. (2012) ''Machine learning: a probabilistic perspective'' MIT Press</ref>
 
The universal approximation theorem for [[deep neural network]]s concerns the capacity of networks with bounded width but the depth is allowed to grow. Lu et al.<ref name=ZhouLu/> proved that if the width of a deep neural network with [[ReLU]] activation is strictly larger than the input dimension, then the network can approximate any [[Lebesgue integration|Lebesgue integrable function]]; if the width is smaller or equal to the input dimension, then a deep neural network is not a universal approximator.
The [[universal approximation theorem]] concerns the capacity of [[feedforward neural networks]] with a single hidden layer of finite size to approximate [[continuous functions]].<ref name="ReferenceB"/><ref name="cyb"/><ref name="horn"/><ref name="Haykin, Simon 1998"/><ref name="Hassoun, M. 1995 p. 48"/>
 
The [[probabilistic]] interpretation<ref name="MURPHY" /> derives from the field of [[machine learning]]. It features inference,<ref name="BOOK2014" /><ref name="BENGIODEEP" /><ref name="BENGIO2012" /><ref name="SCHIDHUB" /><ref name="SCHOLARDBNS" /><ref name="MURPHY" /> as well as the [[optimization]] concepts of [[training]] and [[test (assessment)|testing]], related to fitting and [[generalization]], respectively. More specifically, the probabilistic interpretation considers the activation nonlinearity as a [[cumulative distribution function]].<ref name="MURPHY" /> The probabilistic interpretation led to the introduction of [[dropout (neural networks)|dropout]] as [[Regularization (mathematics)|regularizer]] in neural networks. The probabilistic interpretation was introduced by researchers including [[John Hopfield|Hopfield]], [[Bernard Widrow|Widrow]] and [[Kumpati S. Narendra|Narendra]] and popularized in surveys such as the one by [[Christopher Bishop|Bishop]].<ref name="prml">{{cite book|title=Pattern Recognition and Machine Learning|author=Bishop, Christopher M.|year=2006|publisher=Springer|url=http://users.isr.ist.utl.pt/~wurmd/Livros/school/Bishop%20-%20Pattern%20Recognition%20And%20Machine%20Learning%20-%20Springer%20%202006.pdf|isbn=978-0-387-31073-2|access-date=2017-08-06|archive-date=2017-01-11|archive-url=https://web.archive.org/web/20170111005101/http://users.isr.ist.utl.pt/~wurmd/Livros/school/Bishop%20-%20Pattern%20Recognition%20And%20Machine%20Learning%20-%20Springer%20%202006.pdf|url-status=live}}</ref>
In 1989, the first proof was published by [[George Cybenko]] for [[sigmoid function|sigmoid]] activation functions<ref name=cyb /> and was generalised to feed-forward multi-layer architectures in 1991 by Kurt Hornik.<ref name=horn />
 
== History ==
The [[probabilistic]] interpretation<ref name="MURPHY" /> derives from the field of [[machine learning]]. It features inference,<ref name="BOOK2014" /><ref name="BENGIODEEP" /><ref name="BENGIO2012" /><ref name="SCHIDHUB" /><ref name="SCHOLARDBNS" /><ref name="MURPHY" /> as well as the [[optimization]] concepts of [[training]] and [[test (assessment)|testing]], related to fitting and [[generalization]] respectively. More specifically, the probabilistic interpretation considers the activation nonlinearity as a [[cumulative distribution function]].<ref name="MURPHY" /> See [[Deep belief network]]. The probabilistic interpretation led to the introduction of [[dropout (neural networks)|dropout]] as [[Regularization (mathematics)|regularizer]] in neural networks.<ref name="DROPOUT">{{cite arXiv |last1=Hinton |first1=G. E. |last2=Srivastava| first2 =N.|last3=Krizhevsky| first3=A.| last4 =Sutskever| first4=I.| last5=Salakhutdinov| first5=R.R.|eprint=1207.0580 |class=math.LG |title=Improving neural networks by preventing co-adaptation of feature detectors |date=2012}}</ref>
 
=== Before 1980 ===
The probabilistic interpretation was introduced and popularized by [[Geoff Hinton]], [[Yoshua Bengio]], [[Yann LeCun]] and [[Juergen Schmidhuber]].
 
There are two [[Types of artificial neural networks|types]] of artificial neural network (ANN): [[feedforward neural network]] (FNN) or [[multilayer perceptron]] (MLP) and [[recurrent neural networks]] (RNN). RNNs have cycles in their connectivity structure, FNNs don't. In the 1920s, [[Wilhelm Lenz]] and [[Ernst Ising]] created the [[Ising model]]<ref name="ising1925">{{Cite web|url=https://www.hs-augsburg.de/~harsch/anglica/Chronology/20thC/Ising/isi_fm00.html|title=bibliotheca Augustana|website=www.hs-augsburg.de}}</ref><ref name="brush67">{{cite journal |doi=10.1103/RevModPhys.39.883|title=History of the Lenz-Ising Model|year=1967|last1=Brush|first1=Stephen G.|journal=Reviews of Modern Physics|volume=39|issue=4|pages=883–893|bibcode=1967RvMP...39..883B}}</ref> which is essentially a non-learning RNN architecture consisting of neuron-like threshold elements. In 1972, [[Shun'ichi Amari]] made this architecture adaptive.<ref name="Amari1972">{{cite journal |last1=Amari |first1=Shun-Ichi |title=Learning patterns and pattern sequences by self-organizing nets of threshold elements|journal= IEEE Transactions |date=1972 |volume=C |issue=21 |pages=1197–1206 }}</ref><ref name="DLhistory"/> His learning RNN was republished by [[John Hopfield]] in 1982.<ref name="Hopfield1982">{{cite journal |last1=Hopfield |first1=J. J. |title=Neural networks and physical systems with emergent collective computational abilities |journal= Proceedings of the National Academy of Sciences|date=1982 |volume=79 |issue=8 |pages=2554–2558 |doi=10.1073/pnas.79.8.2554 |pmid=6953413 |pmc=346238 |bibcode=1982PNAS...79.2554H |doi-access=free }}</ref> Other early [[recurrent neural network]]s were published by Kaoru Nakano in 1971.<ref name="Nakano1971">{{cite book |last1=Nakano |first1=Kaoru |chapter=Learning Process in a Model of Associative Memory |title=Pattern Recognition and Machine Learning |date=1971|pages=172–186 |doi=10.1007/978-1-4615-7566-5_15 |isbn=978-1-4615-7568-9 }}</ref><ref name="Nakano1972">{{cite journal |last1=Nakano |first1=Kaoru |title=Associatron-A Model of Associative Memory|journal= IEEE Transactions on Systems, Man, and Cybernetics |date=1972 |volume=SMC-2 |issue=3|pages=380–388 |doi=10.1109/TSMC.1972.4309133 }}</ref> Already in 1948, [[Alan Turing]] produced work on "Intelligent Machinery" that was not published in his lifetime,<ref name="turing1948">{{cite book |last1=Turing |first1=Alan |chapter=Intelligent Machinery |editor-last=Ince |editor-first=D.C. |title=Collected Works of AM Turing: Mechanical Intelligence |volume=1 |page=107 |publisher=Elsevier Science Publishers |year=1992 |orig-date=1948 |isbn=0-444-88058-5}}</ref> containing "ideas related to artificial evolution and learning RNNs".<ref name="DLhistory"/>
==History==
The first general, working learning algorithm for supervised deep feedforward multilayer perceptrons was published by [[Alexey Grigorevich Ivakhnenko|Ivakhnenko]] and Lapa in 1965.<ref name="ivak1965">{{Cite book|title=Cybernetic Predicting Devices|last=Ivakhnenko|first=Alexey|publisher=Naukova Dumka|year=1965|isbn=|___location=Kiev|pages=}}</ref> A 1971 paper<ref name="ivak1971">{{Cite journal|last=Ivakhnenko|first=Alexey|date=1971|title=Polynomial theory of complex systems|url=|journal=IEEE Transactions on Systems, Man and Cybernetics (4)|pages=364–378|doi=|pmid=|access-date=}}</ref> described a deep network with 8 layers trained by the [[Group method of data handling]] algorithm which is still popular in the current millennium{{Citation needed|date=October 2016}}. These ideas were implemented in a computer identification system "Alpha", which demonstrated the learning process. Other Deep Learning working architectures, specifically those built from [[artificial neural networks]] (ANN), date back to the [[Neocognitron]] introduced by [[Kunihiko Fukushima]] in 1980.<ref name="FUKU1980">{{cite journal | last1 = Fukushima | first1 = K. | year = 1980 | title = Neocognitron: A self-organizing neural network model for a mechanism of pattern recognition unaffected by shift in position | url = | journal = Biol. Cybern. | volume = 36 | issue = | pages = 193–202 | doi=10.1007/bf00344251 | pmid=7370364}}</ref> The ANNs themselves date back even further. The challenge was how to train networks with multiple layers.
In 1989, [[Yann LeCun]] et al. were able to apply the standard [[backpropagation]] algorithm, which had been around as the reverse mode of [[automatic differentiation]] since 1970,<ref name="lin1970">[[Seppo Linnainmaa]] (1970). The representation of the cumulative rounding error of an algorithm as a Taylor expansion of the local rounding errors. Master's Thesis (in Finnish), Univ. Helsinki, 6-7.</ref><ref name="grie2012">Griewank, Andreas (2012). Who Invented the Reverse Mode of Differentiation?. Optimization Stories, Documenta Matematica, Extra Volume ISMP (2012), 389-400.</ref><ref name="WERBOS1974">P. Werbos., "Beyond Regression: New Tools for Prediction and Analysis in the Behavioral Sciences," ''PhD thesis, Harvard University'', 1974.</ref><ref name="werbos1982">[[Paul Werbos]] (1982). Applications of advances in nonlinear sensitivity analysis. In System modeling and optimization (pp. 762-770). Springer Berlin Heidelberg. [http://werbos.com/Neural/SensitivityIFIPSeptember1981.pdf Online]</ref> to a deep neural network with the purpose of recognizing handwritten [[ZIP code]]s on mail. Despite the success of applying the algorithm, the time to train the network on this dataset was approximately 3 days, making it impractical for general use.<ref name="LECUN1989">LeCun ''et al.'', "Backpropagation Applied to Handwritten Zip Code Recognition," ''Neural Computation'', 1, pp. 541–551, 1989.</ref>
 
[[Frank Rosenblatt]] (1958)<ref>{{Cite journal |last=Rosenblatt |first=F. |date=1958 |title=The perceptron: A probabilistic model for information storage and organization in the brain. |url=https://doi.apa.org/doi/10.1037/h0042519 |journal=Psychological Review |language=en |volume=65 |issue=6 |pages=386–408 |doi=10.1037/h0042519 |pmid=13602029 |issn=1939-1471}}</ref> proposed the perceptron, an MLP with 3 layers: an input layer, a hidden layer with randomized weights that did not learn, and an output layer. He later published a 1962 book that also introduced variants and computer experiments, including a version with four-layer perceptrons "with adaptive preterminal networks" where the last two layers have learned weights (here he credits H. D. Block and B. W. Knight).<ref name="rosenblatt1962">{{cite book |last=Rosenblatt |first=Frank |author-link=Frank Rosenblatt |title=Principles of Neurodynamics |publisher=Spartan, New York |year=1962}}</ref>{{rp|section 16}} The book cites an earlier network by R. D. Joseph (1960)<ref name="joseph1960">{{cite book |last=Joseph |first=R. D. |title=Contributions to Perceptron Theory, Cornell Aeronautical Laboratory Report No. VG-11 96--G-7, Buffalo |year=1960}}</ref> "functionally equivalent to a variation of" this four-layer system (the book mentions Joseph over 30 times). Should Joseph therefore be considered the originator of proper adaptive [[multilayer perceptrons]] with learning hidden units? Unfortunately, the learning algorithm was not a functional one, and fell into oblivion.
In 1993, [[Jürgen Schmidhuber]]'s neural history compressor<ref name="SCHMID1992"/> implemented as an unsupervised stack of [[recurrent neural networks]] (RNNs) solved a "Very Deep Learning" task<ref name="SCHIDHUB"/> that requires more than 1,000 subsequent layers in an RNN unfolded in time.<ref name="schmidhuber1993">[[Jürgen Schmidhuber]] (1993). Habilitation thesis, TUM, 1993. Page 150 ff demonstrates credit assignment across the equivalent of 1,200 layers in an unfolded RNN. [ftp://ftp.idsia.ch/pub/juergen/habilitation.pdf Online]</ref>
In 1994, [[André C. P. L. F. de Carvalho]], together with [[Mike C. Fairhurst]] and [[David Bisset]], published a work with experimental results of a several layers boolean neural network, also known as weightless neural network, composed by two modules, a self-organising feature extraction neural network module followed by a classification neural network module, which were independently and sequentially trained.<ref>{{Cite journal|title = An integrated Boolean neural network for pattern classification |journal = Pattern Recognition Letters|date = 1994-08-08|pages = 807–813|volume = 15|issue = 8|doi = 10.1016/0167-8655(94)90009-4|first = Andre C. L. F. |last1 = de Carvalho|first2 = Mike C.|last2 = Fairhurst|first3 = David|last3 = Bisset}}</ref>
In 1995, [[Brendan Frey]] demonstrated that it was possible to train a network containing six fully connected layers and several hundred hidden units using the [[wake-sleep algorithm]], which was co-developed with [[Peter Dayan]] and [[Geoffrey Hinton]].<ref>{{Cite journal|title = The wake-sleep algorithm for unsupervised neural networks |journal = Science|date = 1995-05-26|pages = 1158–1161|volume = 268|issue = 5214|doi = 10.1126/science.7761831|first = Geoffrey E.|last = Hinton|first2 = Peter|last2 = Dayan|first3 = Brendan J.|last3 = Frey|first4 = Radford|last4 = Neal}}</ref> However, training took two days. Many factors contribute to the slow speed, one being the [[vanishing gradient problem]] analyzed in 1991 by [[Sepp Hochreiter]].<ref name="HOCH1991">S. Hochreiter., "[http://people.idsia.ch/~juergen/SeppHochreiter1991ThesisAdvisorSchmidhuber.pdf Untersuchungen zu dynamischen neuronalen Netzen]," ''Diploma thesis. Institut f. Informatik, Technische Univ. Munich. Advisor: J. Schmidhuber'', 1991.</ref><ref name="HOCH2001">S. Hochreiter ''et al.'', "Gradient flow in recurrent nets: the difficulty of learning long-term dependencies," ''In S. C. Kremer and J. F. Kolen, editors, A Field Guide to Dynamical Recurrent Neural Networks. IEEE Press'', 2001.</ref>
 
The first working deep learning algorithm was the [[Group method of data handling]], a method to train arbitrarily deep neural networks, published by [[Alexey Ivakhnenko]] and Lapa in 1965. They regarded it as a form of polynomial regression,<ref name="ivak1965">{{cite book|first1=A. G. |last1=Ivakhnenko |first2=V. G. |last2=Lapa |title=Cybernetics and Forecasting Techniques|url={{google books |plainurl=y |id=rGFgAAAAMAAJ}}|year=1967|publisher=American Elsevier Publishing Co.|isbn=978-0-444-00020-0}}</ref> or a generalization of Rosenblatt's perceptron to handle more complex, nonlinear, and hierarchical relationships.<ref>{{Cite journal |last=Ivakhnenko |first=A.G. |date=March 1970 |title=Heuristic self-organization in problems of engineering cybernetics |url=https://linkinghub.elsevier.com/retrieve/pii/0005109870900920 |journal=Automatica |language=en |volume=6 |issue=2 |pages=207–219 |doi=10.1016/0005-1098(70)90092-0}}</ref> A 1971 paper described a deep network with eight layers trained by this method,<ref name="ivak1971">{{Cite journal|last=Ivakhnenko|first=Alexey|date=1971|title=Polynomial theory of complex systems|url=http://gmdh.net/articles/history/polynomial.pdf|journal=IEEE Transactions on Systems, Man, and Cybernetics|pages=364–378|doi=10.1109/TSMC.1971.4308320|volume=SMC-1|issue=4|access-date=2019-11-05|archive-date=2017-08-29|archive-url=https://web.archive.org/web/20170829230621/http://www.gmdh.net/articles/history/polynomial.pdf|url-status=live}}</ref> which is based on layer by layer training through regression analysis. Superfluous hidden units are pruned using a separate validation set. Since the activation functions of the nodes are Kolmogorov-Gabor polynomials, these were also the first deep networks with multiplicative units or "gates".<ref name="DLhistory"/>
While by 1991 such neural networks were used for recognizing isolated 2-D hand-written digits, recognizing 3-D objects was done by matching 2-D images with a handcrafted 3-D object model. Juyang Weng ''et al.'' suggested that a human brain does not use a monolithic 3-D object model, and in 1992 they published Cresceptron,<ref name="Weng1992">J. Weng, N. Ahuja and T. S. Huang, "[http://www.cse.msu.edu/~weng/research/CresceptronIJCNN1992.pdf Cresceptron: a self-organizing neural network which grows adaptively]," ''Proc. International Joint Conference on Neural Networks'', Baltimore, Maryland, vol I, pp. 576-581, June, 1992.</ref><ref name="Weng1993">J. Weng, N. Ahuja and T. S. Huang, "[http://www.cse.msu.edu/~weng/research/CresceptronICCV1993.pdf Learning recognition and segmentation of 3-D objects from 2-D images]," ''Proc. 4th International Conf. Computer Vision'', Berlin, Germany, pp. 121-128, May, 1993.</ref><ref name="Weng1997">J. Weng, N. Ahuja and T. S. Huang, "[http://www.cse.msu.edu/~weng/research/CresceptronIJCV.pdf Learning recognition and segmentation using the Cresceptron]," ''International Journal of Computer Vision'', vol. 25, no. 2, pp. 105-139, Nov. 1997.</ref> a method for performing 3-D object recognition directly from cluttered scenes. Cresceptron is a cascade of layers similar to [[Neocognitron]]. But while Neocognitron required a human programmer to hand-merge features, Cresceptron ''automatically'' learned an open number of unsupervised features in each layer, where each feature is represented by a convolution kernel. Cresceptron also segmented each learned object from a cluttered scene through back-analysis through the network. [[Max pooling]], now often adopted by deep neural networks (e.g. [[ImageNet]] tests), was first used in Cresceptron to reduce the position resolution by a factor of (2x2) to 1 through the cascade for better generalization. Despite these advantages, simpler models that use task-specific handcrafted features such as [[Gabor filter]]s and [[support vector machine]]s (SVMs) were a popular choice in the 1990s and 2000s, because of the computational cost of ANNs at the time, and a great lack of understanding of how the brain autonomously wires its biological networks.
 
The first deep learning [[multilayer perceptron]] trained by [[stochastic gradient descent]]<ref name="robbins1951">{{Cite journal | last1 = Robbins | first1 = H. | author-link = Herbert Robbins| last2 = Monro | first2 = S. | doi = 10.1214/aoms/1177729586 | title = A Stochastic Approximation Method | journal = The Annals of Mathematical Statistics | volume = 22 | issue = 3 | pages = 400 | year = 1951 | doi-access = free }}</ref> was published in 1967 by [[Shun'ichi Amari]].<ref name="Amari1967">{{cite journal |last1=Amari |first1=Shun'ichi |author-link=Shun'ichi Amari|title=A theory of adaptive pattern classifier|journal= IEEE Transactions |date=1967 |volume=EC |issue=16 |pages=279–307}}</ref> In computer experiments conducted by Amari's student Saito, a five layer MLP with two modifiable layers learned [[Knowledge representation|internal representations]] to classify non-linearily separable pattern classes.<ref name="DLhistory">{{cite arXiv |eprint=2212.11279 |class=cs.NE |first=Jürgen |last=Schmidhuber |author-link=Jürgen Schmidhuber |title=Annotated History of Modern AI and Deep Learning |date=2022}}</ref> Subsequent developments in hardware and hyperparameter tunings have made end-to-end [[stochastic gradient descent]] the currently dominant training technique.
In the long history of speech recognition, both shallow and deep learning (e.g., recurrent nets) of artificial neural networks have been explored for many years.<ref name="Morgan1993">Morgan, Bourlard, Renals, Cohen, Franco (1993) "Hybrid neural network/hidden Markov model systems for continuous speech recognition. ICASSP/IJPRAI"</ref><ref name="Robinson1992">T. Robinson. (1992) A real-time recurrent error propagation network word recognition system, ICASSP.</ref><ref name="Waibel1989">Waibel, Hanazawa, Hinton, Shikano, Lang. (1989) "Phoneme recognition using time-delay neural networks. IEEE Transactions on Acoustics, Speech and Signal Processing."</ref>
But these methods never won over the non-uniform internal-handcrafting Gaussian [[mixture model]]/[[Hidden Markov model]] (GMM-HMM) technology based on generative models of speech trained discriminatively.<ref name="Baker2009">{{cite journal | last1 = Baker | first1 = J. | last2 = Deng | first2 = Li | last3 = Glass | first3 = Jim | last4 = Khudanpur | first4 = S. | last5 = Lee | first5 = C.-H. | last6 = Morgan | first6 = N. | last7 = O'Shaughnessy | first7 = D. | year = 2009 | title = Research Developments and Directions in Speech Recognition and Understanding, Part 1 | url = | journal = IEEE Signal Processing Magazine | volume = 26 | issue = 3| pages = 75–80 | doi=10.1109/msp.2009.932166}}</ref>
A number of key difficulties have been methodologically analyzed, including gradient diminishing<ref name="HOCH1991"/> and weak temporal correlation structure in the neural predictive models.<ref name="Bengio1991">Y. Bengio (1991). "Artificial Neural Networks and their Application to Speech/Sequence Recognition," Ph.D. thesis, McGill University, Canada.</ref><ref name="Deng1994">{{cite journal | last1 = Deng | first1 = L. | last2 = Hassanein | first2 = K. | last3 = Elmasry | first3 = M. | year = 1994 | title = Analysis of correlation structure for a neural predictive model with applications to speech recognition | url = | journal = Neural Networks | volume = 7 | issue = 2| pages = 331–339 | doi=10.1016/0893-6080(94)90027-2}}</ref>
Additional difficulties were the lack of big training data and weaker computing power in these early days. Thus, most speech recognition researchers who understood such barriers moved away from neural nets to pursue generative modeling. An exception was at [[SRI International]] in the late 1990s. Funded by the US government's [[National Security Agency|NSA]] and [[DARPA]], SRI conducted research on deep neural networks in speech and speaker recognition. The speaker recognition team, led by [https://www.linkedin.com/in/larryheck Larry Heck], achieved the first significant success with deep neural networks in speech processing as demonstrated in the 1998 [http://www.nist.gov/itl/iad/mig/sre.cfm NIST (National Institute of Standards and Technology) Speaker Recognition evaluation] and later published in the journal of Speech Communication.<ref name="Heck2000">{{cite journal | last1 = Heck | first1 = L. | last2 = Konig | first2 = Y. | last3 = Sonmez | first3 = M. | last4 = Weintraub | first4 = M. | year = 2000 | title = Robustness to Telephone Handset Distortion in Speaker Recognition by Discriminative Feature Design | url = | journal = Speech Communication | volume = 31 | issue = 2| pages = 181–192 | doi=10.1016/s0167-6393(99)00077-1}}</ref> While SRI established success with deep neural networks in speaker recognition, they were unsuccessful in demonstrating similar success in speech recognition. Hinton et al. and Deng et al. reviewed part of this recent history about how their collaboration with each other and then with colleagues across four groups (University of Toronto, Microsoft, Google, and IBM) ignited a renaissance of deep feedforward neural networks in speech recognition.<ref name=HintonDengYu2012/><ref name="ReferenceICASSP2013">{{cite journal|last1=Deng|first1=L.|last2=Hinton|first2=G.|last3=Kingsbury|first3=B.|title=New types of deep neural network learning for speech recognition and related applications: An overview (ICASSP)| date=2013}}</ref><ref name="HintonKeynoteICASSP2013">Keynote talk: Recent Developments in Deep Neural Networks. ICASSP, 2013 (by Geoff Hinton).</ref><ref name="interspeech2014Keynote">Keynote talk: "Achievements and Challenges of Deep Learning - From Speech Analysis and Recognition To Language and Multimodal Processing," Interspeech, September 2014.</ref>
 
In 1969, [[Kunihiko Fukushima]] introduced the [[rectifier (neural networks)|ReLU]] (rectified linear unit) [[activation function]].<ref name="Fukushima1969" /><ref name="DLhistory" /> The rectifier has become the most popular activation function for deep learning.<ref>{{cite arXiv |eprint=1710.05941 |class=cs.NE |first1=Prajit |last1=Ramachandran |first2=Zoph |last2=Barret |title=Searching for Activation Functions |date=October 16, 2017 |last3=Quoc |first3=V. Le}}</ref>
Today, however, many aspects of speech recognition have been taken over by a deep learning method called [[Long short-term memory]] (LSTM), a [[recurrent neural network]] published by [[Sepp Hochreiter]] & [[Jürgen Schmidhuber]] in 1997.<ref name="lstm">[[Sepp Hochreiter|Hochreiter, Sepp]]; and [[Jürgen Schmidhuber|Schmidhuber, Jürgen]]; ''Long Short-Term Memory'', Neural Computation, 9(8):1735–1780, 1997</ref> LSTM RNNs avoid the [[vanishing gradient problem]] and can learn "Very Deep Learning" tasks<ref name="SCHIDHUB"/> that require memories of events that happened thousands of discrete time steps ago, which is important for speech. In 2003, LSTM started to become competitive with traditional speech recognizers on certain tasks.<ref name="graves2003">Alex Graves, Douglas Eck, Nicole Beringer, and [[Jürgen Schmidhuber]] (2003). Biologically Plausible Speech Recognition with LSTM Neural Nets. 1st Intl. Workshop on Biologically Inspired Approaches to Advanced Information Technology, Bio-ADIT 2004, Lausanne, Switzerland, p. 175-184, 2004. [ftp://ftp.idsia.ch/pub/juergen/bioadit2004.pdf Online]</ref> Later it was combined with CTC<ref name="graves2006">Alex Graves, Santiago Fernandez, Faustino Gomez, and [[Jürgen Schmidhuber]] (2006). Connectionist temporal classification: Labelling unsegmented sequence data with recurrent neural nets. Proceedings of ICML’06, pp. 369–376.</ref> in stacks of LSTM RNNs.<ref name="fernandez2007keyword">Santiago Fernandez, Alex Graves, and Jürgen Schmidhuber (2007). An application of recurrent neural networks to discriminative keyword spotting. Proceedings of ICANN (2), pp. 220–229.</ref> In 2015, Google's speech recognition reportedly experienced a dramatic performance jump of 49% through CTC-trained LSTM, which is now available through [[Google Voice Search]] to all [[smartphone]] users,<ref name="sak2015">Haşim Sak, Andrew Senior, Kanishka Rao, Françoise Beaufays and Johan Schalkwyk (September 2015): [http://googleresearch.blogspot.ch/2015/09/google-voice-search-faster-and-more.html Google voice search: faster and more accurate.]</ref> and has become a show case of deep learning.
 
Deep learning architectures for [[convolutional neural network]]s (CNNs) with convolutional layers and downsampling layers began with the [[Neocognitron]] introduced by [[Kunihiko Fukushima]] in 1979, though not trained by backpropagation.<ref name="FUKU1979">{{cite journal |last1=Fukushima |first1=K. |year=1979 |title=Neural network model for a mechanism of pattern recognition unaffected by shift in position—Neocognitron |journal=Trans. IECE (In Japanese)|volume= J62-A |issue=10 |pages=658–665 |doi=10.1007/bf00344251 |pmid=7370364 |s2cid=206775608}}</ref><ref name="FUKU1980">{{cite journal |last1=Fukushima |first1=K. |year=1980 |title=Neocognitron: A self-organizing neural network model for a mechanism of pattern recognition unaffected by shift in position |journal=Biol. Cybern. |volume=36 |issue=4 |pages=193–202 |doi=10.1007/bf00344251 |pmid=7370364 |s2cid=206775608}}</ref>
The use of the expression "Deep Learning" in the context of [[Artificial Neural Networks]] was introduced by Igor Aizenberg and colleagues in 2000.<ref name="aizenberg2000">Igor Aizenberg, Naum N. Aizenberg, Joos P.L. Vandewalle (2000). Multi-Valued and Universal Binary Neurons: Theory, Learning and Applications. Springer Science & Business Media.</ref> A Google Ngram chart shows that the usage of the term has gained traction (actually has taken off) since 2000.<ref name="DLchart">Google Ngram chart of the usage of the expression "deep learning" posted by Jürgen Schmidhuber (2015) [https://plus.google.com/100849856540000067209/posts/7N6z251w2Wd?pid=6127540521703625346&oid=100849856540000067209 Online]</ref>
In 2006, a publication by [[Geoffrey Hinton]] and Ruslan Salakhutdinov drew additional attention by showing how many-layered [[feedforward neural network]] could be effectively pre-trained one layer at a time, treating each layer in turn as an [[unsupervised learning|unsupervised]] [[restricted Boltzmann machine]], then fine-tuning it using [[supervised learning|supervised]] [[backpropagation]].<ref name="HINTON2007">G. E. Hinton., "Learning multiple layers of representation," ''Trends in Cognitive Sciences'', 11, pp. 428–434, 2007.</ref> In 1992, Schmidhuber had already implemented a very similar idea for the more general case of unsupervised deep hierarchies of [[recurrent neural network]]s, and also experimentally shown its benefits for speeding up supervised learning.<ref name="SCHMID1992">J. Schmidhuber., "Learning complex, extended sequences using the principle of history compression," ''Neural Computation'', 4, pp. 234–242, 1992.</ref><ref name="SCHMID1991">J. Schmidhuber., "My First Deep Learning System of 1991 + Deep Learning Timeline 1962–2013." [http://people.idsia.ch/~juergen/firstdeeplearner.html Online]</ref>
 
[[Backpropagation]] is an efficient application of the [[chain rule]] derived by [[Gottfried Wilhelm Leibniz]] in 1673<ref name="leibniz1676">{{Cite book |last=Leibniz |first=Gottfried Wilhelm Freiherr von |url=https://books.google.com/books?id=bOIGAAAAYAAJ&q=leibniz+altered+manuscripts&pg=PA90 |title=The Early Mathematical Manuscripts of Leibniz: Translated from the Latin Texts Published by Carl Immanuel Gerhardt with Critical and Historical Notes (Leibniz published the chain rule in a 1676 memoir) |date=1920 |publisher=Open court publishing Company |isbn=9780598818461 |language=en}}</ref> to networks of differentiable nodes. The terminology "back-propagating errors" was actually introduced in 1962 by Rosenblatt,<ref name="rosenblatt1962" /> but he did not know how to implement this, although [[Henry J. Kelley]] had a continuous precursor of backpropagation in 1960 in the context of [[control theory]].<ref name="kelley1960">{{cite journal |last1=Kelley |first1=Henry J. |author-link=Henry J. Kelley |year=1960 |title=Gradient theory of optimal flight paths |journal=ARS Journal |volume=30 |issue=10 |pages=947–954 |doi=10.2514/8.5282}}</ref> The modern form of backpropagation was first published in [[Seppo Linnainmaa]]'s master thesis (1970).<ref name="lin19703">{{cite thesis |first=Seppo |last=Linnainmaa |author-link=Seppo Linnainmaa |year=1970 |type=Masters |title=The representation of the cumulative rounding error of an algorithm as a Taylor expansion of the local rounding errors |language=fi |publisher=University of Helsinki |page=6–7}}</ref><ref name="lin19763">{{cite journal |last1=Linnainmaa |first1=Seppo |author-link=Seppo Linnainmaa |year=1976 |title=Taylor expansion of the accumulated rounding error |journal=BIT Numerical Mathematics |volume=16 |issue=2 |pages=146–160 |doi=10.1007/bf01931367 |s2cid=122357351}}</ref><ref name="DLhistory" /> G.M. Ostrovski et al. republished it in 1971.<ref name="ostrowski1971">Ostrovski, G.M., Volin,Y.M., and Boris, W.W. (1971). On the computation of derivatives. Wiss. Z. Tech. Hochschule for Chemistry, 13:382–384.</ref><ref name="backprop"/> [[Paul Werbos]] applied backpropagation to neural networks in 1982<ref name="werbos1982">{{cite book |last=Werbos |first=Paul |author-link=Paul Werbos |title=System modeling and optimization |publisher=Springer |year=1982 |pages=762–770 |chapter=Applications of advances in nonlinear sensitivity analysis |access-date=2 July 2017 |chapter-url=http://werbos.com/Neural/SensitivityIFIPSeptember1981.pdf |archive-url=https://web.archive.org/web/20160414055503/http://werbos.com/Neural/SensitivityIFIPSeptember1981.pdf |archive-date=14 April 2016 |url-status=live}}</ref> (his 1974 PhD thesis, reprinted in a 1994 book,<ref name="werbos1974">{{cite book |last=Werbos |first=Paul J. |title=The Roots of Backpropagation : From Ordered Derivatives to Neural Networks and Political Forecasting |___location=New York |publisher=John Wiley & Sons |year=1994 |isbn=0-471-59897-6 }}</ref> did not yet describe the algorithm<ref name="backprop">{{cite web | last = Schmidhuber | first = Juergen | title = Who Invented Backpropagation? | author-link=Juergen Schmidhuber| publisher = IDSIA, Switzerland | url = https://people.idsia.ch/~juergen/who-invented-backpropagation.html | date = 25 Oct 2014 | access-date = 14 Sep 2024 | archive-url = http://web.archive.org/web/20240730110408/https://people.idsia.ch/~juergen/who-invented-backpropagation.html | archive-date = 30 July 2024 | quote = }}</ref>). In 1986, [[David E. Rumelhart]] et al. popularised backpropagation but did not cite the original work.<ref>{{Cite journal |last1=Rumelhart |first1=David E. |last2=Hinton |first2=Geoffrey E. |last3=Williams |first3=Ronald J. |date=October 1986 |title=Learning representations by back-propagating errors |url=https://www.nature.com/articles/323533a0 |journal=Nature |language=en |volume=323 |issue=6088 |pages=533–536 |doi=10.1038/323533a0 |bibcode=1986Natur.323..533R |issn=1476-4687}}</ref><ref name="rumelhart1986">Rumelhart, David E., Geoffrey E. Hinton, and R. J. Williams. "[https://apps.dtic.mil/dtic/tr/fulltext/u2/a164453.pdf Learning Internal Representations by Error Propagation] {{Webarchive|url=https://web.archive.org/web/20221013070443/https://apps.dtic.mil/dtic/tr/fulltext/u2/a164453.pdf |date=2022-10-13 }}". David E. Rumelhart, James L. McClelland, and the PDP research group. (editors), Parallel distributed processing: Explorations in the microstructure of cognition, Volume 1: Foundation. MIT Press, 1986.</ref>
Since its resurgence, deep learning has become part of many state-of-the-art systems in various disciplines, particularly computer vision and [[automatic speech recognition]] (ASR). Results on commonly used evaluation sets such as [[TIMIT]] (ASR) and [[MNIST database|MNIST]] ([[image classification]]), as well as a range of large-vocabulary speech recognition tasks are constantly being improved with new applications of deep learning.<ref name=HintonDengYu2012/><ref>{{cite journal|url=https://www.microsoft.com/en-us/research/publication/new-types-of-deep-neural-network-learning-for-speech-recognition-and-related-applications-an-overview/|title=New types of deep neural network learning for speech recognition and related applications: An overview|first1=Li|last1=Deng|first2=Geoffrey|last2=Hinton|first3=Brian|last3=Kingsbury|date=1 May 2013|publisher=|via=research.microsoft.com}}</ref><ref name="MS2013">L. Deng et al. Recent Advances in Deep Learning for Speech Research at Microsoft, ICASSP, 2013.</ref> Recently, it was shown that deep learning architectures in the form of [[convolutional neural network]]s have been nearly best performing;<ref name="CNNspeech2013">L. Deng, O. Abdel-Hamid, and D. Yu, A deep convolutional neural network using heterogeneous pooling for trading acoustic invariance with phonetic confusion, ICASSP, 2013.</ref><ref name="SAIN2013">T. Sainath ''et al.'', "Convolutional neural networks for LVCSR," ''ICASSP'', 2013.</ref> however, these are more widely used in computer vision than in ASR, and modern large scale speech recognition is typically based on CTC<ref name="graves2006"/> for LSTM.<ref name=lstm/><ref name="sak2015"/><ref name="sak2014">Hasim Sak and Andrew Senior and Francoise Beaufays (2014). Long Short-Term Memory recurrent neural network architectures for large scale acoustic modeling. Proceedings of Interspeech 2014.</ref><ref name="liwu2015">Xiangang Li, Xihong Wu (2015). Constructing Long Short-Term Memory based Deep Recurrent Neural Networks for Large Vocabulary Speech Recognition [http://arxiv.org/abs/1410.4281 arXiv:1410.4281]</ref><ref name="zen2015">Heiga Zen and Hasim Sak (2015). Unidirectional Long Short-Term Memory Recurrent Neural Network with Recurrent Output Layer for Low-Latency Speech Synthesis. In Proceedings of ICASSP, pp. 4470-4474.</ref>
 
=== 1980s-2000s ===
The real impact of deep learning in industry apparently began in the early 2000s, when CNNs already processed an estimated 10% to 20% of all the checks written in the US in the early 2000s, according to [[Yann LeCun]].<ref name="lecun2016slides">[[Yann LeCun]] (2016). Slides on Deep Learning [https://indico.cern.ch/event/510372/ Online]</ref> Industrial applications of deep learning to large-scale speech recognition started around 2010. In late 2009, Li Deng invited Geoffrey Hinton to work with him and colleagues at Microsoft Research in Redmond, Washington to apply deep learning to speech recognition. They co-organized the 2009 NIPS Workshop on Deep Learning for Speech Recognition. The workshop was motivated by the limitations of deep generative models of speech, and the possibility that the big-compute, big-data era warranted a serious try of deep neural nets (DNN). It was believed that pre-training DNNs using generative models of deep belief nets (DBN) would overcome the main difficulties of neural nets encountered in the 1990s.<ref name="HintonKeynoteICASSP2013"/> However, early into this research at Microsoft, it was discovered that without pre-training, but using large amounts of training data, and especially DNNs designed with corresponding large, context-dependent output layers, produced error rates dramatically lower than then-state-of-the-art GMM-HMM and also than more advanced generative model-based speech recognition systems. This finding was verified by several other major speech recognition research groups.<ref name="HintonDengYu2012">{{cite journal | last1 = Hinton | first1 = G. | last2 = Deng | first2 = L. | last3 = Yu | first3 = D. | last4 = Dahl | first4 = G. | last5 = Mohamed | first5 = A. | last6 = Jaitly | first6 = N. | last7 = Senior | first7 = A. | last8 = Vanhoucke | first8 = V. | last9 = Nguyen | first9 = P. | last10 = Sainath | first10 = T. | last11 = Kingsbury | first11 = B. | year = 2012 | title = Deep Neural Networks for Acoustic Modeling in Speech Recognition --- The shared views of four research groups | url = | journal = IEEE Signal Processing Magazine | volume = 29 | issue = 6| pages = 82–97 | doi=10.1109/msp.2012.2205597}}</ref><ref name="patent2011">D. Yu, L. Deng, G. Li, and F. Seide (2011). "Discriminative pretraining of deep neural networks," U.S. Patent Filing.</ref> Further, the nature of recognition errors produced by the two types of systems was found to be characteristically different,<ref name="ReferenceICASSP2013"/><ref name="NIPS2009">NIPS Workshop: Deep Learning for Speech Recognition and Related Applications, Whistler, BC, Canada, Dec. 2009 (Organizers: Li Deng, Geoff Hinton, D. Yu).</ref>
offering technical insights into how to integrate deep learning into the existing highly efficient, run-time speech decoding system deployed by all major players in speech recognition industry. The history of this significant development in deep learning has been described and analyzed in recent books and articles.<ref name=BOOK2014 /><ref name="ReferenceA">{{cite journal|last1=Yu|first1=D.|last2=Deng|first2=L.|title=Automatic Speech Recognition: A Deep Learning Approach (Publisher: Springer)| date=2014}}</ref><ref>IEEE (2015)http://blogs.technet.com/b/inside_microsoft_research/archive/2015/12/03/deng-receives-prestigious-ieee-technical-achievement-award.aspx</ref>
 
The [[time delay neural network]] (TDNN) was introduced in 1987 by [[Alex Waibel]] to apply CNN to phoneme recognition. It used convolutions, weight sharing, and backpropagation.<ref name=Waibel1987>{{cite conference |title=Phoneme Recognition Using Time-Delay Neural Networks |last1=Waibel |first1=Alex |date=December 1987 |___location=Tokyo, Japan |conference=Meeting of the Institute of Electrical, Information and Communication Engineers (IEICE) | url=https://isl.anthropomatik.kit.edu/pdf/Waibel1987a.pdf}}</ref><ref name="speechsignal">[[Alex Waibel|Alexander Waibel]] et al., ''[http://www.inf.ufrgs.br/~engel/data/media/file/cmp121/waibel89_TDNN.pdf Phoneme Recognition Using Time-Delay Neural Networks]'' IEEE Transactions on Acoustics, Speech, and Signal Processing, Volume 37, No. 3, pp. 328. – 339 March 1989.</ref> In 1988, Wei Zhang applied a backpropagation-trained CNN to alphabet recognition.<ref name="wz1988">{{cite journal |last=Zhang |first=Wei |date=1988 |title=Shift-invariant pattern recognition neural network and its optical architecture |url=https://drive.google.com/file/d/1nN_5odSG_QVae54EsQN_qSz-0ZsX6wA0/view?usp=sharing |journal=Proceedings of Annual Conference of the Japan Society of Applied Physics}}</ref>
Advances in hardware have also been important in enabling the renewed interest in deep learning. In 2009, [[Nvidia]] was involved in what was called the “big bang” of deep learning, “as deep-learning neural networks were combined with Nvidia graphics processing units (GPUs).”<ref>{{cite web|url=https://venturebeat.com/2016/04/05/nvidia-ceo-bets-big-on-deep-learning-and-vr/|title=Nvidia CEO bets big on deep learning and VR|date=April 5, 2016|publisher=''[[Venture Beat]]''}}</ref> That year, the [[Google Brain]] used Nvidia GPUs to create Deep Neural Networks capable of machine learning, where [[Andrew Ng]] determined that GPUs could increase the speed of deep-learning systems by about 100 times.<ref>{{cite web|url=http://www.economist.com/news/special-report/21700756-artificial-intelligence-boom-based-old-idea-modern-twist-not|title=From not working to neural networking|publisher=''[[The Economist]]''}}</ref> In particular, powerful [[graphics processing unit]]s (GPUs) are well-suited for the kind of number crunching, matrix/vector math involved in machine learning.<ref name="jung2004">{{cite journal | last1 = Oh | first1 = K.-S. | last2 = Jung | first2 = K. | year = 2004 | title = GPU implementation of neural networks | url = | journal = Pattern Recognition | volume = 37 | issue = 6| pages = 1311–1314 | doi=10.1016/j.patcog.2004.01.013}}</ref><ref name="chellapilla2006">Chellapilla, K., Puri, S., and Simard, P. (2006). High performance convolutional neural networks for document processing. International Workshop on Frontiers in Handwriting Recognition.</ref> GPUs have been shown to speed up training algorithms by orders of magnitude, bringing running times of weeks back to days.<ref name="CIRESAN2010">D. C. Ciresan ''et al.'', "Deep Big Simple Neural Nets for Handwritten Digit Recognition," ''Neural Computation'', 22, pp. 3207–3220, 2010.</ref><ref name="RAINA2009">R. Raina, A. Madhavan, A. Ng., "Large-scale Deep Unsupervised Learning using Graphics Processors," ''Proc. 26th Int. Conf. on Machine Learning'', 2009.</ref> Specialized hardware and algorithm optimizations can also be used for efficient processing of DNNs.<ref name="sze2017">
In 1989, [[Yann LeCun]] et al. created a CNN called [[LeNet]] for [[Handwriting recognition|recognizing handwritten ZIP code]]s on mail. Training required 3 days.<ref name="LECUN1989">LeCun ''et al.'', "Backpropagation Applied to Handwritten Zip Code Recognition", ''Neural Computation'', 1, pp. 541–551, 1989.</ref> In 1990, Wei Zhang implemented a CNN on [[optical computing]] hardware.<ref name="wz1990">{{cite journal |last=Zhang |first=Wei |date=1990 |title=Parallel distributed processing model with local space-invariant interconnections and its optical architecture |url=https://drive.google.com/file/d/0B65v6Wo67Tk5ODRzZmhSR29VeDg/view?usp=sharing |journal=Applied Optics |volume=29 |issue=32 |pages=4790–7 |bibcode=1990ApOpt..29.4790Z |doi=10.1364/AO.29.004790 |pmid=20577468}}</ref> In 1991, a CNN was applied to medical image object segmentation<ref>{{cite journal |last=Zhang |first=Wei |date=1991 |title=Image processing of human corneal endothelium based on a learning network |url=https://drive.google.com/file/d/0B65v6Wo67Tk5cm5DTlNGd0NPUmM/view?usp=sharing |journal=Applied Optics |volume=30 |issue=29 |pages=4211–7 |bibcode=1991ApOpt..30.4211Z |doi=10.1364/AO.30.004211 |pmid=20706526}}</ref> and breast cancer detection in mammograms.<ref>{{cite journal |last=Zhang |first=Wei |date=1994 |title=Computerized detection of clustered microcalcifications in digital mammograms using a shift-invariant artificial neural network |url=https://drive.google.com/file/d/0B65v6Wo67Tk5Ml9qeW5nQ3poVTQ/view?usp=sharing |journal=Medical Physics |volume=21 |issue=4 |pages=517–24 |bibcode=1994MedPh..21..517Z |doi=10.1118/1.597177 |pmid=8058017}}</ref> [[LeNet]]-5 (1998), a 7-level CNN by [[Yann LeCun]] et al., that classifies digits, was applied by several banks to recognize hand-written numbers on checks digitized in 32x32 pixel images.<ref name="lecun98">{{cite journal |last=LeCun |first=Yann |author2=Léon Bottou |author3=Yoshua Bengio |author4=Patrick Haffner |year=1998 |title=Gradient-based learning applied to document recognition |url=http://yann.lecun.com/exdb/publis/pdf/lecun-01a.pdf |journal=Proceedings of the IEEE |volume=86 |issue=11 |pages=2278–2324 |citeseerx=10.1.1.32.9552 |doi=10.1109/5.726791 |s2cid=14542261 |access-date=October 7, 2016}}</ref>
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[[Recurrent neural network]]s (RNN)<ref name="ising1925"/><ref name="Amari1972"/> were further developed in the 1980s. Recurrence is used for sequence processing, and when a recurrent network is unrolled, it mathematically resembles a deep feedforward layer. Consequently, they have similar properties and issues, and their developments had mutual influences. In RNN, two early influential works were the [[Recurrent neural network#Jordan network|Jordan network]] (1986)<ref>{{Cite journal |last=Jordan |first=Michael I. |date=1986 |title=Attractor dynamics and parallelism in a connectionist sequential machine |url=https://escholarship.org/uc/item/1fg2j76h |journal=Proceedings of the Annual Meeting of the Cognitive Science Society |language=en |volume=8 }}</ref> and the [[Recurrent neural network#Elman network|Elman network]] (1990),<ref>{{Cite journal |last=Elman |first=Jeffrey L. |date=March 1990 |title=Finding Structure in Time |url=https://onlinelibrary.wiley.com/doi/10.1207/s15516709cog1402_1 |journal=Cognitive Science |language=en |volume=14 |issue=2 |pages=179–211 |doi=10.1207/s15516709cog1402_1 |issn=0364-0213}}</ref> which applied RNN to study problems in [[cognitive psychology]].
== Artificial neural networks ==
Some of the most successful deep learning methods involve artificial [[neural network]]s. Artificial neural networks are inspired by the 1959 biological model proposed by [[Nobel laureate]]s [[David H. Hubel]] & [[Torsten Wiesel]], who found two types of cells in the [[primary visual cortex]]: [[simple cell]]s and [[complex cell]]s. Many artificial neural networks can be viewed as cascading models<ref name="Weng1992"/><ref name="Weng1993"/><ref name="Weng1997"/><ref>{{cite journal | last1 = Riesenhuber | first1 = M | last2 = Poggio | first2 = T | year = 1999 | title = Hierarchical models of object recognition in cortex | doi = 10.1038/14819 | journal = Nature Neuroscience | volume = 2 | issue = 11| pages = 1019–1025 }}</ref> of cell types inspired by these biological observations.
 
In the 1980s, backpropagation did not work well for deep learning with long credit assignment paths. To overcome this problem, in 1991, [[Jürgen Schmidhuber]] proposed a hierarchy of RNNs pre-trained one level at a time by [[self-supervised learning]] where each RNN tries to predict its own next input, which is the next unexpected input of the RNN below.<ref name="chunker1991">{{cite journal |last1=Schmidhuber |first1=Jürgen |date= April 1991 |title=Neural Sequence Chunkers | author-link=Jürgen Schmidhuber |url=https://people.idsia.ch/~juergen/FKI-148-91ocr.pdf|journal= TR FKI-148, TU Munich}}</ref><ref name="schmidhuber1992">{{cite journal |last1=Schmidhuber |first1=Jürgen |year=1992 |title=Learning complex, extended sequences using the principle of history compression (based on TR FKI-148, 1991) |url=https://sferics.idsia.ch/pub/juergen/chunker.pdf|journal=Neural Computation |volume=4 |issue=2 |pages=234–242 |doi=10.1162/neco.1992.4.2.234 |s2cid=18271205 }}</ref> This "neural history compressor" uses [[predictive coding]] to learn [[Knowledge representation|internal representations]] at multiple self-organizing time scales. This can substantially facilitate downstream deep learning. The RNN hierarchy can be ''collapsed'' into a single RNN, by [[Knowledge distillation|distilling]] a higher level ''chunker'' network into a lower level ''automatizer'' network.<ref name="chunker1991" /><ref name="schmidhuber1992" /><ref name=DLhistory/> In 1993, a neural history compressor solved a "Very Deep Learning" task that required more than 1000 subsequent [[Layer (deep learning)|layers]] in an RNN unfolded in time.<ref name="schmidhuber1993">{{Cite book |last=Schmidhuber |first=Jürgen |url=https://sferics.idsia.ch/pub/juergen/habilitation.pdf |archive-url=https://web.archive.org/web/20220516075450/https://sferics.idsia.ch/pub/juergen/habilitation.pdf |url-status=dead |archive-date=May 16, 2022 |title=Habilitation thesis: System modeling and optimization |year=1993}} Page 150 ff demonstrates credit assignment across the equivalent of 1,200 layers in an unfolded RNN.</ref> The "P" in [[ChatGPT]] refers to such pre-training.
Fukushima's Neocognitron introduced [[convolution]]al neural networks partially trained by [[unsupervised learning]] with human-directed features in the neural plane. [[Yann LeCun]] et al. (1989) applied supervised [[backpropagation]] to such architectures.<ref name=LeCun1989>Y. LeCun, B. Boser, J. S. Denker, D. Henderson, R. E. Howard, W. Hubbard, L. D. Jackel. 1989 ''Backpropagation Applied to Handwritten Zip Code Recognition.'' Neural Computation, 1(4):541–551.</ref> Weng et al. (1992) published convolutional neural networks Cresceptron<ref name="Weng1992"/><ref name="Weng1993"/><ref name="Weng1997"/> for 3-D object recognition from images of cluttered scenes and segmentation of such objects from images.
 
[[Sepp Hochreiter]]'s diploma thesis (1991)<ref name="HOCH1991">S. Hochreiter., "[http://people.idsia.ch/~juergen/SeppHochreiter1991ThesisAdvisorSchmidhuber.pdf Untersuchungen zu dynamischen neuronalen Netzen]". {{Webarchive|url=https://web.archive.org/web/20150306075401/http://people.idsia.ch/~juergen/SeppHochreiter1991ThesisAdvisorSchmidhuber.pdf |date=2015-03-06 }}. ''Diploma thesis. Institut f. Informatik, Technische Univ. Munich. Advisor: J. Schmidhuber'', 1991.</ref> implemented the neural history compressor,<ref name="chunker1991" /> and identified and analyzed the [[vanishing gradient problem]].<ref name="HOCH1991" /><ref name="HOCH2001">{{cite book|chapter-url={{google books |plainurl=y |id=NWOcMVA64aAC}}|title=A Field Guide to Dynamical Recurrent Networks|last=Hochreiter|first=S.|display-authors=etal|date=15 January 2001|publisher=John Wiley & Sons|isbn=978-0-7803-5369-5|chapter=Gradient flow in recurrent nets: the difficulty of learning long-term dependencies|editor-last2=Kremer|editor-first2=Stefan C.|editor-first1=John F.|editor-last1=Kolen}}</ref> Hochreiter proposed recurrent [[Residual neural network|residual]] connections to solve the vanishing gradient problem. This led to the [[long short-term memory]] (LSTM), published in 1995.<ref>{{Cite Q|Q98967430}}</ref> LSTM can learn "very deep learning" tasks<ref name="SCHIDHUB" /> with long credit assignment paths that require memories of events that happened thousands of discrete time steps before. That LSTM was not yet the modern architecture, which required a "forget gate", introduced in 1999,<ref name="lstm1999">{{Cite book |doi = 10.1049/cp:19991218|chapter = Learning to forget: Continual prediction with LSTM|title = 9th International Conference on Artificial Neural Networks: ICANN '99|volume = 1999|pages = 850–855|year = 1999|last1 = Gers|first1 = Felix| last2 = Schmidhuber|first2 = Jürgen| last3 = Cummins|first3 = Fred| isbn = 0-85296-721-7}}</ref> which became the standard RNN architecture.
An obvious need for recognizing general 3-D objects is least shift invariance and tolerance to deformation. [[Max pooling|Max-pooling]] appeared to be first proposed by Cresceptron<ref name="Weng1992"/><ref name="Weng1993"/> to enable the network to tolerate small-to-large deformation in a hierarchical way, while using convolution. Max-pooling helps, but does not guarantee, shift-invariance at the pixel level.<ref name="Weng1997"/>
 
In 1991, [[Jürgen Schmidhuber]] also published adversarial neural networks that contest with each other in the form of a [[zero-sum game]], where one network's gain is the other network's loss.<ref name="curiosity1991">{{cite conference| title = A possibility for implementing curiosity and boredom in model-building neural controllers | last1 = Schmidhuber | first1 = Jürgen | author-link = Jürgen Schmidhuber | date = 1991 | publisher = MIT Press/Bradford Books| book-title = Proc. SAB'1991| pages = 222–227}}</ref><ref name="fun2010">{{cite journal|last1=Schmidhuber|first1=Jürgen|author-link=Jürgen Schmidhuber|year=2010|title=Formal Theory of Creativity, Fun, and Intrinsic Motivation (1990-2010)|journal= IEEE Transactions on Autonomous Mental Development|volume=2|issue=3|pages=230–247|doi=10.1109/TAMD.2010.2056368 |bibcode=2010ITAMD...2..230S |s2cid=234198 }}</ref> The first network is a [[generative model]] that models a [[probability distribution]] over output patterns. The second network learns by [[gradient descent]] to predict the reactions of the environment to these patterns. This was called "artificial curiosity". In 2014, this principle was used in [[generative adversarial network]]s (GANs).<ref name="gancurpm2020">{{Cite journal|last=Schmidhuber|first=Jürgen| author-link = Jürgen Schmidhuber |date=2020|title=Generative Adversarial Networks are Special Cases of Artificial Curiosity (1990) and also Closely Related to Predictability Minimization (1991)|journal=Neural Networks |language=en|volume=127|pages=58–66|doi=10.1016/j.neunet.2020.04.008 |pmid=32334341 |arxiv=1906.04493 |s2cid=216056336 }}</ref>
With the advent of the [[back-propagation]] algorithm based on [[automatic differentiation]],<ref name="lin1970"/><ref name="WERBOS1974"/><ref name="werbos1982"/><ref name="grie2008">Griewank, Andreas and Walther, A.. Principles and Techniques of Algorithmic Differentiation, Second Edition. SIAM, 2008.</ref><ref name="kelley1960">{{cite journal | last1 = Kelley | first1 = Henry J. | authorlink = Henry J. Kelley | year = 1960 | title = Gradient theory of optimal flight paths | url = http://arc.aiaa.org/doi/abs/10.2514/8.5282?journalCode=arsj | journal = Ars Journal | volume = 30 | issue = 10| pages = 947–954 | doi=10.2514/8.5282}}</ref><ref name="bryson1961">[[Arthur E. Bryson]] (1961, April). A gradient method for optimizing multi-stage allocation processes. In Proceedings of the Harvard Univ. Symposium on digital computers and their applications.</ref><ref name="dreyfus1962">{{cite journal | last1 = Dreyfus | first1 = Stuart | authorlink = Stuart Dreyfus | year = 1962 | title = The numerical solution of variational problems | url = https://www.researchgate.net/publication/256244271_The_numerical_solution_of_variational_problems | journal = Journal of Mathematical Analysis and Applications | volume = 5 | issue = 1| pages = 30–45 | doi=10.1016/0022-247x(62)90004-5}}</ref><ref name="dreyfus1973">{{cite journal | last1 = Dreyfus | first1 = Stuart | authorlink = Stuart Dreyfus | year = 1973 | title = The computational solution of optimal control problems with time lag | url = | journal = IEEE Transactions on Automatic Control | volume = 18 | issue = 4| pages = 383–385 | doi=10.1109/tac.1973.1100330}}</ref><ref name="ROMELNAT">Rumelhart, D. E., Hinton, G. E. & Williams, R. J. , "Learning representations by back-propagating errors" ''nature'', 1974.</ref><ref name="dreyfus1990">[[Stuart Dreyfus]] (1990). Artificial Neural Networks, Back Propagation and the Kelley-Bryson Gradient Procedure. J. Guidance, Control and Dynamics, 1990.</ref> many researchers tried to train supervised deep [[artificial neural network]]s from scratch, initially with little success. [[Sepp Hochreiter]]'s diploma thesis of 1991<ref name="HOCH1991"/><ref name="HOCH2001"/> formally identified the reason for this failure as the [[vanishing gradient problem]], which affects many-layered feedforward networks and [[recurrent neural network]]s. Recurrent networks are trained by unfolding them into very deep feedforward networks, where a new layer is created for each time step of an input sequence processed by the network. As errors propagate from layer to layer, they shrink exponentially with the number of layers, impeding the tuning of neuron weights which is based on those errors.
 
During 1985–1995, inspired by statistical mechanics, several architectures and methods were developed by [[Terry Sejnowski]], [[Peter Dayan]], [[Geoffrey Hinton]], etc., including the [[Boltzmann machine]],<ref>{{Cite journal |last1=Ackley |first1=David H. |last2=Hinton |first2=Geoffrey E. |last3=Sejnowski |first3=Terrence J. |date=1985-01-01 |title=A learning algorithm for boltzmann machines |url=https://www.sciencedirect.com/science/article/pii/S0364021385800124 |journal=Cognitive Science |volume=9 |issue=1 |pages=147–169 |doi=10.1016/S0364-0213(85)80012-4 |issn=0364-0213}}</ref> [[restricted Boltzmann machine]],<ref>{{cite book |last=Smolensky |first=Paul |title=Parallel Distributed Processing: Explorations in the Microstructure of Cognition, Volume 1: Foundations |title-link=Connectionism |publisher=MIT Press |year=1986 |isbn=0-262-68053-X |editor1-last=Rumelhart |editor1-first=David E. |pages=[https://archive.org/details/paralleldistribu00rume/page/194 194–281] |chapter=Chapter 6: Information Processing in Dynamical Systems: Foundations of Harmony Theory |editor2-last=McLelland |editor2-first=James L. |chapter-url=https://stanford.edu/~jlmcc/papers/PDP/Volume%201/Chap6_PDP86.pdf}}</ref> [[Helmholtz machine]],<ref name="nc95">{{Cite journal |last1=Peter |first1=Dayan |last2=Hinton |first2=Geoffrey E. |last3=Neal |first3=Radford M. |last4=Zemel |first4=Richard S. |date=1995 |title=The Helmholtz machine. |journal=Neural Computation |volume=7 |issue=5 |pages=889–904 |doi=10.1162/neco.1995.7.5.889 |pmid=7584891 |s2cid=1890561 |hdl-access=free |author-link1=Peter Dayan |author-link2=Geoffrey Hinton |author-link3=Radford M. Neal |author-link4=Richard Zemel |hdl=21.11116/0000-0002-D6D3-E}} {{closed access}}</ref> and the [[wake-sleep algorithm]].<ref name=":1">{{Cite journal |last1=Hinton |first1=Geoffrey E. |author-link=Geoffrey Hinton |last2=Dayan |first2=Peter |last3=Frey |first3=Brendan J. |last4=Neal |first4=Radford |date=1995-05-26 |title=The wake-sleep algorithm for unsupervised neural networks |journal=Science |volume=268 |issue=5214 |pages=1158–1161 |bibcode=1995Sci...268.1158H |doi=10.1126/science.7761831 |pmid=7761831 |s2cid=871473 |author-link2=Peter Dayan |author-link3=Brendan Frey}}</ref> These were designed for unsupervised learning of deep generative models. However, those were more computationally expensive compared to backpropagation. Boltzmann machine learning algorithm, published in 1985, was briefly popular before being eclipsed by the backpropagation algorithm in 1986. (p.&nbsp;112 <ref>{{Cite book |last=Sejnowski |first=Terrence J. |title=The Deep Learning Revolution |date=2018 |publisher=[[The MIT Press]] |isbn=978-0-262-03803-4 |___location=Cambridge, Massachusetts}}</ref>). A 1988 network became state of the art in [[protein structure prediction]], an early application of deep learning to bioinformatics.<ref>{{Cite journal |last1=Qian |first1=Ning |last2=Sejnowski |first2=Terrence J. |date=1988-08-20 |title=Predicting the secondary structure of globular proteins using neural network models |url=https://dx.doi.org/10.1016/0022-2836%2888%2990564-5 |journal=Journal of Molecular Biology |volume=202 |issue=4 |pages=865–884 |doi=10.1016/0022-2836(88)90564-5 |pmid=3172241 |issn=0022-2836}}</ref>
To overcome this problem, several methods were proposed. One is [[Jürgen Schmidhuber]]'s multi-level hierarchy of networks (1992) pre-trained one level at a time by unsupervised learning, fine-tuned by [[backpropagation]].<ref name="SCHMID1992"/> Here each level learns a compressed representation of the observations that is fed to the next level.
 
Both shallow and deep learning (e.g., recurrent nets) of ANNs for [[speech recognition]] have been explored for many years.<ref>{{Cite journal|last1=Morgan|first1=Nelson|last2=Bourlard |first2=Hervé |last3=Renals |first3=Steve |last4=Cohen |first4=Michael|last5=Franco |first5=Horacio |date=1 August 1993 |title=Hybrid neural network/hidden markov model systems for continuous speech recognition |journal=International Journal of Pattern Recognition and Artificial Intelligence|volume=07|issue=4|pages=899–916|doi=10.1142/s0218001493000455|issn=0218-0014}}</ref><ref name="Robinson1992">{{Cite journal|last=Robinson|first=T.|author-link=Tony Robinson (speech recognition)|date=1992|title=A real-time recurrent error propagation network word recognition system|url=http://dl.acm.org/citation.cfm?id=1895720|journal=ICASSP|pages=617–620|isbn=9780780305328|series=Icassp'92|access-date=2017-06-12|archive-date=2021-05-09|archive-url=https://web.archive.org/web/20210509123135/https://dl.acm.org/doi/10.5555/1895550.1895720|url-status=live}}</ref><ref>{{Cite journal|last1=Waibel|first1=A.|last2=Hanazawa|first2=T.|last3=Hinton|first3=G.|last4=Shikano|first4=K.|last5=Lang|first5=K. J.|date=March 1989|title=Phoneme recognition using time-delay neural networks|journal=IEEE Transactions on Acoustics, Speech, and Signal Processing|volume=37|issue=3|pages=328–339|doi=10.1109/29.21701|issn=0096-3518|hdl=10338.dmlcz/135496|s2cid=9563026 |url=http://dml.cz/bitstream/handle/10338.dmlcz/135496/Kybernetika_38-2002-6_2.pdf|access-date=2019-09-24|archive-date=2021-04-27|archive-url=https://web.archive.org/web/20210427001446/https://dml.cz/bitstream/handle/10338.dmlcz/135496/Kybernetika_38-2002-6_2.pdf|url-status=live}}</ref> These methods never outperformed non-uniform internal-handcrafting Gaussian [[mixture model]]/[[Hidden Markov model]] (GMM-HMM) technology based on generative models of speech trained discriminatively.<ref name="Baker2009">{{cite journal | last1 = Baker | first1 = J. | last2 = Deng | first2 = Li | last3 = Glass | first3 = Jim | last4 = Khudanpur | first4 = S. | last5 = Lee | first5 = C.-H. | last6 = Morgan | first6 = N. | last7 = O'Shaughnessy | first7 = D. | year = 2009 | title = Research Developments and Directions in Speech Recognition and Understanding, Part 1 | journal = IEEE Signal Processing Magazine | volume = 26 | issue = 3| pages = 75–80 | doi=10.1109/msp.2009.932166| bibcode = 2009ISPM...26...75B | hdl = 1721.1/51891 | s2cid = 357467 }}</ref> Key difficulties have been analyzed, including gradient diminishing<ref name="HOCH1991" /> and weak temporal correlation structure in neural predictive models.<ref name="Bengio1991">{{Cite web|url=https://www.researchgate.net/publication/41229141|title=Artificial Neural Networks and their Application to Speech/Sequence Recognition|last=Bengio|first=Y.|date=1991|publisher=McGill University Ph.D. thesis|access-date=2017-06-12|archive-date=2021-05-09|archive-url=https://web.archive.org/web/20210509123131/https://www.researchgate.net/publication/41229141_Artificial_neural_networks_and_their_application_to_sequence_recognition|url-status=live}}</ref><ref name="Deng1994">{{cite journal | last1 = Deng | first1 = L. | last2 = Hassanein | first2 = K. | last3 = Elmasry | first3 = M. | year = 1994 | title = Analysis of correlation structure for a neural predictive model with applications to speech recognition | journal = Neural Networks | volume = 7 | issue = 2| pages = 331–339 | doi=10.1016/0893-6080(94)90027-2}}</ref> Additional difficulties were the lack of training data and limited computing power.
Another method is the [[long short-term memory]] (LSTM) network of [[Sepp Hochreiter|Hochreiter]] & [[Jürgen Schmidhuber|Schmidhuber]] (1997).<ref name="lstm"/> In 2009, deep multidimensional LSTM networks won three ICDAR 2009 competitions in connected handwriting recognition, without any prior knowledge about the three languages to be learned.<ref name="graves2009">Graves, Alex; and Schmidhuber, Jürgen; ''Offline Handwriting Recognition with Multidimensional Recurrent Neural Networks'', in Bengio, Yoshua; Schuurmans, Dale; Lafferty, John; Williams, Chris K. I.; and Culotta, Aron (eds.), ''Advances in Neural Information Processing Systems 22 (NIPS'22), December 7th–10th, 2009, Vancouver, BC'', Neural Information Processing Systems (NIPS) Foundation, 2009, pp. 545–552</ref><ref>{{cite journal | last1 = Graves | first1 = A. | last2 = Liwicki | first2 = M. | last3 = Fernandez | first3 = S. | last4 = Bertolami | first4 = R. | last5 = Bunke | first5 = H. | last6 = Schmidhuber | first6 = J. | year = 2009 | title = A Novel Connectionist System for Improved Unconstrained Handwriting Recognition | doi = 10.1109/tpami.2008.137 | journal = IEEE Transactions on Pattern Analysis and Machine Intelligence | volume = 31 | issue = 5| pages = 855–868}}</ref>
 
Most [[speech recognition]] researchers moved away from neural nets to pursue generative modeling. An exception was at [[SRI International]] in the late 1990s. Funded by the US government's [[National Security Agency|NSA]] and [[DARPA]], SRI researched in speech and [[speaker recognition]]. The speaker recognition team led by [[Larry Heck]] reported significant success with deep neural networks in speech processing in the 1998 [[National Institute of Standards and Technology|NIST]] Speaker Recognition benchmark.<ref name="Doddington2000">{{cite journal | last1 = Doddington | first1 = G. | last2 = Przybocki | first2 = M. | last3 = Martin | first3 = A. | last4 = Reynolds | first4 = D. | year = 2000 | title = The NIST speaker recognition evaluation ± Overview, methodology, systems, results, perspective | journal = Speech Communication | volume = 31 | issue = 2| pages = 225–254 | doi=10.1016/S0167-6393(99)00080-1}}</ref><ref name="Heck2000">{{cite journal |last1=Heck |first1=L. |last2=Konig |first2=Y. |last3=Sonmez |first3=M. |last4=Weintraub |first4=M. |year=2000 |title=Robustness to Telephone Handset Distortion in Speaker Recognition by Discriminative Feature Design |journal=Speech Communication |volume=31 |issue=2 |pages=181–192 |doi=10.1016/s0167-6393(99)00077-1}}</ref> It was deployed in the Nuance Verifier, representing the first major industrial application of deep learning.<ref>L.P Heck and R. Teunen. "Secure and Convenient Transactions with Nuance Verifier". Nuance Users Conference, April 1998.</ref>
Sven Behnke in 2003 relied only on the sign of the gradient ([[Rprop]]) when training his Neural Abstraction Pyramid<ref>
{{cite book
|author=Sven Behnke
|year=2003
|title=Hierarchical Neural Networks for Image Interpretation.
|series=Lecture Notes in Computer Science |volume=2766
|publisher=Springer
|url=http://www.ais.uni-bonn.de/books/LNCS2766.pdf
}}</ref> to solve problems like image reconstruction and face localization.
 
The principle of elevating "raw" features over hand-crafted optimization was first explored successfully in the architecture of deep autoencoder on the "raw" spectrogram or linear [[Filter bank|filter-bank]] features in the late 1990s,<ref name="Heck2000" /> showing its superiority over the [[Mel-frequency cepstrum|Mel-Cepstral]] features that contain stages of fixed transformation from spectrograms. The raw features of speech, [[waveform]]s, later produced excellent larger-scale results.<ref>{{Cite web|url=https://www.researchgate.net/publication/266030526|title=Acoustic Modeling with Deep Neural Networks Using Raw Time Signal for LVCSR (PDF Download Available)|website=ResearchGate|access-date=14 June 2017|archive-date=9 May 2021|archive-url=https://web.archive.org/web/20210509123218/https://www.researchgate.net/publication/266030526_Acoustic_Modeling_with_Deep_Neural_Networks_Using_Raw_Time_Signal_for_LVCSR|url-status=live}}</ref>
Other methods also use unsupervised pre-training to structure a neural network, making it first learn generally useful [[feature detection (computer vision)|feature detectors]]. Then the network is trained further by supervised [[back-propagation]] to classify labeled data. The deep model of Hinton et al. (2006) involves learning the distribution of a high-level representation using successive layers of binary or real-valued [[latent variable]]s. It uses a [[restricted Boltzmann machine]] (Smolensky, 1986<ref name="smolensky1986">
{{cite book
|last1=Smolensky |first1=P. |authorlink1=Paul Smolensky
|year=1986
|chapter=Information processing in dynamical systems: Foundations of harmony theory.
|title=Parallel Distributed Processing: Explorations in the Microstructure of Cognition
|editors=D. E. Rumelhart, J. L. McClelland, & the PDP Research Group
|volume=1
|pages=194–281
|url=http://portal.acm.org/citation.cfm?id=104290
}}</ref>) to model each new layer of higher level features. Each new layer guarantees an increase on the [[Lower bound|lower-bound]] of the [[log likelihood]] of the data, thus improving the model, if trained properly. Once sufficiently many layers have been learned, the deep architecture may be used as a [[generative model]] by reproducing the data when sampling down the model (an "ancestral pass") from the top level feature activations.<ref name="hinton2006">{{cite journal
|doi=10.1162/neco.2006.18.7.1527
|last1=Hinton |first1=G. E. |authorlink1=Geoffrey Hinton
|last2=Osindero |first2=S.
|last3=Teh |first3=Y.
|year=2006
|title=A fast learning algorithm for deep belief nets
|journal=[[Neural Computation (journal)|Neural Computation]]
|volume=18
|issue=7 |pages=1527–1554
|url=http://www.cs.toronto.edu/~hinton/absps/fastnc.pdf
|pmid=16764513
}}</ref>
Hinton reports that his models are effective feature extractors over high-dimensional, structured data.<ref>{{Cite journal | last1 = Hinton | first1 = G. | title = Deep belief networks | doi = 10.4249/scholarpedia.5947 | journal = Scholarpedia | volume = 4 | issue = 5 | pages = 5947 | year = 2009 | pmid = | pmc = | url = http://www.scholarpedia.org/article/Deep_belief_networks}}</ref>
 
=== 2000s ===
In 2012, the [[Google Brain]] team led by [[Andrew Ng]] and [[Jeff Dean (computer scientist)|Jeff Dean]] created a neural network that learned to recognize higher-level concepts, such as cats, only from watching unlabeled images taken from [[YouTube]] videos.<ref name="markoff2012">{{cite news
Neural networks entered a lull, and simpler models that use task-specific handcrafted features such as [[Gabor filter]]s and [[support vector machine]]s (SVMs) became the preferred choices in the 1990s and 2000s, because of artificial neural networks' computational cost and a lack of understanding of how the brain wires its biological networks.{{Citation needed|date=August 2024}}
|title= How Many Computers to Identify a Cat? 16,000.
|newspaper = New York Times
|author=John Markoff
|url=https://www.nytimes.com/2012/06/26/technology/in-a-big-network-of-computers-evidence-of-machine-learning.html
|date=25 June 2012
}}</ref><ref name="ng2012">
{{cite arXiv
|title= Building High-level Features Using Large Scale Unsupervised Learning
|last1=Ng |first1=Andrew
|last2=Dean |first2=Jeff
|arxiv=1112.6209
|year=2012
}}</ref>
 
In 2003, LSTM became competitive with traditional speech recognizers on certain tasks.<ref name="graves2003">{{Cite web |last1=Graves |first1=Alex |last2=Eck |first2=Douglas |last3=Beringer |first3=Nicole |last4=Schmidhuber |first4=Jürgen |date=2003 |title=Biologically Plausible Speech Recognition with LSTM Neural Nets |url=ftp://ftp.idsia.ch/pub/juergen/bioadit2004.pdf |access-date=2016-04-09 |website=1st Intl. Workshop on Biologically Inspired Approaches to Advanced Information Technology, Bio-ADIT 2004, Lausanne, Switzerland |archive-url=https://web.archive.org/web/20170706014710/ftp://ftp.idsia.ch/pub/juergen/bioadit2004.pdf |archive-date=2017-07-06 |url-status=dead |pages=175–184}}</ref> In 2006, [[Alex Graves (computer scientist)|Alex Graves]], Santiago Fernández, Faustino Gomez, and Schmidhuber combined it with [[connectionist temporal classification]] (CTC)<ref name="graves2006">{{Cite journal |last1=Graves |first1=Alex |author1-link=Alex Graves (computer scientist) |last2=Fernández |first2=Santiago |last3=Gomez |first3=Faustino |last4=Schmidhuber |first4=Jürgen |author4-link=Jürgen Schmidhuber |date=2006 |title=Connectionist temporal classification: Labelling unsegmented sequence data with recurrent neural networks |journal=Proceedings of the International Conference on Machine Learning, ICML 2006 |pages=369–376 |citeseerx=10.1.1.75.6306}}</ref> in stacks of LSTMs.<ref name="fernandez2007keyword">Santiago Fernandez, Alex Graves, and Jürgen Schmidhuber (2007). [https://mediatum.ub.tum.de/doc/1289941/file.pdf An application of recurrent neural networks to discriminative keyword spotting] {{Webarchive|url=https://web.archive.org/web/20181118164457/https://mediatum.ub.tum.de/doc/1289941/file.pdf|date=2018-11-18}}. Proceedings of ICANN (2), pp. 220–229.</ref> In 2009, it became the first RNN to win a [[pattern recognition]] contest, in connected [[handwriting recognition]].<ref>Graves, Alex; and Schmidhuber, Jürgen; ''Offline Handwriting Recognition with Multidimensional Recurrent Neural Networks'', in Bengio, Yoshua; Schuurmans, Dale; Lafferty, John; Williams, Chris K. I.; and Culotta, Aron (eds.), ''Advances in Neural Information Processing Systems 22 (NIPS'22), December 7th–10th, 2009, Vancouver, BC'', Neural Information Processing Systems (NIPS) Foundation, 2009, pp. 545–552</ref><ref name="SCHIDHUB" />
Other methods rely on the sheer processing power of modern computers, in particular, [[GPU]]s. In 2010, Dan Ciresan and colleagues<ref name="CIRESAN2010"/> in [[Jürgen Schmidhuber]]'s group at the Swiss AI Lab [[IDSIA]] showed that despite the above-mentioned "vanishing gradient problem," the superior processing power of GPUs makes plain [[back-propagation]] feasible for deep feedforward neural networks with many layers. The method outperformed all other machine learning techniques on the old, famous MNIST handwritten digits problem of [[Yann LeCun]] and colleagues at [[NYU]].
 
In 2006, publications by [[Geoffrey Hinton|Geoff Hinton]], [[Russ Salakhutdinov|Ruslan Salakhutdinov]], Osindero and [[Yee Whye Teh|Teh]]<ref>{{Cite journal |last=Hinton |first=Geoffrey E. |date=1 October 2007 |title=Learning multiple layers of representation |url=http://www.cell.com/trends/cognitive-sciences/abstract/S1364-6613(07)00217-3 |url-status=live |journal=Trends in Cognitive Sciences |volume=11 |issue=10 |pages=428–434 |doi=10.1016/j.tics.2007.09.004 |issn=1364-6613 |pmid=17921042 |s2cid=15066318 |archive-url=https://web.archive.org/web/20131011071435/http://www.cell.com/trends/cognitive-sciences/abstract/S1364-6613(07)00217-3 |archive-date=11 October 2013 |access-date=12 June 2017}}</ref><ref name="hinton06">{{Cite journal |last1=Hinton |first1=G. E. |author-link1=Geoff Hinton |last2=Osindero |first2=S. |last3=Teh |first3=Y. W. |year=2006 |title=A Fast Learning Algorithm for Deep Belief Nets |url=http://www.cs.toronto.edu/~hinton/absps/fastnc.pdf |url-status=live |journal=[[Neural Computation (journal)|Neural Computation]] |volume=18 |issue=7 |pages=1527–1554 |doi=10.1162/neco.2006.18.7.1527 |pmid=16764513 |s2cid=2309950 |archive-url=https://web.archive.org/web/20151223164129/http://www.cs.toronto.edu/~hinton/absps/fastnc.pdf |archive-date=2015-12-23 |access-date=2011-07-20}}</ref> [[deep belief network]]s were developed for generative modeling. They are trained by training one restricted Boltzmann machine, then freezing it and training another one on top of the first one, and so on, then optionally [[Fine-tuning (deep learning)|fine-tuned]] using supervised backpropagation.<ref name="HINTON2007">G. E. Hinton., "[http://www.csri.utoronto.ca/~hinton/absps/ticsdraft.pdf Learning multiple layers of representation]". {{Webarchive|url=https://web.archive.org/web/20180522112408/http://www.csri.utoronto.ca/~hinton/absps/ticsdraft.pdf|date=2018-05-22}}. ''Trends in Cognitive Sciences'', 11, pp. 428–434, 2007.</ref> They could model high-dimensional probability distributions, such as the distribution of [[MNIST database|MNIST images]], but convergence was slow.<ref>{{Cite journal |last=Hinton |first=Geoffrey E. |date=October 2007 |title=Learning multiple layers of representation |url=https://linkinghub.elsevier.com/retrieve/pii/S1364661307002173 |journal=Trends in Cognitive Sciences |language=en |volume=11 |issue=10 |pages=428–434 |doi=10.1016/j.tics.2007.09.004|pmid=17921042 }}</ref><ref>{{Cite journal |last1=Hinton |first1=Geoffrey E. |last2=Osindero |first2=Simon |last3=Teh |first3=Yee-Whye |date=July 2006 |title=A Fast Learning Algorithm for Deep Belief Nets |url=https://direct.mit.edu/neco/article/18/7/1527-1554/7065 |journal=Neural Computation |language=en |volume=18 |issue=7 |pages=1527–1554 |doi=10.1162/neco.2006.18.7.1527 |pmid=16764513 |issn=0899-7667}}</ref><ref>{{Cite journal |last=Hinton |first=Geoffrey E. |date=2009-05-31 |title=Deep belief networks |journal=Scholarpedia |language=en |volume=4 |issue=5 |pages=5947 |doi=10.4249/scholarpedia.5947 |doi-access=free |bibcode=2009SchpJ...4.5947H |issn=1941-6016}}</ref>
At about the same time, in late 2009, deep learning feedforward networks made inroads into speech recognition, as marked by the NIPS Workshop on Deep Learning for Speech Recognition. Intensive collaborative work between Microsoft Research and University of Toronto researchers demonstrated by mid-2010 in Redmond that deep neural networks interfaced with a hidden Markov model with context-dependent states that define the neural network output layer can drastically reduce errors in large-vocabulary speech recognition tasks such as voice search. The same deep neural net model was shown to scale up to Switchboard tasks about one year later at Microsoft Research Asia. Even earlier, in 2007, LSTM<ref name=lstm/> trained by CTC<ref name="graves2006"/> started to get excellent results in certain applications.<ref name="fernandez2007keyword"/> This method is now widely used, for example, in Google's greatly improved speech recognition for all smartphone users.<ref name="sak2015"/>
 
The impact of deep learning in industry began in the early 2000s, when CNNs already processed an estimated 10% to 20% of all the checks written in the US, according to Yann LeCun.<ref name="lecun2016slides">[[Yann LeCun]] (2016). Slides on Deep Learning [https://indico.cern.ch/event/510372/ Online] {{Webarchive|url=https://web.archive.org/web/20160423021403/https://indico.cern.ch/event/510372/|date=2016-04-23}}</ref> Industrial applications of deep learning to large-scale speech recognition started around 2010.
As of 2011, the state of the art in deep learning feedforward networks alternates convolutional layers and max-pooling layers,<ref name="ciresan2011">D. C. Ciresan, U. Meier, J. Masci, L. M. Gambardella, J. Schmidhuber. Flexible, High Performance Convolutional Neural Networks for Image Classification. International Joint Conference on Artificial Intelligence (IJCAI-2011, Barcelona), 2011.</ref><ref name="martines2013">{{cite journal | last1 = Martines | first1 = H. | last2 = Bengio | first2 = Y. | last3 = Yannakakis | first3 = G. N. | year = 2013 | title = Learning Deep Physiological Models of Affect | url = | journal = IEEE Computational Intelligence | volume = 8 | issue = 2| pages = 20–33 | doi=10.1109/mci.2013.2247823}}</ref> topped by several fully connected or sparsely connected layer followed by a final classification layer. Training is usually done without any unsupervised pre-training. Since 2011, GPU-based implementations<ref name="ciresan2011"/> of this approach won many pattern recognition contests, including the IJCNN 2011 Traffic Sign Recognition Competition,<ref name="ciresan2011NN">D. C. Ciresan, U. Meier, J. Masci, J. Schmidhuber. Multi-Column Deep Neural Network for Traffic Sign Classification. Neural Networks, 2012.</ref> the ISBI 2012 Segmentation of neuronal structures in EM stacks challenge,<ref name="ciresan2012NIPS">D. Ciresan, A. Giusti, L. Gambardella, J. Schmidhuber. Deep Neural Networks Segment Neuronal Membranes in Electron Microscopy Images. In Advances in Neural Information Processing Systems (NIPS 2012), Lake Tahoe, 2012.</ref> the [[ImageNet Competition]],<ref name="krizhevsky2012"/> and others.
 
The 2009 NIPS Workshop on Deep Learning for Speech Recognition was motivated by the limitations of deep generative models of speech, and the possibility that given more capable hardware and large-scale data sets that deep neural nets might become practical. It was believed that pre-training DNNs using generative models of deep belief nets (DBN) would overcome the main difficulties of neural nets. However, it was discovered that replacing pre-training with large amounts of training data for straightforward backpropagation when using DNNs with large, context-dependent output layers produced error rates dramatically lower than then-state-of-the-art Gaussian mixture model (GMM)/Hidden Markov Model (HMM) and also than more-advanced generative model-based systems.<ref name="HintonDengYu2012">{{cite journal | last1 = Hinton | first1 = G. | last2 = Deng | first2 = L. | last3 = Yu | first3 = D. | last4 = Dahl | first4 = G. | last5 = Mohamed | first5 = A. | last6 = Jaitly | first6 = N. | last7 = Senior | first7 = A. | last8 = Vanhoucke | first8 = V. | last9 = Nguyen | first9 = P. | last10 = Sainath | first10 = T. | author10-link = Tara Sainath | last11 = Kingsbury | first11 = B. | year = 2012 | title = Deep Neural Networks for Acoustic Modeling in Speech Recognition: The Shared Views of Four Research Groups| journal = IEEE Signal Processing Magazine | volume = 29 | issue = 6| pages = 82–97 | doi=10.1109/msp.2012.2205597 | bibcode = 2012ISPM...29...82H| s2cid = 206485943 }}</ref> The nature of the recognition errors produced by the two types of systems was characteristically different,<ref name="ReferenceICASSP2013" /> offering technical insights into how to integrate deep learning into the existing highly efficient, run-time speech decoding system deployed by all major speech recognition systems.<ref name="BOOK2014" /><ref name="ReferenceA">{{cite book|last2=Deng|first2=L.|date=2014|title=Automatic Speech Recognition: A Deep Learning Approach (Publisher: Springer)|url={{google books |plainurl=y |id=rUBTBQAAQBAJ}}|isbn=978-1-4471-5779-3|last1=Yu|first1=D.|publisher=Springer }}</ref><ref>{{cite web|title=Deng receives prestigious IEEE Technical Achievement Award - Microsoft Research|url=https://www.microsoft.com/en-us/research/blog/deng-receives-prestigious-ieee-technical-achievement-award/|website=Microsoft Research|date=3 December 2015|access-date=16 March 2018|archive-date=16 March 2018|archive-url=https://web.archive.org/web/20180316084821/https://www.microsoft.com/en-us/research/blog/deng-receives-prestigious-ieee-technical-achievement-award/|url-status=live}}</ref> Analysis around 2009–2010, contrasting the GMM (and other generative speech models) vs. DNN models, stimulated early industrial investment in deep learning for speech recognition.<ref name="ReferenceICASSP2013" /> That analysis was done with comparable performance (less than 1.5% in error rate) between discriminative DNNs and generative models.<ref name="HintonDengYu2012" /><ref name="ReferenceICASSP2013">{{cite web| last1=Deng| first1=L.| last2=Hinton| first2=G.| last3=Kingsbury| first3=B.| date=May 2013| title=New types of deep neural network learning for speech recognition and related applications: An overview (ICASSP)| url=https://www.microsoft.com/en-us/research/wp-content/uploads/2016/02/ICASSP-2013-DengHintonKingsbury-revised.pdf| publisher=Microsoft| access-date=27 December 2023| archive-date=2017-09-26| archive-url=https://web.archive.org/web/20170926190920/https://www.microsoft.com/en-us/research/wp-content/uploads/2016/02/ICASSP-2013-DengHintonKingsbury-revised.pdf| url-status=live}}</ref><ref name="interspeech2014Keynote">{{Cite web|url=https://www.superlectures.com/interspeech2014/downloadFile?id=6&type=slides&filename=achievements-and-challenges-of-deep-learning-from-speech-analysis-and-recognition-to-language-and-multimodal-processing|title=Keynote talk: 'Achievements and Challenges of Deep Learning - From Speech Analysis and Recognition To Language and Multimodal Processing'|last=Li|first=Deng|date=September 2014|website=Interspeech|access-date=2017-06-12|archive-date=2017-09-26|archive-url=https://web.archive.org/web/20170926190732/https://www.superlectures.com/interspeech2014/downloadFile?id=6&type=slides&filename=achievements-and-challenges-of-deep-learning-from-speech-analysis-and-recognition-to-language-and-multimodal-processing|url-status=live}}</ref>
Such supervised deep learning methods also were the first artificial pattern recognizers to achieve human-competitive performance on certain tasks.<ref name="ciresan2011CVPR">D. C. Ciresan, U. Meier, J. Schmidhuber. Multi-column Deep Neural Networks for Image Classification. IEEE Conf. on Computer Vision and Pattern Recognition CVPR 2012.
In 2010, researchers extended deep learning from [[TIMIT]] to large vocabulary speech recognition, by adopting large output layers of the DNN based on context-dependent HMM states constructed by [[decision tree]]s.<ref name="Roles2010">{{cite journal|last1=Yu|first1=D.|last2=Deng|first2=L.|date=2010|title=Roles of Pre-Training and Fine-Tuning in Context-Dependent DBN-HMMs for Real-World Speech Recognition|url=https://www.microsoft.com/en-us/research/publication/roles-of-pre-training-and-fine-tuning-in-context-dependent-dbn-hmms-for-real-world-speech-recognition/|journal=NIPS Workshop on Deep Learning and Unsupervised Feature Learning|access-date=2017-06-14|archive-date=2017-10-12|archive-url=https://web.archive.org/web/20171012095148/https://www.microsoft.com/en-us/research/publication/roles-of-pre-training-and-fine-tuning-in-context-dependent-dbn-hmms-for-real-world-speech-recognition/|url-status=live}}</ref><ref>{{Cite book|last1=Seide|first1=F.|last2=Li|first2=G.|last3=Yu|first3=D.|title=Interspeech 2011 |chapter=Conversational speech transcription using context-dependent deep neural networks |date=2011 |chapter-url=https://www.microsoft.com/en-us/research/publication/conversational-speech-transcription-using-context-dependent-deep-neural-networks |pages=437–440|doi=10.21437/Interspeech.2011-169|s2cid=398770 |access-date=2017-06-14|archive-date=2017-10-12|archive-url=https://web.archive.org/web/20171012095522/https://www.microsoft.com/en-us/research/publication/conversational-speech-transcription-using-context-dependent-deep-neural-networks/|url-status=live}}</ref><ref>{{Cite journal|last1=Deng|first1=Li|last2=Li|first2=Jinyu|last3=Huang|first3=Jui-Ting|last4=Yao|first4=Kaisheng|last5=Yu|first5=Dong|last6=Seide|first6=Frank|last7=Seltzer|first7=Mike|last8=Zweig|first8=Geoff|last9=He|first9=Xiaodong|date=1 May 2013|title=Recent Advances in Deep Learning for Speech Research at Microsoft|url=https://www.microsoft.com/en-us/research/publication/recent-advances-in-deep-learning-for-speech-research-at-microsoft/|journal=Microsoft Research|access-date=14 June 2017|archive-date=12 October 2017|archive-url=https://web.archive.org/web/20171012044053/https://www.microsoft.com/en-us/research/publication/recent-advances-in-deep-learning-for-speech-research-at-microsoft/|url-status=live}}</ref><ref name="ReferenceA" />
</ref>
 
=== Deep learning revolution ===
To overcome the barriers of weak AI represented by deep learning, it is necessary to go beyond deep learning architectures, because biological brains use both shallow and deep circuits as reported by brain anatomy<ref name="VanEssen1991">D. J. Felleman and D. C. Van Essen, "[http://cercor.oxfordjournals.org/content/1/1/1.1.full.pdf+html Distributed hierarchical processing in the primate cerebral cortex]," ''Cerebral Cortex'', 1, pp. 1-47, 1991.</ref> displaying a wide variety of invariance. Weng<ref name="Weng2012">J. Weng, "[http://www.amazon.com/Natural-Artificial-Intelligence-Introduction-Computational/dp/0985875720 Natural and Artificial Intelligence: Introduction to Computational Brain-Mind]," BMI Press, ISBN 978-0985875725, 2012.</ref> argued that the brain self-wires largely according to signal statistics and, therefore, a serial cascade cannot catch all major statistical dependencies. ANNs were able to guarantee shift invariance to deal with small and large natural objects in large cluttered scenes, only when invariance extended beyond shift, to all ANN-learned concepts, such as ___location, type (object class label), scale, lighting. This was realized in Developmental Networks (DNs)<ref name="Weng2011">J. Weng, "[http://www.cse.msu.edu/~weng/research/WhyPass-Weng-NI-2011.pdf Why Have We Passed `Neural Networks Do not Abstract Well'?]," ''Natural Intelligence: the INNS Magazine'', vol. 1, no.1, pp. 13-22, 2011.</ref> whose embodiments are Where-What Networks, WWN-1 (2008)<ref name="Weng08">Z. Ji, J. Weng, and D. Prokhorov, "[http://www.cse.msu.edu/~weng/research/ICDL08_0077.pdf Where-What Network 1: Where and What Assist Each Other Through Top-down Connections]," ''Proc. 7th International Conference on Development and Learning (ICDL'08)'', Monterey, CA, Aug. 9-12, pp. 1-6, 2008.</ref> through WWN-7 (2013).<ref name="Weng13">X. Wu, G. Guo, and J. Weng, "[http://www.cse.msu.edu/~weng/research/WWN7-Wu-ICBM-2013.pdf Skull-closed Autonomous Development: WWN-7 Dealing with Scales]," ''Proc. International Conference on Brain-Mind'', July 27–28, East Lansing, Michigan, pp. +1-9, 2013.</ref>
[[File:AI-ML-DL.svg|thumb|How deep learning is a subset of machine learning and how machine learning is a subset of artificial intelligence (AI)]]
 
The deep learning revolution started around CNN- and GPU-based computer vision.
== Deep neural network architectures ==
{{technical|section|date=July 2016}}
There are huge numbers of variants of deep architectures. Most of them are branched from some original parent architectures. It is not always possible to compare the performance of multiple architectures all together, because they are not all evaluated on the same data sets. Deep learning is a fast-growing field, and new architectures, variants, or algorithms appear every few weeks.
 
Although CNNs trained by backpropagation had been around for decades and GPU implementations of NNs for years,<ref name="jung2004">{{cite journal |last1=Oh |first1=K.-S. |last2=Jung |first2=K. |year=2004 |title=GPU implementation of neural networks |journal=Pattern Recognition |volume=37 |issue=6 |pages=1311–1314 |bibcode=2004PatRe..37.1311O |doi=10.1016/j.patcog.2004.01.013}}</ref> including CNNs,<ref name="chellapilla2006">{{Citation |last1=Chellapilla |first1=Kumar |title=High performance convolutional neural networks for document processing |date=2006 |url=https://hal.inria.fr/inria-00112631/document |access-date=2021-02-14 |archive-url=https://web.archive.org/web/20200518193413/https://hal.inria.fr/inria-00112631/document |archive-date=2020-05-18 |url-status=live |last2=Puri |first2=Sidd |last3=Simard |first3=Patrice}}</ref> faster implementations of CNNs on GPUs were needed to progress on computer vision. Later, as deep learning becomes widespread, specialized hardware and algorithm optimizations were developed specifically for deep learning.<ref name="sze2017">{{cite arXiv |eprint=1703.09039 |class=cs.CV |first1=Vivienne |last1=Sze |first2=Yu-Hsin |last2=Chen |author1-link=Vivienne Sze |title=Efficient Processing of Deep Neural Networks: A Tutorial and Survey |last3=Yang |first3=Tien-Ju |last4=Emer |first4=Joel |year=2017}}</ref>
=== Brief discussion of deep neural networks ===
 
A key advance for the deep learning revolution was hardware advances, especially GPU. Some early work dated back to 2004.<ref name="jung2004" /><ref name="chellapilla2006" /> In 2009, Raina, Madhavan, and [[Andrew Ng]] reported a 100M deep belief network trained on 30 Nvidia [[GeForce GTX 280]] GPUs, an early demonstration of GPU-based deep learning. They reported up to 70 times faster training.<ref>{{Cite book |last1=Raina |first1=Rajat |last2=Madhavan |first2=Anand |last3=Ng |first3=Andrew Y. |chapter=Large-scale deep unsupervised learning using graphics processors |date=2009-06-14 |title=Proceedings of the 26th Annual International Conference on Machine Learning |chapter-url=https://doi.org/10.1145/1553374.1553486 |series=ICML '09 |___location=New York, NY, USA |publisher=Association for Computing Machinery |pages=873–880 |doi=10.1145/1553374.1553486 |isbn=978-1-60558-516-1}}</ref>
A ''deep neural network'' (DNN) is an [[artificial neural network]] (ANN) with multiple hidden layers of units between the input and output layers.<ref name="BENGIODEEP" /><ref name="SCHIDHUB" /> Similar to shallow ANNs, DNNs can model complex non-linear relationships. DNN architectures, e.g., for [[object detection]] and [[Natural language processing|parsing]], generate compositional models where the object is expressed as a layered composition of image primitives.<ref>Szegedy, Christian, Alexander Toshev, and Dumitru Erhan. "Deep neural networks for object detection." Advances in Neural Information Processing Systems. 2013.</ref> The extra layers enable composition of features from lower layers, giving the potential of modeling complex data with fewer units than a similarly performing shallow network.<ref name="BENGIODEEP" />
 
In 2011, a CNN named ''DanNet<ref name=":3">{{Cite journal |last1=Cireşan |first1=Dan Claudiu |last2=Meier |first2=Ueli |last3=Gambardella |first3=Luca Maria |last4=Schmidhuber |first4=Jürgen |date=21 September 2010 |title=Deep, Big, Simple Neural Nets for Handwritten Digit Recognition |journal=Neural Computation |volume=22 |issue=12 |pages=3207–3220 |arxiv=1003.0358 |doi=10.1162/neco_a_00052 |issn=0899-7667 |pmid=20858131 |s2cid=1918673}}</ref>''<ref name=":6">{{Cite journal|last1=Ciresan|first1=D. C.|last2=Meier|first2=U.|last3=Masci|first3=J.|last4=Gambardella|first4=L.M.|last5=Schmidhuber|first5=J.|date=2011|title=Flexible, High Performance Convolutional Neural Networks for Image Classification|url=http://ijcai.org/papers11/Papers/IJCAI11-210.pdf|journal=International Joint Conference on Artificial Intelligence|doi=10.5591/978-1-57735-516-8/ijcai11-210|access-date=2017-06-13|archive-date=2014-09-29|archive-url=https://web.archive.org/web/20140929094040/http://ijcai.org/papers11/Papers/IJCAI11-210.pdf|url-status=live}}</ref> by Dan Ciresan, Ueli Meier, Jonathan Masci, [[Luca Maria Gambardella]], and [[Jürgen Schmidhuber]] achieved for the first time superhuman performance in a visual pattern recognition contest, outperforming traditional methods by a factor of 3.<ref name="SCHIDHUB" /> It then won more contests.<ref name=":8">{{Cite book|url=http://papers.nips.cc/paper/4741-deep-neural-networks-segment-neuronal-membranes-in-electron-microscopy-images.pdf|title=Advances in Neural Information Processing Systems 25|last1=Ciresan|first1=Dan|last2=Giusti|first2=Alessandro|last3=Gambardella|first3=Luca M.|last4=Schmidhuber|first4=Jürgen|date=2012|publisher=Curran Associates, Inc.|editor-last=Pereira|editor-first=F.|pages=2843–2851|editor-last2=Burges|editor-first2=C. J. C.|editor-last3=Bottou|editor-first3=L.|editor-last4=Weinberger|editor-first4=K. Q.|access-date=2017-06-13|archive-date=2017-08-09|archive-url=https://web.archive.org/web/20170809081713/http://papers.nips.cc/paper/4741-deep-neural-networks-segment-neuronal-membranes-in-electron-microscopy-images.pdf|url-status=live}}</ref><ref name="ciresan2013miccai">{{Cite book |last1=Ciresan |first1=D. |title=Medical Image Computing and Computer-Assisted Intervention – MICCAI 2013 |last2=Giusti |first2=A. |last3=Gambardella |first3=L.M. |last4=Schmidhuber |first4=J. |date=2013 |isbn=978-3-642-38708-1 |series=Lecture Notes in Computer Science |volume=7908 |pages=411–418 |chapter=Mitosis Detection in Breast Cancer Histology Images with Deep Neural Networks |doi=10.1007/978-3-642-40763-5_51 |pmid=24579167 |issue=Pt 2}}</ref> They also showed how [[Max pooling|max-pooling]] CNNs on GPU improved performance significantly.<ref name=":9" />
DNNs are typically designed as [[feedforward neural network|feedforward]] networks, but research has very successfully applied [[recurrent neural network]]s, especially LSTM,<ref name=lstm/><ref name="gers2002"/> for applications such as [[language model]]ing.<ref name="gers2001"/><ref name="NIPS2014"/><ref name="vinyals2016"/><ref name="gillick2015"/><ref name="MIKO2010">T. Mikolov ''et al.'', "Recurrent neural network based language model," ''Interspeech'', 2010.</ref> [[convolutional neural network|Convolutional deep neural networks]] (CNNs) are used in computer vision where their success is well-documented.<ref name="LECUN86">{{cite journal |last1=LeCun |first1=Y. |display-authors=etal |year= |title=Gradient-based learning applied to document recognition |url= |journal=Proceedings of the IEEE |volume=86 |issue=11 |pages=2278–2324 |doi=10.1109/5.726791}}</ref> CNNs also have been applied to [[acoustic model]]ing for automatic speech recognition (ASR), where they have shown success over previous models.<ref name="SAIN2013"/> For simplicity, a look at training DNNs is given here.
 
In 2012, [[Andrew Ng]] and [[Jeff Dean (computer scientist)|Jeff Dean]] created an FNN that learned to recognize higher-level concepts, such as cats, only from watching unlabeled images taken from [[YouTube]] videos.<ref name="ng2012">{{cite arXiv |eprint=1112.6209 |class=cs.LG |first1=Andrew |last1=Ng |first2=Jeff |last2=Dean |title=Building High-level Features Using Large Scale Unsupervised Learning |year=2012}}</ref>
==== Backpropagation ====
 
In October 2012, [[AlexNet]] by [[Alex Krizhevsky]], [[Ilya Sutskever]], and [[Geoffrey Hinton]]<ref name="krizhevsky2012" /> won the large-scale [[ImageNet competition]] by a significant margin over shallow machine learning methods. Further incremental improvements included the [[VGG-19|VGG-16]] network by [[Karen Simonyan (scientist)|Karen Simonyan]] and [[Andrew Zisserman]]<ref name="VGG">{{cite arXiv|last1=Simonyan |first1=Karen |last2=Andrew |first2=Zisserman |title=Very Deep Convolution Networks for Large Scale Image Recognition |year=2014 |class=cs.CV |eprint=1409.1556}}</ref> and Google's [[Inceptionv3]].<ref name="szegedy">{{Cite journal |last=Szegedy |first=Christian |date=2015 |title=Going deeper with convolutions |url=https://static.googleusercontent.com/media/research.google.com/en//pubs/archive/43022.pdf |journal=Cvpr2015|arxiv=1409.4842 }}</ref>
A DNN can be [[discriminative model|discriminatively]] trained with the standard [[backpropagation]] algorithm. According to various sources,<ref name="SCHIDHUB"/><ref name="scholarpedia"/><ref name="dreyfus1990"/><ref name="mizutani2000">Eiji Mizutani, [[Stuart Dreyfus]], Kenichi Nishio (2000). On derivation of MLP backpropagation from the Kelley-Bryson optimal-control gradient formula and its application. Proceedings of the IEEE International Joint Conference on Neural Networks (IJCNN 2000), Como Italy, July 2000. [http://queue.ieor.berkeley.edu/People/Faculty/dreyfus-pubs/ijcnn2k.pdf Online]</ref>
basics of continuous backpropagation were derived in the context of [[control theory]] by [[Henry J. Kelley]]<ref name="kelley1960"/> in 1960 and by [[Arthur E. Bryson]] in 1961,<ref name="bryson1961"/> using principles of [[dynamic programming]]. In 1962, [[Stuart Dreyfus]] published a simpler derivation based only on the [[chain rule]].<ref name="dreyfus1962"/> [[Vapnik]] cites reference<ref>Bryson, A.E.; W.F. Denham; S.E. Dreyfus. Optimal programming problems with inequality constraints. I: Necessary conditions for extremal solutions. AIAA J. 1, 11 (1963) 2544-2550</ref> in his book on [[Support Vector Machines]]. [[Arthur E. Bryson]] and [[Yu-Chi Ho]] described it as a multi-stage dynamic system optimization method in 1969.<ref>{{cite book|title=Artificial Intelligence A Modern Approach|author1=[[Stuart J. Russell|Stuart Russell]]|author2=[[Peter Norvig]]|quote=The most popular method for learning in multilayer networks is called Back-propagation. |page=578}}</ref><ref>{{cite book|title=Applied optimal control: optimization, estimation, and control|authors=Arthur Earl Bryson, Yu-Chi Ho|year=1969|pages=481|publisher=Blaisdell Publishing Company or Xerox College Publishing}}</ref>
In 1970, [[Seppo Linnainmaa]] finally published the general method for [[automatic differentiation]] (AD) of discrete connected networks of nested [[differentiable]] functions.<ref name="lin1970"/><ref name="lin1976">{{cite journal | last1 = Linnainmaa | first1 = Seppo | authorlink = Seppo Linnainmaa | year = 1976 | title = Taylor expansion of the accumulated rounding error | url = | journal = BIT Numerical Mathematics | volume = 16 | issue = 2| pages = 146–160 | doi=10.1007/bf01931367}}</ref> This corresponds to the modern version of backpropagation which is efficient even when the networks are sparse.<ref name="SCHIDHUB"/><ref name="scholarpedia"/><ref name="grie2012"/><ref name="grie2008"/>
In 1973, [[Stuart Dreyfus]] used backpropagation to adapt [[parameter]]s of controllers in proportion to error gradients.<ref name="dreyfus1973"/> In 1974, [[Paul Werbos]] mentioned the possibility of applying this principle to [[artificial neural networks]],<ref name="werbos1974">[[Paul Werbos]] (1974). Beyond regression: New tools for prediction and analysis in the behavioral sciences. PhD thesis, Harvard University.</ref> and in 1982, he applied Linnainmaa's AD method to neural networks in the way that is widely used today.<ref name="scholarpedia"/><ref name="werbos1982"/>
In 1986, [[David E. Rumelhart]], [[Geoffrey E. Hinton]] and [[Ronald J. Williams]] showed through computer experiments that this method can generate useful internal representations of incoming data in hidden layers of neural networks.<ref name="ROMELNAT"/>
In 1993, Eric A. Wan was the first<ref name="SCHIDHUB"/> to win an international pattern recognition contest through backpropagation.<ref name="wan1993">Eric A. Wan (1993). Time series prediction by using a connectionist network with internal delay lines. In SANTA FE INSTITUTE STUDIES IN THE SCIENCES OF COMPLEXITY-PROCEEDINGS (Vol. 15, pp. 195-195). Addison-Wesley Publishing Co.</ref>
 
The success in image classification was then extended to the more challenging task of [[Automatic image annotation|generating descriptions]] (captions) for images, often as a combination of CNNs and LSTMs.<ref name="1411.4555">{{cite arXiv |eprint=1411.4555 |class=cs.CV |first1=Oriol |last1=Vinyals |first2=Alexander |last2=Toshev |title=Show and Tell: A Neural Image Caption Generator |last3=Bengio |first3=Samy |last4=Erhan |first4=Dumitru |year=2014}}.</ref><ref name="1411.4952">{{cite arXiv |eprint=1411.4952 |class=cs.CV |first1=Hao |last1=Fang |first2=Saurabh |last2=Gupta |title=From Captions to Visual Concepts and Back |last3=Iandola |first3=Forrest |last4=Srivastava |first4=Rupesh |last5=Deng |first5=Li |last6=Dollár |first6=Piotr |last7=Gao |first7=Jianfeng |last8=He |first8=Xiaodong |last9=Mitchell |first9=Margaret |last10=Platt |first10=John C |last11=Lawrence Zitnick |first11=C |last12=Zweig |first12=Geoffrey |year=2014}}.</ref><ref name="1411.2539">{{cite arXiv |eprint=1411.2539 |class=cs.LG |first1=Ryan |last1=Kiros |first2=Ruslan |last2=Salakhutdinov |title=Unifying Visual-Semantic Embeddings with Multimodal Neural Language Models |last3=Zemel |first3=Richard S |year=2014}}.</ref>
The weight updates of backpropagation can be done via [[stochastic gradient descent]] using the following equation:
 
In 2014, the state of the art was training “very deep neural network” with 20 to 30 layers.<ref>{{Citation |last1=Simonyan |first1=Karen |title=Very Deep Convolutional Networks for Large-Scale Image Recognition |date=2015-04-10 |arxiv=1409.1556 |last2=Zisserman |first2=Andrew}}</ref> Stacking too many layers led to a steep reduction in [[Training, validation, and test data sets|training]] accuracy,<ref name="prelu">{{cite arXiv |eprint=1502.01852 |class=cs.CV |first1=Kaiming |last1=He |first2=Xiangyu |last2=Zhang |title=Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classification |last3=Ren |first3=Shaoqing |last4=Sun |first4=Jian |year=2016}}</ref> known as the "degradation" problem.<ref name="resnet">{{Cite conference |last1=He |first1=Kaiming |last2=Zhang |first2=Xiangyu |last3=Ren |first3=Shaoqing |last4=Sun |first4=Jian |date=10 Dec 2015 |title=Deep Residual Learning for Image Recognition |arxiv=1512.03385}}</ref> In 2015, two techniques were developed to train very deep networks: the Highway Network was published in May 2015, and the [[residual neural network]] (ResNet)<ref name="resnet20152">{{Cite conference |last1=He |first1=Kaiming |last2=Zhang |first2=Xiangyu |last3=Ren |first3=Shaoqing |last4=Sun |first4=Jian |title=2016 IEEE Conference on Computer Vision and Pattern Recognition (CVPR) |chapter=Deep Residual Learning for Image Recognition |date=2016 |___location=Las Vegas, NV, USA |publisher=IEEE |pages=770–778 |arxiv=1512.03385 |doi=10.1109/CVPR.2016.90 |isbn=978-1-4673-8851-1 }}</ref> in Dec 2015. ResNet behaves like an open-gated Highway Net.
:<math> w_{ij}(t + 1) = w_{ij}(t) + \eta\frac{\partial C}{\partial w_{ij}} +\xi(t) </math>
 
Around the same time, deep learning started impacting the field of art. Early examples included [[DeepDream|Google DeepDream]] (2015), and [[neural style transfer]] (2015),<ref>{{cite arXiv |eprint=1508.06576 |class=cs.CV |first1=Leon A. |last1=Gatys |first2=Alexander S. |last2=Ecker |title=A Neural Algorithm of Artistic Style |date=26 August 2015 |first3=Matthias |last3=Bethge}}</ref> both of which were based on pretrained image classification neural networks, such as [[VGG-19]].
Here, <math> \eta </math> is the learning rate, <math> C </math> is the [[loss function|cost function]] and <math>\xi(t)</math> a stochastic term. The choice of the cost function depends on factors such as the learning type (supervised, unsupervised, [[Reinforcement learning|reinforcement]], etc.) and the [[activation function]]. For example, when performing supervised learning on a [[multiclass classification]] problem, common choices for the activation function and cost function are the [[softmax activation function|softmax]] function and [[cross entropy]] function, respectively. The softmax function is defined as <math> p_j = \frac{\exp(x_j)}{\sum_k \exp(x_k)} </math> where <math> p_j </math> represents the class probability (output of the unit <math> j </math>) and <math> x_j </math> and <math> x_k </math> represent the total input to units <math> j </math> and <math> k </math> of the same level respectively. Cross entropy is defined as <math> C = -\sum_j d_j \log(p_j) </math> where <math> d_j </math> represents the target probability for output unit <math> j </math> and <math> p_j </math> is the probability output for <math> j </math> after applying the activation function.<ref name="HINTON2012">G. E. Hinton ''et al.''., "Deep Neural Networks for Acoustic Modeling in Speech Recognition: The shared views of four research groups," ''IEEE Signal Processing Magazine'', pp. 82–97, November 2012.</ref>
 
[[Generative adversarial network]] (GAN) by ([[Ian Goodfellow]] et al., 2014)<ref name="GANnips">{{cite conference |last1=Goodfellow |first1=Ian |last2=Pouget-Abadie |first2=Jean |last3=Mirza |first3=Mehdi |last4=Xu |first4=Bing |last5=Warde-Farley |first5=David |last6=Ozair |first6=Sherjil |last7=Courville |first7=Aaron |last8=Bengio |first8=Yoshua |year=2014 |title=Generative Adversarial Networks |url=https://papers.nips.cc/paper/5423-generative-adversarial-nets.pdf |conference=Proceedings of the International Conference on Neural Information Processing Systems (NIPS 2014) |pages=2672–2680 |archive-url=https://web.archive.org/web/20191122034612/http://papers.nips.cc/paper/5423-generative-adversarial-nets.pdf |archive-date=22 November 2019 |access-date=20 August 2019 |url-status=live}}</ref> (based on [[Jürgen Schmidhuber]]'s principle of artificial curiosity<ref name="curiosity1991"/><ref name="gancurpm2020"/>)
These can be used to output object bounding boxes in the form of a binary mask. They are also used for multi-scale regression to increase localization precision. DNN-based regression can learn features that capture geometric information in addition to being a good classifier. They remove the limitation of designing a model which will capture parts and their relations explicitly. This helps to learn a wide variety of objects. The model consists of multiple layers, each of which has a [[rectified linear unit]] for non-linear transformation. Some layers are convolutional, while others are fully connected. Every convolutional layer has an additional max pooling. The network is trained to minimize L2 error for predicting the mask ranging over the entire training set containing bounding boxes represented as masks.
became state of the art in generative modeling during 2014-2018 period. Excellent image quality is achieved by [[Nvidia]]'s [[StyleGAN]] (2018)<ref name="SyncedReview2018">{{Cite web |date=December 14, 2018 |title=GAN 2.0: NVIDIA's Hyperrealistic Face Generator |url=https://syncedreview.com/2018/12/14/gan-2-0-nvidias-hyperrealistic-face-generator/ |access-date=October 3, 2019 |website=SyncedReview.com}}</ref> based on the Progressive GAN by Tero Karras et al.<ref name="progressiveGAN2017">{{cite arXiv |eprint=1710.10196 |class=cs.NE |first1=T. |last1=Karras |first2=T. |last2=Aila |title=Progressive Growing of GANs for Improved Quality, Stability, and Variation |date=26 February 2018 |last3=Laine |first3=S. |last4=Lehtinen |first4=J.}}</ref> Here the GAN generator is grown from small to large scale in a pyramidal fashion. Image generation by GAN reached popular success, and provoked discussions concerning [[deepfake]]s.<ref>{{Cite web |title=Prepare, Don't Panic: Synthetic Media and Deepfakes |url=https://lab.witness.org/projects/synthetic-media-and-deep-fakes/ |url-status=live |archive-url=https://web.archive.org/web/20201202231744/https://lab.witness.org/projects/synthetic-media-and-deep-fakes/ |archive-date=2 December 2020 |access-date=25 November 2020 |publisher=witness.org}}</ref> [[Diffusion model]]s (2015)<ref>{{Cite journal |last1=Sohl-Dickstein |first1=Jascha |last2=Weiss |first2=Eric |last3=Maheswaranathan |first3=Niru |last4=Ganguli |first4=Surya |date=2015-06-01 |title=Deep Unsupervised Learning using Nonequilibrium Thermodynamics |url=http://proceedings.mlr.press/v37/sohl-dickstein15.pdf |journal=Proceedings of the 32nd International Conference on Machine Learning |language=en |publisher=PMLR |volume=37 |pages=2256–2265|arxiv=1503.03585 }}</ref> eclipsed GANs in generative modeling since then, with systems such as [[DALL-E|DALL·E 2]] (2022) and [[Stable Diffusion]] (2022).
 
In 2015, Google's speech recognition improved by 49% by an LSTM-based model, which they made available through [[Google Voice Search]] on [[smartphone]].<ref name="GoogleVoiceTranscription">Google Research Blog. The neural networks behind Google Voice transcription. August 11, 2015. By Françoise Beaufays http://googleresearch.blogspot.co.at/2015/08/the-neural-networks-behind-google-voice.html</ref><ref name="sak2015">{{Cite web |last1=Sak |first1=Haşim |last2=Senior |first2=Andrew |last3=Rao |first3=Kanishka |last4=Beaufays |first4=Françoise |last5=Schalkwyk |first5=Johan |date=September 2015 |title=Google voice search: faster and more accurate |url=http://googleresearch.blogspot.ch/2015/09/google-voice-search-faster-and-more.html |url-status=live |archive-url=https://web.archive.org/web/20160309191532/http://googleresearch.blogspot.ch/2015/09/google-voice-search-faster-and-more.html |archive-date=2016-03-09 |access-date=2016-04-09}}</ref>
==== Problems with deep neural networks ====
As with ANNs, many issues can arise with DNNs if they are naively trained. Two common issues are [[overfitting]] and computation time.
 
DNNs are prone to overfitting because of the added layers of abstraction, which allow them to model rare dependencies in the training data. [[Regularization (mathematics)|Regularization]] methods such as
Ivakhnenko's unit pruning<ref name="ivak1971"/>
or [[weight decay]] (<math> \ell_2 </math>-regularization) or [[sparse matrix|sparsity]] (<math> \ell_1 </math>-regularization) can be applied during training to help combat overfitting.<ref name="BENGIO2013">Y. Bengio ''et al.''., "Advances in optimizing recurrent networks," ''ICASSP'', 2013.</ref> A more recent regularization method applied to DNNs is [[Dropout (neural networks)|dropout]] regularization. In dropout, some number of units are randomly omitted from the hidden layers during training. This helps to break the rare dependencies that can occur in the training data.<ref name="DAHL2013">G. Dahl ''et al.''., "Improving DNNs for LVCSR using rectified linear units and dropout," ''ICASSP'', 2013.</ref>
 
The dominant method for training these structures has been error-correction training (such as [[backpropagation]] with [[gradient descent]]) due to its ease of implementation and its tendency to converge to better [[Local optimum|local optima]] than other training methods. However, these methods can be computationally expensive, especially for DNNs. There are many training parameters to be considered with a DNN, such as the size (number of layers and number of units per layer), the learning rate and initial weights. [[Hyperparameter optimization#Grid search|Sweeping through the parameter space]] for optimal parameters may not be feasible due to the cost in time and computational resources. Various 'tricks' such as using mini-batching (computing the gradient on several training examples at once rather than individual examples)<ref name="RBMTRAIN">G. E. Hinton., "A Practical Guide to Training Restricted Boltzmann Machines," ''Tech. Rep. UTML TR 2010-003, Dept. CS., Univ. of Toronto'', 2010.</ref> have been shown to speed up computation. The large processing throughput of GPUs has produced significant speedups in training, due to the matrix and vector computations required being well suited for GPUs.<ref name="SCHIDHUB" /> Radical alternatives to backprop such as [[Extreme Learning Machines]],<ref>{{cite journal | last1 = Huang | first1 = Guang-Bin | last2 = Zhu | first2 = Qin-Yu | last3 = Siew | first3 = Chee-Kheong | year = 2006 | title = Extreme learning machine: theory and applications | url = | journal = Neurocomputing | volume = 70 | issue = 1| pages = 489–501 | doi=10.1016/j.neucom.2005.12.126}}</ref> "No-prop" networks,<ref>{{cite journal | last1 = Widrow | first1 = Bernard | display-authors = etal | year = 2013 | title = The no-prop algorithm: A new learning algorithm for multilayer neural networks | url = | journal = Neural Networks | volume = 37 | issue = | pages = 182–188 | doi=10.1016/j.neunet.2012.09.020}}</ref> training without backtracking,<ref>{{cite arXiv |last=Ollivier |first=Yann |last2=Charpiat |first2=Guillaume |year=2015 |title=Training recurrent networks without backtracking |arxiv=1507.07680}}</ref> "weightless" networks,<ref>Aleksander, Igor, et al. "A brief introduction to Weightless Neural Systems." ESANN. 2009.</ref> and [[holographic associative memory|non-connectionist neural networks]] are gaining attention.
 
=== First deep learning networks of 1965: GMDH ===
 
According to a historic survey,<ref name="SCHIDHUB"/> the first functional Deep Learning networks with many layers were published by [[Alexey Grigorevich Ivakhnenko]] and V. G. Lapa in 1965.<ref name="ivak1965"/><ref name="ivak1967">[[Alexey Grigorevich Ivakhnenko]] and V. G. Lapa and R. N. McDonough (1967). Cybernetics and forecasting techniques. American Elsevier, NY.</ref> The learning algorithm was called the [[Group Method of Data Handling]] or GMDH.<ref name="ivak1968">{{cite journal | last1 = Grigorevich Ivakhnenko | first1 = Alexey | authorlink = Alexey Grigorevich Ivakhnenko | year = 1968 | title = The [[group method of data handling]] – a rival of the method of stochastic approximation | url = | journal = Soviet Automatic Control | volume = 13 | issue = 3| pages = 43–55 }}</ref> GMDH features fully automatic structural and parametric optimization of models. The activation functions of the network nodes are Kolmogorov-Gabor polynomials that permit additions and multiplications.
Ivakhnenko's 1971 paper<ref name="ivak1971"/> describes the learning of a deep feedforward multilayer perceptron with eight layers, already much deeper than many later networks. The [[supervised learning]] network is grown layer by layer, where each layer is trained by [[regression analysis]]. From time to time useless neurons are detected using a validation set, and pruned through [[regularization (mathematics)|regularization]]. The size and depth of the resulting network depends on the problem. Variants of this method are still being used today.<ref name="kondo2008">{{cite journal | last1 = Kondo | first1 = T. | last2 = Ueno | first2 = J. | year = 2008 | title = Multi-layered GMDH-type neural network self-selecting optimum neural network architecture and its application to 3-dimensional medical image recognition of blood vessels | url = | journal = International Journal of Innovative Computing,Information and Control | volume = 4 | issue = 1| pages = 175–187 }}</ref>
 
=== Convolutional neural networks ===
{{main article|Convolutional neural network}}
CNNs have become the method of choice for processing visual and other two-dimensional data.<ref name="LECUN1989"/><ref name="lecun2016slides"/>
A CNN is composed of one or more [[convolution]]al layers with fully connected layers (matching those in typical artificial neural networks) on top. It also uses tied weights and pooling layers. In particular, max-pooling<ref name="Weng1993"/> is often used in Fukushima's convolutional architecture.<ref name="FUKU1980"/> This architecture allows CNNs to take advantage of the 2D structure of input data. In comparison with other deep architectures, convolutional neural networks have shown superior results in both image and speech applications. They can also be trained with standard backpropagation. CNNs are easier to train than other regular, deep, feed-forward neural networks and have many fewer parameters to estimate, making them a highly attractive architecture to use.<ref name="STANCNN">{{cite web|url=http://ufldl.stanford.edu/tutorial/supervised/ConvolutionalNeuralNetwork/|title=Unsupervised Feature Learning and Deep Learning Tutorial|publisher=}}</ref> Examples of applications in Computer Vision include [[DeepDream]].<ref name=deepdream>{{cite journal|first1=Christian |last1=Szegedy |first2=Wei |last2=Liu |first3=Yangqing |last3=Jia|first4=Pierre |last4=Sermanet|first5=Scott |last5=Reed|first6=Dragomir |last6=Anguelov|first7=Dumitru |last7=Erhan|first8=Vincent |last8=Vanhoucke|first9=Andrew |last9=Rabinovich|title = Going Deeper with Convolutions|journal= Computing Research Repository|arxiv= 1409.4842|year=2014 }}</ref> See the main article on [[Convolutional neural network]]s for numerous additional references.
 
===Neural history compressor===
 
The [[vanishing gradient problem]]<ref name="HOCH1991"/>
of [[automatic differentiation]] or [[backpropagation]] in neural networks
was partially overcome in 1992 by an early generative model called the neural history compressor, implemented as an unsupervised stack of [[recurrent neural networks]] (RNNs).<ref name="SCHMID1992"/> The RNN at the input level learns to predict its next input from the previous input history. Only unpredictable inputs of some RNN in the hierarchy become inputs to the next higher level RNN which therefore recomputes its internal state only rarely. Each higher level RNN thus learns a compressed representation of the information in the RNN below. This is done such that the input sequence can be precisely reconstructed from the sequence representation at the highest level. The system effectively minimises the description length or the negative [[logarithm]] of the probability of the data.<ref name="scholarpedia"/>
If there is a lot of learnable predictability in the incoming data sequence, then the highest level RNN can use supervised learning to easily classify even deep sequences with very long time intervals between important events. In 1993, such a system already solved a "Very Deep Learning" task that requires more than 1000 subsequent layers in an RNN unfolded in time.<ref name="schmidhuber1993"/>
 
It is also possible to distill the entire RNN hierarchy into only two RNNs called the "conscious" chunker (higher level) and the "subconscious" automatizer (lower level).<ref name="SCHMID1992"/> Once the chunker has learned to predict and compress inputs that are still unpredictable by the automatizer, the automatizer is forced in the next learning phase to predict or imitate through special additional units the hidden units of the more slowly changing chunker. This makes it easy for the automatizer to learn appropriate, rarely changing memories across very long time intervals. This in turn helps the automatizer to make many of its once unpredictable inputs predictable, such that the chunker can focus on the remaining still unpredictable events, to compress the data even further.<ref name="SCHMID1992"/>
 
===Recursive neural networks===
{{main article|Recursive neural network}}
 
A [[recursive neural network]]<ref>{{cite journal|doi=10.1109/ICNN.1996.548916|title=Learning task-dependent distributed representations by backpropagation through structure|last1=Goller|first1=C.|last2=Küchler|first2=A.|journal=Neural Networks, 1996., IEEE}}</ref> is created by applying the same set of weights [[recursion|recursively]] over a differentiable graph-like structure, by traversing the structure in [[topological sort|topological order]]. Such networks are typically also trained by the reverse mode of [[automatic differentiation]].<ref name="lin1970"/><ref name="grie2008"/>
They were introduced to learn [[distributed representation]]s of structure, such as [[mathematical logic|logical terms]].
A special case of recursive neural networks is the RNN itself whose structure corresponds to a linear chain. Recursive neural networks have been applied to [[natural language processing]].<ref>{{cite journal|last1=Socher|first1=Richard|last2=Lin|first2=Cliff|last3=Ng|first3=Andrew Y.|last4=Manning|first4=Christopher D.|title=Parsing Natural Scenes and Natural Language with Recursive Neural Networks|journal=The 28th International Conference on Machine Learning (ICML 2011)}}</ref> The Recursive Neural Tensor Network uses a tensor-based composition function for all nodes in the tree.<ref>{{cite journal|last1=Socher|first1=Richard|last2=Perelygin|first2=Alex|last3=Y. Wu|first3=Jean|last4=Chuang|first4=Jason|last5=D. Manning|first5=Christopher|last6=Y. Ng|first6=Andrew|last7=Potts|first7=Christopher|title=Recursive Deep Models for Semantic Compositionality Over a Sentiment Treebank|journal=EMNLP 2013|url=http://nlp.stanford.edu/~socherr/EMNLP2013_RNTN.pdf}}</ref>
 
===Long short-term memory===
{{main article|Long short-term memory}}
 
Numerous researchers now use variants of a deep learning RNN called
the [[Long short-term memory]] (LSTM) network published by Hochreiter & Schmidhuber in 1997.<ref name=lstm/> It is a system that unlike traditional RNNs doesn't have the [[vanishing gradient problem]].
LSTM is normally augmented by recurrent gates called forget gates.<ref name="gers2002">{{cite journal | last1 = Gers | first1 = Felix | authorlink3 = Jürgen Schmidhuber | last2 = Schraudolph | first2 = Nicholas | last3 = Schmidhuber | first3 = Jürgen | year = 2002 | title = Learning precise timing with LSTM recurrent networks | url = | journal = Journal of Machine Learning Research | volume = 3 | issue = | pages = 115–143 }}</ref> LSTM RNNs prevent backpropagated errors from vanishing or exploding.<ref name="HOCH1991"/> Instead errors can flow backwards through unlimited numbers of virtual layers in LSTM RNNs unfolded in space. That is, LSTM can learn "Very Deep Learning" tasks<ref name="SCHIDHUB"/> that require memories of events that happened thousands or even millions of discrete time steps ago. Problem-specific LSTM-like topologies can be evolved.<ref name="bayer2009">Justin Bayer, Daan Wierstra, Julian Togelius, and Jürgen Schmidhuber (2009). Evolving memory cell structures for sequence learning. Proceedings of ICANN (2), pp. 755–764.</ref>
LSTM works even when there are long delays, and it can handle signals that have a mix of low and high frequency components.
 
Today, many applications use stacks of LSTM RNNs<ref name="fernandez2007">Santiago Fernandez, Alex Graves, and [[Jürgen Schmidhuber]] (2007). Sequence labelling in structured domains with hierarchical recurrent neural networks. Proceedings of IJCAI.</ref> and train them by Connectionist Temporal Classification (CTC)<ref name="graves2006"/> to find an RNN weight matrix that maximizes the probability of the label sequences in a training set, given the corresponding input sequences. CTC achieves both alignment and recognition. In 2009, CTC-trained LSTM was the first RNN to win pattern recognition contests, when it won several competitions in connected [[handwriting recognition]].<ref name="SCHIDHUB"/><ref name="graves2009"/> Already in 2003, LSTM started to become competitive with traditional speech recognizers on certain tasks.<ref name="graves2003"/> In 2007, the combination with CTC achieved first good results on speech data.<ref name="fernandez2007keyword"/> Since then, this approach has revolutionised [[speech recognition]]. In 2014, the Chinese search giant [[Baidu]] used CTC-trained RNNs to break the Switchboard Hub5'00 speech recognition benchmark, without using any traditional speech processing methods.<ref name="hannun2014">Awni Hannun, Carl Case, Jared Casper, Bryan Catanzaro, Greg Diamos, Erich Elsen, Ryan Prenger, Sanjeev Satheesh, Shubho Sengupta, Adam Coates, [[Andrew Ng]] (2014). Deep Speech: Scaling up end-to-end speech recognition. [http://arxiv.org/abs/1412.5567 arXiv:1412.5567]</ref>
LSTM also improved large-vocabulary speech recognition,<ref name="sak2014"/><ref name="liwu2015"/> text-to-speech synthesis,<ref name="fan2014">Fan, Y., Qian, Y., Xie, F., and Soong, F. K. (2014). TTS synthesis with bidirectional LSTM based recurrent neural networks. In Proceedings of Interspeech.</ref> also for Google Android,<ref name="scholarpedia"/><ref name="zen2015"/> and photo-real talking heads.<ref name="fan2015">Bo Fan, Lijuan Wang, Frank K. Soong, and Lei Xie (2015). Photo-Real Talking Head with Deep Bidirectional LSTM. In Proceedings of ICASSP 2015.</ref> In 2015, Google's speech recognition reportedly experienced a dramatic performance jump of 49% through CTC-trained LSTM, which is now available through [[Google Voice]] to billions of smartphone users.<ref name="sak2015"/>
 
LSTM has also become very popular in the field of [[Natural Language Processing]].
Unlike previous models based on [[Hidden Markov model|HMMs]] and similar concepts, LSTM can learn to recognise [[context-sensitive languages]].<ref name="gers2001">{{cite journal | last1 = Gers | first1 = Felix A. | authorlink2 = Jürgen Schmidhuber | last2 = Schmidhuber | first2 = Jürgen | year = 2001 | title = LSTM Recurrent Networks Learn Simple Context Free and Context Sensitive Languages | url = | journal = IEEE TNN | volume = 12 | issue = 6| pages = 1333–1340 | doi=10.1109/72.963769}}</ref> LSTM improved machine translation,<ref name="NIPS2014"/> [[Language modeling]]<ref name="vinyals2016">Rafal Jozefowicz, Oriol Vinyals, Mike Schuster, Noam Shazeer, Yonghui Wu (2016). Exploring the Limits of Language Modeling. [http://arxiv.org/abs/1602.02410 arXiv]</ref> and Multilingual Language Processing.<ref name="gillick2015">Dan Gillick, Cliff Brunk, Oriol Vinyals, Amarnag Subramanya (2015). Multilingual Language Processing From Bytes. [http://arxiv.org/abs/1512.00103 arXiv]</ref> LSTM combined with [[Convolutional Neural Network]]s (CNNs) also improved automatic image captioning<ref name="vinyals2015">Oriol Vinyals, Alexander Toshev, Samy Bengio, and Dumitru Erhan (2015). Show and Tell: A Neural Image Caption Generator. [http://arxiv.org/abs/1411.4555 arXiv]</ref> and a plethora of other applications.
 
=== Deep belief networks ===
{{main article|Deep belief network}}
 
[[File:Restricted Boltzmann machine.svg|thumb| A [[restricted Boltzmann machine]] (RBM) with fully connected visible and hidden units. Note there are no hidden-hidden or visible-visible connections.]]
 
A deep belief network (DBN) is a probabilistic, [[generative model]] made up of multiple layers of hidden units. It can be considered a [[Function composition|composition]] of simple learning modules that make up each layer.<ref name="SCHOLARDBNS" />
 
A DBN can be used to generatively pre-train a DNN by using the learned DBN weights as the initial DNN weights. Back-propagation or other discriminative algorithms can then be applied for fine-tuning of these weights. This is particularly helpful when limited training data are available, because poorly initialized weights can significantly hinder the learned model's performance. These pre-trained weights are in a region of the weight space that is closer to the optimal weights than are randomly chosen initial weights. This allows for both improved modeling and faster convergence of the fine-tuning phase.<ref name="LAROCH2007">{{cite journal | last1 = Larochelle | first1 = H. | display-authors = etal | year = | title = An empirical evaluation of deep architectures on problems with many factors of variation | url = | journal = Proc. 24th Int. Conf. Machine Learning | volume = 2007 | issue = | pages = 473–480 }}</ref>
 
A DBN can be efficiently trained in an unsupervised, layer-by-layer manner, where the layers are typically made of [[restricted Boltzmann machine]]s (RBM). An RBM is an [[undirected graph|undirected]], generative energy-based model with a "visible" input layer and a hidden layer, and connections between the layers but not within layers. The training method for RBMs proposed by Geoffrey Hinton for use with training "Product of Expert" models is called [[contrastive divergence]] (CD).<ref name="POE">G. E. Hinton., [http://www.cs.toronto.edu/~fritz/absps/nccd.pdf "Training Product of Experts by Minimizing Contrastive Divergence,"] ''Neural Computation'', 14, pp. 1771–1800, 2002.</ref> CD provides an approximation to the [[maximum likelihood]] method that would ideally be applied for learning the weights of the RBM.<ref name="RBMTRAIN" /><ref name="RBMTutorial">{{cite journal | last1 = Fischer | first1 = A. | last2 = Igel | first2 = C. | year = 2014 | title = Training Restricted Boltzmann Machines: An Introduction | url = http://image.diku.dk/igel/paper/TRBMAI.pdf | format = PDF | journal = Pattern Recognition | volume = 47 | issue = | pages = 25–39 | doi=10.1016/j.patcog.2013.05.025}}</ref> In training a single RBM, weight updates are performed with [[gradient descent|gradient ascent]] via the following equation: <math> \Delta w_{ij}(t+1) = w_{ij}(t) + \eta\frac{\partial \log(p(v))}{\partial w_{ij}} </math>. Here, <math>p(v)</math> is the probability of a visible vector, which is given by <math>p(v) = \frac{1}{Z}\sum_he^{-E(v,h)}</math>. <math> Z </math> is the partition function (used for normalizing) and <math>E(v,h)</math> is the energy function assigned to the state of the network. A lower energy indicates the network is in a more "desirable" configuration. The gradient <math>\frac{\partial \log(p(v))}{\partial w_{ij}}</math> has the simple form <math>\langle v_ih_j\rangle_\text{data} - \langle v_ih_j\rangle_\text{model}</math> where <math>\langle\cdots\rangle_p</math> represent averages with respect to distribution <math>p</math>. The issue arises in sampling <math>\langle v_ih_j\rangle_\text{model}</math> because this requires running alternating [[Gibbs sampling]] for a long time. CD replaces this step by running alternating Gibbs sampling for <math>n</math> steps (values of <math>n = 1</math> have empirically been shown to perform well). After <math>n</math> steps, the data are sampled and that sample is used in place of <math>\langle v_ih_j\rangle_\text{model}</math>. The CD procedure works as follows:<ref name="RBMTRAIN" />
 
# Initialize the visible units to a training vector.
# Update the hidden units in parallel given the visible units: <math>p(h_j = 1 \mid \textbf{V}) = \sigma(b_j + \sum_i v_iw_{ij})</math>. <math>\sigma</math> is the [[sigmoid function]] and <math>b_j</math> is the bias of <math>h_j</math>.
# Update the visible units in parallel given the hidden units: <math>p(v_i = 1 \mid \textbf{H}) = \sigma(a_i + \sum_j h_jw_{ij})</math>. <math>a_i</math> is the bias of <math>v_i</math>. This is called the "reconstruction" step.
# Re-update the hidden units in parallel given the reconstructed visible units using the same equation as in step 2.
# Perform the weight update: <math>\Delta w_{ij} \propto \langle v_ih_j\rangle_\text{data} - \langle v_ih_j\rangle_\text{reconstruction}</math>.
 
Once an RBM is trained, another RBM is "stacked" atop it, taking its input from the final already-trained layer. The new visible layer is initialized to a training vector, and values for the units in the already-trained layers are assigned using the current weights and biases. The new RBM is then trained with the procedure above. This whole process is repeated until some desired stopping criterion is met.<ref name="BENGIODEEP"/>
 
Although the approximation of CD to maximum likelihood is very crude ( has been shown to not follow the gradient of any function), it has been empirically shown to be effective in training deep architectures.<ref name="RBMTRAIN"/>
 
=== Convolutional deep belief networks ===
A recent achievement in deep learning is the use of convolutional deep belief networks (CDBN). CDBNs have structure very similar to a [[convolutional neural network]]s and are trained similar to deep belief networks. Therefore, they exploit the 2D structure of images, like CNNs do, and make use of pre-training like [[deep belief network]]s. They provide a generic structure which can be used in many image and signal processing tasks. Recently, many benchmark results on standard image datasets like CIFAR<ref name="CDBN-CIFAR">[http://www.cs.toronto.edu/~kriz/conv-cifar10-aug2010.pdf Convolutional Deep Belief Networks on CIFAR-10]</ref> have been obtained using CDBNs.<ref name="CDBN">{{cite journal|url=http://doi.acm.org/10.1145/1553374.1553453|title=Convolutional Deep Belief Networks for Scalable Unsupervised Learning of Hierarchical Representations|first1=Honglak|last1=Lee|first2=Roger|last2=Grosse|first3=Rajesh|last3=Ranganath|first4=Andrew Y.|last4=Ng|date=1 January 2009|publisher=ACM|pages=609–616|via=ACM Digital Library|doi=10.1145/1553374.1553453|journal=Proceedings of the 26th Annual International Conference on Machine Learning - ICML '09}}</ref>
 
=== Large memory storage and retrieval neural networks ===
 
Large memory storage and retrieval neural networks (LAMSTAR)<ref name=book2013>D. Graupe, "Principles of Artificial Neural Networks.3rd Edition", World Scientific Publishers, 2013.</ref><ref name=GrPatent>D. Graupe," Large memory storage and retrieval (LAMSTAR) network, US Patent 5920852 A", April 1996.</ref> are fast deep learning neural networks of many layers which can use many filters simultaneously. These filters may be nonlinear, stochastic, logic, [[non-stationary]], or even non-analytical. They are biologically motivated and continuously learning.
Deep learning is part of state-of-the-art systems in various disciplines, particularly computer vision and [[automatic speech recognition]] (ASR). Results on commonly used evaluation sets such as [[TIMIT]] (ASR) and [[MNIST database|MNIST]] ([[image classification]]), as well as a range of large-vocabulary speech recognition tasks have steadily improved.<ref name="HintonDengYu2012" /><ref>{{Cite book |last1=Singh |first1=Premjeet |title=2021 International Conference on Computer Communication and Informatics (ICCCI) |last2=Saha |first2=Goutam |last3=Sahidullah |first3=Md |year=2021 |isbn=978-1-7281-5875-4 |pages=1–4 |chapter=Non-linear frequency warping using constant-Q transformation for speech emotion recognition |doi=10.1109/ICCCI50826.2021.9402569 |arxiv=2102.04029 |s2cid=231846518}}</ref> Convolutional neural networks were superseded for ASR by [[LSTM]].<ref name="sak2015" /><ref name="sak2014">{{Cite web |last1=Sak |first1=Hasim |last2=Senior |first2=Andrew |last3=Beaufays |first3=Francoise |date=2014 |title=Long Short-Term Memory recurrent neural network architectures for large scale acoustic modeling |url=https://static.googleusercontent.com/media/research.google.com/en//pubs/archive/43905.pdf |url-status=dead |archive-url=https://web.archive.org/web/20180424203806/https://static.googleusercontent.com/media/research.google.com/en//pubs/archive/43905.pdf |archive-date=24 April 2018}}</ref><ref name="liwu2015">{{cite arXiv |eprint=1410.4281 |class=cs.CL |first1=Xiangang |last1=Li |first2=Xihong |last2=Wu |title=Constructing Long Short-Term Memory based Deep Recurrent Neural Networks for Large Vocabulary Speech Recognition |year=2014}}</ref><ref name="zen2015">{{Cite web |last1=Zen |first1=Heiga |last2=Sak |first2=Hasim |date=2015 |title=Unidirectional Long Short-Term Memory Recurrent Neural Network with Recurrent Output Layer for Low-Latency Speech Synthesis |url=https://static.googleusercontent.com/media/research.google.com/en//pubs/archive/43266.pdf |url-status=live |archive-url=https://web.archive.org/web/20210509123113/https://static.googleusercontent.com/media/research.google.com/en//pubs/archive/43266.pdf |archive-date=2021-05-09 |access-date=2017-06-13 |website=Google.com |publisher=ICASSP |pages=4470–4474}}</ref> but are more successful in computer vision.
A LAMSTAR neural network may serve as a dynamic neural network in spatial or time ___domain or both. Its speed is provided by [[Hebbian]] link-weights (Chapter 9 of in D. Graupe, 2013<ref name=book2013a>D. Graupe, "Principles of Artificial Neural Networks.3rd Edition", World Scientific Publishers, 2013, pp.203-274.</ref>), which serve to integrate the various and usually different filters (preprocessing functions) into its many layers and to dynamically rank the significance of the various layers and functions relative to a given task for deep learning. This grossly imitates biological learning which integrates outputs various preprocessors ([[cochlea]], [[retina]], ''etc.'') and cortexes ([[Auditory cortex|auditory]], [[Visual cortex|visual]], ''etc.'') and their various regions. Its deep learning capability is further enhanced by using inhibition, correlation and by its ability to cope with incomplete data, or "lost" neurons or layers even at the midst of a task. Furthermore, it is fully transparent due to its link weights. The link-weights also allow dynamic determination of innovation and redundancy, and facilitate the ranking of layers, of filters or of individual neurons relative to a task.
 
[[Yoshua Bengio]], [[Geoffrey Hinton]] and [[Yann LeCun]] were awarded the 2018 [[Turing Award]] for "conceptual and engineering breakthroughs that have made deep neural networks a critical component of computing".<ref>{{Cite web |title=2018 ACM A.M. Turing Award Laureates |url=https://awards.acm.org/about/2018-turing |access-date=2024-08-07 |website=awards.acm.org |language=en}}</ref>
LAMSTAR has been applied to many medical<ref name=Nigam>V. P. Nigam, D. Graupe, (2004),"A neural-network-based detection of epilepsy", ''Neurological Research'', 26(1): 55-60.</ref><ref name=Waxman>{{cite journal | last1 = Waxman | first1 = J. | last2 = Graupe | first2 = D. | last3 = Carley | first3 = C W. | year = 2010 | title = Automated prediction of apnea and hypopnea, using a LAMSTAR artificial neural network | url = | journal = American Journal of Respiratory and Critical Care Medicine | volume = 171 | issue = 7| pages = 727–733 }}</ref><ref name=GrGrZh>{{cite journal | last1 = Graupe | first1 = D. | last2 = Graupe | first2 = M. H. | last3 = Zhong | first3 = Y. | last4 = Jackson | first4 = R. K. | year = 2008 | title = Blind adaptive filtering for non-invasive extraction of the fetal electrocardiogram and its non-stationarities | url = | journal = Proc. Inst. Mech Eng., UK, Part H: Journal of Engineering in Medicine | volume = 222 | issue = 8| pages = 1221–1234 | doi=10.1243/09544119jeim417}}</ref> and financial predictions (see Graupe, 2013<ref name=book2013b>D. Graupe, "Principles of Artificial Neural Networks.3rd Edition", World Scientific Publishers, 2013, pp.240-253.</ref> Section 9C), adaptive filtering of noisy speech in unknown noise,<ref name=GrAbon>{{cite journal | last1 = Graupe | first1 = D. | last2 = Abon | first2 = J. | year = 2002 | title = A Neural Network for Blind Adaptive Filtering of Unknown Noise from Speech | url = | journal = Intelligent Engineering Systems Through Artificial Neural Networks | volume = 12 | issue = | pages = 683–688 }}</ref> still-image recognition<ref name=Homayon>{{cite journal | last1 = Homayon | first1 = S. | year = 2015 | title = Iris Recognition for Personal Identification Using LAMSTAR Neural Network | url = | journal = International Journal of Computer Science and Information Technology | volume = 7 | issue = 1 }}</ref> (Graupe, 2013<ref name=book2013c>D. Graupe, "Principles of Artificial Neural Networks.3rd Edition", World Scientific Publishers", 2013, pp.253-274.</ref> Section 9D), video image recognition,<ref name=Girado>{{cite journal | last1 = Girado | first1 = J. I. | last2 = Sandin | first2 = D. J. | last3 = DeFanti | first3 = T. A. | year = 2003 | title = Real-time camera-based face detection using amodified LAMSTAR neural network system | url = | journal = Proc. SPIE 5015, Applications of Artificial Neural Networks in Image Processing VIII | volume = | issue = | page = | doi = 10.1117/12.477405 }}</ref> software security,<ref name=VenkSel>{{cite journal | last1 = Venkatachalam | first1 = V | last2 = Selvan | first2 = S. | year = 2007 | title = Intrusion Detection using an Improved Competitive Learning Lamstar Network | url = | journal = International Journal of Computer Science and Network Security | volume = 7 | issue = 2| pages = 255–263 }}</ref> adaptive control of non-linear systems,<ref name=GrSmol>D. Graupe, M. Smollack, (2007), "Control of unstable nonlinear and nonstationary systems using LAMSTAR neural networks", Proceedings of 10th IASTED on Intelligent Control, Sect.592, 141-144.</ref> and others. LAMSTAR had a much faster computing speed and somewhat lower error than a convolutional neural network based on [[ReLU]]-function filters and max pooling, in 20 comparative studies.<ref name.<ref name=book1016>D. Graupe, "Deep Learning Neural Networks.Design and Case Studies", World Scientific Publishers, 2016, pp.57-110.</ref>
 
== Neural networks ==
These applications demonstrate delving into aspects of the data that are hidden from shallow learning networks or even from the human senses (eye, ear), such as in the cases of predicting onset of [[sleep apnea]] events,<ref name="Waxman"/> of an electrocardiogram of a fetus as recorded from skin-surface electrodes placed on the mother's abdomen early in pregnancy,<ref name="GrGrZh"/> of financial prediction (Section 9C in Graupe, 2013),<ref name="book2013"/> or in blind filtering of noisy speech.<ref name="GrAbon"/>
{{Main|Artificial neural network}}
 
{{multiple image
LAMSTAR was proposed in 1996 ({{US Patent|5920852 A}}) and was further developed by D Graupe and H Kordylewski 1997-2002.<ref name="GKmidwet">{{cite journal | last1 = Graupe | first1 = H. Kordylewski | year = 1996 | title = Network based on SOM (self-organizing-map) modules combined with statistical decision tools | url = | journal = Proc. IEEE 39th Midwest Conf. on Circuits and Systems | volume = 1 | issue = | pages = 471–475 }}</ref><ref name="GKsoftware">D, Graupe, H. Kordylewski, (1998), "A large memory storage and retrieval neural network for adaptive retrieval and diagnosis", International Journal of Software Engineering and Knowledge Engineering, 1998.</ref><ref name=Kordylew>{{cite journal | last1 = Kordylewski | first1 = H. | last2 = Graupe | first2 = D | last3 = Liu | first3 = K. | year = | title = A novel large-memory neural network as an aid in medical diagnosis applications | url = | journal = IEEE Transactions on Information Technology in Biomedicine | volume = 5 | issue = 3| pages = 202–209 | doi=10.1109/4233.945291}}</ref> A modified version, known as LAMSTAR 2, was developed by N C Schneider and D Graupe in 2008.<ref name="Schn">{{cite journal | last1 = Schneider | first1 = N.C. | last2 = Graupe | year = 2008 | title = A modified LAMSTAR neural network and its applications | url = | journal = International journal of neural systems | volume = 18 | issue = 4| pages = 331–337 | doi=10.1142/s0129065708001634}}</ref><ref name=book2013d>D. Graupe, "Principles of Artificial Neural Networks.3rd Edition", World Scientific Publishers, 2013, p.217.</ref>
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| image1 = Simplified neural network training example.svg
| alt1 =
| caption1 = Simplified example of training a neural network in object detection: The network is trained by multiple images that are known to depict [[starfish]] and [[sea urchin]]s, which are correlated with "nodes" that represent visual [[Feature (computer vision)|features]]. The starfish match with a ringed texture and a star outline, whereas most sea urchins match with a striped texture and oval shape. However, the instance of a ring textured sea urchin creates a weakly weighted association between them.
| image2 = Simplified neural network example.svg
| alt2 =
| caption2 = Subsequent run of the network on an input image (left):<ref>{{cite book|author=Ferrie, C., & Kaiser, S.|year=2019|title=Neural Networks for Babies|publisher=Sourcebooks|isbn=978-1492671206}}</ref> The network correctly detects the starfish. However, the weakly weighted association between ringed texture and sea urchin also confers a weak signal to the latter from one of two intermediate nodes. In addition, a [[Seashell|shell]] that was not included in the training gives a weak signal for the oval shape, also resulting in a weak signal for the sea urchin output. These weak signals may result in a [[false positive]] result for sea urchin.<br>In reality, textures and outlines would not be represented by single nodes, but rather by associated weight patterns of multiple nodes.}}
'''Artificial neural networks''' ('''ANNs''') or '''[[Connectionism|connectionist]] systems''' are computing systems inspired by the [[biological neural network]]s that constitute animal brains. Such systems learn (progressively improve their ability) to do tasks by considering examples, generally without task-specific programming. For example, in image recognition, they might learn to identify images that contain cats by analyzing example images that have been manually [[Labeled data|labeled]] as "cat" or "no cat" and using the analytic results to identify cats in other images. They have found most use in applications difficult to express with a traditional computer algorithm using [[rule-based programming]].
 
An ANN is based on a collection of connected units called [[artificial neuron]]s, (analogous to biological [[neuron]]s in a [[Brain|biological brain]]). Each connection ([[synapse]]) between neurons can transmit a signal to another neuron. The receiving (postsynaptic) neuron can process the signal(s) and then signal downstream neurons connected to it. Neurons may have state, generally represented by [[real numbers]], typically between 0 and 1. Neurons and synapses may also have a weight that varies as learning proceeds, which can increase or decrease the strength of the signal that it sends downstream.
=== Deep Boltzmann machines ===
 
Typically, neurons are organized in layers. Different layers may perform different kinds of transformations on their inputs. Signals travel from the first (input), to the last (output) layer, possibly after traversing the layers multiple times.
A deep Boltzmann machine (DBM) is a type of binary pairwise [[Markov random field]] ([[Graph (discrete mathematics)#Undirected graph|undirected]] probabilistic [[graphical model]]) with multiple layers of [[Latent variable|hidden]] [[random variables]]. It is a network of symmetrically coupled stochastic [[Binary variable|binary units]]. It comprises a set of visible units <math>\boldsymbol{\nu} \in \{0,1\}^D</math>, and a series of layers of hidden units <math>\boldsymbol{h}^{(1)} \in \{0,1\}^{F_1}, \boldsymbol{h}^{(2)} \in \{0,1\}^{F_2}, \ldots, \boldsymbol{h}^{(L)} \in \{0,1\}^{F_L}</math>. There is no connection between units of the same layer (like [[Restricted Boltzmann machine|RBM]]). For the {{H:title|Deep Boltzmann machine|DBM}}, the probability assigned to vector {{mvar|'''&nu;'''}} is
 
The original goal of the neural network approach was to solve problems in the same way that a human brain would. Over time, attention focused on matching specific mental abilities, leading to deviations from biology such as [[backpropagation]], or passing information in the reverse direction and adjusting the network to reflect that information.
:<math>p(\boldsymbol{\nu}) = \frac{1}{Z}\sum_h e^{\sum_{ij}W_{ij}^{(1)}\nu_i h_j^{(1)} + \sum_{jl}W_{jl}^{(2)}h_j^{(1)}h_l^{(2)}+\sum_{lm}W_{lm}^{(3)}h_l^{(2)}h_m^{(3)}},</math>
 
Neural networks have been used on a variety of tasks, including computer vision, [[speech recognition]], [[machine translation]], [[social network]] filtering, [[general game playing|playing board and video games]] and medical diagnosis.
where <math>\boldsymbol{h} = \{\boldsymbol{h}^{(1)}, \boldsymbol{h}^{(2)}, \boldsymbol{h}^{(3)} \}</math> are the set of hidden units, and <math>\theta = \{\boldsymbol{W}^{(1)}, \boldsymbol{W}^{(2)}, \boldsymbol{W}^{(3)} \} </math> are the model parameters, representing visible-hidden and hidden-hidden interactions. If <math>\boldsymbol{W}^{(2)} = 0</math> and <math>\boldsymbol{W}^{(3)} = 0</math> the network is the well-known [[restricted Boltzmann machine]].<ref name="ref1">{{cite journal
| last1 = Hinton
| first1 = Geoffrey
| last2 = Salakhutdinov
| first2 = Ruslan
| title = A better way to pretrain deep Boltzmann machines
| journal = Advances in Neural
| volume = 3
| pages = 1–9
| date = 2012
| url = http://machinelearning.wustl.edu/mlpapers/paper_files/NIPS2012_1178.pdf}}</ref> Interactions are symmetric because links are undirected. By contrast, in a [[deep belief network]] (DBN) only the top two layers form a restricted Boltzmann machine (which is an undirected [[graphical model]]), but lower layers form a directed generative model.
 
As of 2017, neural networks typically have a few thousand to a few million units and millions of connections. Despite this number being several order of magnitude less than the number of neurons on a human brain, these networks can perform many tasks at a level beyond that of humans (e.g., recognizing faces, or playing "Go"<ref>{{Cite journal|last1=Silver|first1=David|last2=Huang|first2=Aja|last3=Maddison|first3=Chris J.|last4=Guez|first4=Arthur|last5=Sifre|first5=Laurent|last6=Driessche|first6=George van den|last7=Schrittwieser|first7=Julian|last8=Antonoglou|first8=Ioannis|last9=Panneershelvam|first9=Veda|s2cid=515925|date=January 2016|title=Mastering the game of Go with deep neural networks and tree search|journal=Nature|volume=529|issue=7587|pages=484–489|doi=10.1038/nature16961|issn=1476-4687|pmid=26819042|bibcode=2016Natur.529..484S}}</ref>).
Like DBNs, DBMs can learn complex and abstract internal representations of the input in tasks such as [[Object recognition|object]] or [[speech recognition]], using limited labeled data to fine-tune the representations built using a large supply of unlabeled sensory input data. However, unlike {{H:title|Deep belief network|DBNs}} and deep convolutional neural networks, they adopt the [[inference]] and training procedure in both directions, bottom-up and top-down pass, which allow the {{H:title|Deep Boltzmann machine|DBMs}} to better unveil the representations of the ambiguous and complex input structures.<ref name="ref3">{{cite journal
| last1 = Hinton
| first1 = Geoffrey
| last2 = Salakhutdinov
| first2 = Ruslan
| title = Efficient Learning of Deep Boltzmann Machines
| volume = 3
| pages = 448–455
| date = 2009
| url = http://machinelearning.wustl.edu/mlpapers/paper_files/AISTATS09_SalakhutdinovH.pdf
}}</ref><ref name="ref4">{{cite journal
| last1 = Bengio
| first1 = Yoshua
| last2 = LeCun
| first2 = Yann
| title = Scaling Learning Algorithms towards AI
| volume = 1
| pages = 1–41
| date = 2007
| url = http://www.iro.umontreal.ca/~lisa/bib/pub_subject/language/pointeurs/bengio+lecun-chapter2007.pdf}}</ref>
 
=== Deep neural networks ===
However, the speed of DBMs limits their performance and functionality. Because exact maximum likelihood learning is intractable for DBMs, we may perform approximate maximum likelihood learning. Another option is to use mean-field inference to estimate data-dependent expectations, and approximation the expected sufficient statistics of the model by using ''[[Markov chain Monte Carlo]]'' ''(MCMC)''.<ref name="ref1" /> This approximate inference, which must be done for each test input, is about 25 to 50 times slower than a single bottom-up pass in DBMs. This makes the joint optimization impractical for large data sets, and seriously restricts the use of DBMs for tasks such as feature representation.<ref name="ref2">{{cite journal
A deep neural network (DNN) is an artificial neural network with multiple layers between the input and output layers.<ref name="BENGIODEEP" /><ref name="SCHIDHUB" /> There are different types of neural networks but they always consist of the same components: neurons, synapses, weights, biases, and functions.<ref name="Nokkada">{{citation |title=A Guide to Deep Learning and Neural Networks |url=https://serokell.io/blog/deep-learning-and-neural-network-guide#components-of-neural-networks |access-date=2020-11-16 |archive-date=2020-11-02 |archive-url=https://web.archive.org/web/20201102151103/https://serokell.io/blog/deep-learning-and-neural-network-guide#components-of-neural-networks |url-status=live }}</ref> These components as a whole function in a way that mimics functions of the human brain, and can be trained like any other ML algorithm.{{Citation needed|date=November 2020}}
| last1 = Larochelle
| first1 = Hugo
| last2 = Salakhutdinov
| first2 = Ruslan
| title = Efficient Learning of Deep Boltzmann Machines
| pages = 693–700
| date = 2010
| url = http://machinelearning.wustl.edu/mlpapers/paper_files/AISTATS2010_SalakhutdinovL10.pdf}}</ref>
 
For example, a DNN that is trained to recognize dog breeds will go over the given image and calculate the probability that the dog in the image is a certain breed. The user can review the results and select which probabilities the network should display (above a certain threshold, etc.) and return the proposed label. Each mathematical manipulation as such is considered a layer,<ref name="Kumar2021">{{cite journal | last1 = Kumar | first1 = Nishant | last2 = Raubal | first2 = Martin | title = Applications of deep learning in congestion detection, prediction and alleviation: A survey | journal = Transportation Research Part C: Emerging Technologies | volume = 133 | article-number = 103432 | year = 2021 | doi = 10.1016/j.trc.2021.103432 | hdl = 10230/42143 | s2cid = 240420107 | doi-access = free | arxiv = 2102.09759 | bibcode = 2021TRPC..13303432K | hdl-access = free }}</ref> and complex DNN have many layers, hence the name "deep" networks.
=== Stacked (de-noising) auto-encoders ===
 
DNNs can model complex non-linear relationships. DNN architectures generate compositional models where the object is expressed as a layered composition of [[Primitive data type|primitives]].<ref>{{Cite journal|last1=Szegedy|first1=Christian|last2=Toshev|first2=Alexander|last3=Erhan|first3=Dumitru|date=2013|title=Deep neural networks for object detection|url=https://papers.nips.cc/paper/5207-deep-neural-networks-for-object-detection|journal=Advances in Neural Information Processing Systems|pages=2553–2561|access-date=2017-06-13|archive-date=2017-06-29|archive-url=https://web.archive.org/web/20170629172111/http://papers.nips.cc/paper/5207-deep-neural-networks-for-object-detection|url-status=live}}</ref> The extra layers enable composition of features from lower layers, potentially modeling complex data with fewer units than a similarly performing shallow network.<ref name="BENGIODEEP"/> For instance, it was proved that sparse [[multivariate polynomial]]s are exponentially easier to approximate with DNNs than with shallow networks.<ref name="rolnickpaper">{{cite conference|last1=Rolnick|first1=David|last2=Tegmark|first2=Max|date=2018|title=The power of deeper networks for expressing natural functions|url=https://openreview.net/pdf?id=SyProzZAW|conference=ICLR 2018|book-title=International Conference on Learning Representations|access-date=2021-01-05|archive-date=2021-01-07|archive-url=https://web.archive.org/web/20210107183647/https://openreview.net/pdf?id=SyProzZAW|url-status=live}}</ref>
The [[auto encoder]] idea is motivated by the concept of a ''good'' representation. For example, for a [[Linear classifier|classifier]], a good representation can be defined as one that will yield a better performing classifier.
 
Deep architectures include many variants of a few basic approaches. Each architecture has found success in specific domains. It is not always possible to compare the performance of multiple architectures, unless they have been evaluated on the same data sets.<ref name="Kumar2021"/>
An ''encoder'' is a deterministic mapping <math>f_\theta</math> that transforms an input vector''''' x''''' into hidden representation '''''y''''', where <math>\theta = \{\boldsymbol{W}, b\}</math>, <math>\boldsymbol{W}</math> is the weight matrix and '''b''' is an offset vector (bias). A ''decoder'' maps back the hidden representation '''y''' to the reconstructed input '''''z ''''' via <math>g_\theta</math>. The whole process of auto encoding is to compare this reconstructed input to the original and try to minimize this error to make the reconstructed value as close as possible to the original.
 
DNNs are typically feedforward networks in which data flows from the input layer to the output layer without looping back. At first, the DNN creates a map of virtual neurons and assigns random numerical values, or "weights", to connections between them. The weights and inputs are multiplied and return an output between 0 and 1. If the network did not accurately recognize a particular pattern, an algorithm would adjust the weights.<ref>{{Cite news|last=Hof|first=Robert D.|title=Is Artificial Intelligence Finally Coming into Its Own?|work=MIT Technology Review|url=https://www.technologyreview.com/s/513696/deep-learning/|access-date=10 July 2018|archive-url=https://web.archive.org/web/20190331092832/https://www.technologyreview.com/s/513696/deep-learning/|archive-date=31 March 2019}}</ref> That way the algorithm can make certain parameters more influential, until it determines the correct mathematical manipulation to fully process the data.
In ''stacked denoising auto encoders'', the partially corrupted output is cleaned (de-noised). This idea was introduced in 2010 by Vincent et al.<ref name="ref9">{{cite journal
| last1 = Vincent
| first1 = Pascal
| last2 = Larochelle
| first2 = Hugo
| last3 = Lajoie
| first3 = Isabelle
| last4 = Bengio
| first4 = Yoshua
| last5 = Manzagol
| first5 = Pierre-Antoine
| title = Stacked Denoising Autoencoders: Learning Useful Representations in a Deep Network with a Local Denoising Criterion
| journal = The Journal of Machine Learning Research
| volume = 11
| pages = 3371–3408
| date = 2010
| url = http://dl.acm.org/citation.cfm?id=1953039}}</ref> with a specific approach to ''good'' representation, a ''good representation is one that can be obtained [[Robustness (computer science)|robustly]] from a corrupted input and that will be useful for recovering the corresponding clean input.'' Implicit in this definition are the following ideas:
 
[[Recurrent neural networks]], in which data can flow in any direction, are used for applications such as [[language model]]ing.<ref name="gers2001">{{cite journal|last1=Gers|first1=Felix A.|last2=Schmidhuber|first2=Jürgen|year=2001|title=LSTM Recurrent Networks Learn Simple Context Free and Context Sensitive Languages|url=http://elartu.tntu.edu.ua/handle/lib/30719|journal=IEEE Transactions on Neural Networks|volume=12|issue=6|pages=1333–1340|doi=10.1109/72.963769|pmid=18249962|bibcode=2001ITNN...12.1333G |s2cid=10192330 |access-date=2020-02-25|archive-date=2020-01-26|archive-url=https://web.archive.org/web/20200126045722/http://elartu.tntu.edu.ua/handle/lib/30719|url-status=live}}</ref><ref name="NIPS2014"/><ref name="vinyals2016">{{cite arXiv |eprint=1602.02410|last1=Jozefowicz|first1=Rafal|title=Exploring the Limits of Language Modeling|last2=Vinyals|first2=Oriol|last3=Schuster|first3=Mike|last4=Shazeer|first4=Noam|last5=Wu|first5=Yonghui|class=cs.CL|year=2016}}</ref><ref name="gillick2015">{{cite arXiv |eprint=1512.00103|last1=Gillick|first1=Dan|title=Multilingual Language Processing from Bytes|last2=Brunk|first2=Cliff|last3=Vinyals|first3=Oriol|last4=Subramanya|first4=Amarnag|class=cs.CL|year=2015}}</ref><ref name="MIKO2010">{{Cite journal|last=Mikolov|first=T.|display-authors=etal|date=2010|title=Recurrent neural network based language model|url=http://www.fit.vutbr.cz/research/groups/speech/servite/2010/rnnlm_mikolov.pdf|journal=Interspeech|pages=1045–1048|doi=10.21437/Interspeech.2010-343|s2cid=17048224 |access-date=2017-06-13|archive-date=2017-05-16|archive-url=https://web.archive.org/web/20170516181940/http://www.fit.vutbr.cz/research/groups/speech/servite/2010/rnnlm_mikolov.pdf|url-status=live}}</ref> Long short-term memory is particularly effective for this use.<ref name=":0">{{Cite journal |last1=Hochreiter |first1=Sepp |last2=Schmidhuber |first2=Jürgen |date=1 November 1997 |title=Long Short-Term Memory |journal=Neural Computation |volume=9 |issue=8 |pages=1735–1780 |doi=10.1162/neco.1997.9.8.1735 |issn=0899-7667 |pmid=9377276 |s2cid=1915014}}</ref><ref name=":10">{{Cite web|url=https://www.researchgate.net/publication/220320057|title=Learning Precise Timing with LSTM Recurrent Networks (PDF Download Available)|website=ResearchGate|access-date=13 June 2017|archive-date=9 May 2021|archive-url=https://web.archive.org/web/20210509123147/https://www.researchgate.net/publication/220320057_Learning_Precise_Timing_with_LSTM_Recurrent_Networks|url-status=live}}</ref>
* The higher level representations are relatively stable and robust to input corruption;
* It is necessary to extract features that are useful for representation of the input distribution.
 
[[Convolutional neural network]]s (CNNs) are used in computer vision.<ref name="LECUN86">{{cite journal |last1=LeCun |first1=Y. |display-authors=etal |year= 1998|title=Gradient-based learning applied to document recognition |journal=Proceedings of the IEEE |volume=86 |issue=11 |pages=2278–2324 |doi=10.1109/5.726791|s2cid=14542261 |url=http://elartu.tntu.edu.ua/handle/lib/38369 }}</ref> CNNs also have been applied to [[acoustic model]]ing for automatic speech recognition (ASR).<ref name=":2">{{Cite book |doi=10.1109/icassp.2013.6639347|isbn=978-1-4799-0356-6|chapter=Deep convolutional neural networks for LVCSR|title=2013 IEEE International Conference on Acoustics, Speech and Signal Processing|pages=8614–8618|year=2013|last1=Sainath|first1=Tara N.|author1-link= Tara Sainath |last2=Mohamed|first2=Abdel-Rahman|last3=Kingsbury|first3=Brian|last4=Ramabhadran|first4=Bhuvana|author4-link=Bhuvana Ramabhadran|s2cid=13816461}}</ref>
The algorithm consists of multiple steps; starts by a [[stochastic mapping]] of <math>\boldsymbol{x}</math> to <math>\tilde{\boldsymbol{x}}</math> through <math>q_D(\tilde{\boldsymbol{x}}|\boldsymbol{x})</math>, this is the corrupting step. Then the corrupted input <math>\tilde{\boldsymbol{x}}</math> passes through a basic auto encoder process and is mapped to a hidden representation <math>\boldsymbol{y} = f_\theta(\tilde{\boldsymbol{x}}) = s(\boldsymbol{W}\tilde{\boldsymbol{x}}+b)</math>. From this hidden representation, we can reconstruct <math>\boldsymbol{z} = g_\theta(\boldsymbol{y})</math>. In the last stage, a [[minimization algorithm]] runs in order to have '''''z''''' as close as possible to uncorrupted input <math>\boldsymbol{x}</math>. The reconstruction error <math>L_H(\boldsymbol{x},\boldsymbol{z})</math> might be either the [[cross-entropy]] loss with an affine-sigmoid decoder, or the squared error loss with an affine decoder.<ref name="ref9" />
 
==== Challenges ====
In order to make a deep architecture, auto encoders stack one on top of another.<ref name="ballard1987">[[Dana H. Ballard]] (1987). Modular learning in neural networks. Proceedings of AAAI, pages 279–284.</ref> Once the encoding function <math>f_\theta</math> of the first denoising auto encoder is learned and used to uncorrupt the input (corrupted input), we can train the second level.<ref name="ref9" />
As with ANNs, many issues can arise with naively trained DNNs. Two common issues are [[overfitting]] and computation time.
 
DNNs are prone to overfitting because of the added layers of abstraction, which allow them to model rare dependencies in the training data. [[Regularization (mathematics)|Regularization]] methods such as Ivakhnenko's unit pruning<ref name="ivak1971"/> or [[weight decay]] (<math> \ell_2 </math>-regularization) or [[sparse matrix|sparsity]] (<math> \ell_1 </math>-regularization) can be applied during training to combat overfitting.<ref>{{Cite book |doi=10.1109/icassp.2013.6639349|isbn=978-1-4799-0356-6|arxiv=1212.0901|citeseerx=10.1.1.752.9151|chapter=Advances in optimizing recurrent networks|title=2013 IEEE International Conference on Acoustics, Speech and Signal Processing|pages=8624–8628|year=2013|last1=Bengio|first1=Yoshua|last2=Boulanger-Lewandowski|first2=Nicolas|last3=Pascanu|first3=Razvan|s2cid=12485056}}</ref> Alternatively [[Dropout (neural networks)|dropout]] regularization randomly omits units from the hidden layers during training. This helps to exclude rare dependencies.<ref name="DAHL2013">{{Cite journal|last=Dahl|first=G.|display-authors=etal|date=2013|title=Improving DNNs for LVCSR using rectified linear units and dropout|url=http://www.cs.toronto.edu/~gdahl/papers/reluDropoutBN_icassp2013.pdf|journal=ICASSP|access-date=2017-06-13|archive-date=2017-08-12|archive-url=https://web.archive.org/web/20170812140509/http://www.cs.toronto.edu/~gdahl/papers/reluDropoutBN_icassp2013.pdf|url-status=live}}</ref> Another interesting recent development is research into models of just enough complexity through an estimation of the intrinsic complexity of the task being modelled. This approach has been successfully applied for multivariate time series prediction tasks such as traffic prediction.<ref name="Kumar2024">{{cite journal| last1 = Kumar | first1 = Nishant | last2 = Martin | first2 = Henry | last3 = Raubal | first3 = Martin | title = Enhancing Deep Learning-Based City-Wide Traffic Prediction Pipelines Through Complexity Analysis | journal = Data Science for Transportation | volume = 6 | article-number = 24| year = 2024
Once the stacked auto encoder is trained, its output can be used as the input to a [[supervised learning]] algorithm such as [[support vector machine]] classifier or a multi-class [[logistic regression]].<ref name="ref9" />
| issue = 3 | doi = 10.1007/s42421-024-00109-x| doi-access = free| hdl = 20.500.11850/695425 | hdl-access = free }}</ref> Finally, data can be augmented via methods such as cropping and rotating such that smaller training sets can be increased in size to reduce the chances of overfitting.<ref>{{Cite web|url=https://www.coursera.org/learn/convolutional-neural-networks/lecture/AYzbX/data-augmentation|title=Data Augmentation - deeplearning.ai {{!}} Coursera|website=Coursera|access-date=30 November 2017|archive-date=1 December 2017|archive-url=https://web.archive.org/web/20171201032606/https://www.coursera.org/learn/convolutional-neural-networks/lecture/AYzbX/data-augmentation|url-status=live}}</ref>
 
DNNs must consider many training parameters, such as the size (number of layers and number of units per layer), the [[learning rate]], and initial weights. [[Hyperparameter optimization#Grid search|Sweeping through the parameter space]] for optimal parameters may not be feasible due to the cost in time and computational resources. Various tricks, such as [[Batch learning|batching]] (computing the gradient on several training examples at once rather than individual examples)<ref name="RBMTRAIN">{{Cite journal|last=Hinton|first=G. E.|date=2010|title=A Practical Guide to Training Restricted Boltzmann Machines|url=https://www.researchgate.net/publication/221166159|journal=Tech. Rep. UTML TR 2010-003|access-date=2017-06-13|archive-date=2021-05-09|archive-url=https://web.archive.org/web/20210509123211/https://www.researchgate.net/publication/221166159_A_brief_introduction_to_Weightless_Neural_Systems|url-status=live}}</ref> speed up computation. Large processing capabilities of many-core architectures (such as GPUs or the Intel Xeon Phi) have produced significant speedups in training, because of the suitability of such processing architectures for the matrix and vector computations.<ref>{{cite book|last1=You|first1=Yang|title=Proceedings of the International Conference for High Performance Computing, Networking, Storage and Analysis on - SC '17|pages=1–12|last2=Buluç|first2=Aydın|last3=Demmel|first3=James|chapter=Scaling deep learning on GPU and knights landing clusters|chapter-url=https://dl.acm.org/citation.cfm?doid=3126908.3126912|publisher=SC '17, ACM|date=November 2017|access-date=5 March 2018|doi=10.1145/3126908.3126912|arxiv=1708.02983 |isbn=9781450351140|s2cid=8869270|url=http://www.escholarship.org/uc/item/6ch40821|archive-date=29 July 2020|archive-url=https://web.archive.org/web/20200729133850/https://escholarship.org/uc/item/6ch40821|url-status=live}}</ref><ref>{{cite journal|last1=Viebke|first1=André|last2=Memeti|first2=Suejb|last3=Pllana|first3=Sabri|last4=Abraham|first4=Ajith|s2cid=14135321|title=CHAOS: a parallelization scheme for training convolutional neural networks on Intel Xeon Phi|journal=The Journal of Supercomputing|volume=75|pages=197–227|doi=10.1007/s11227-017-1994-x|arxiv=1702.07908|bibcode=2017arXiv170207908V|year=2019}}</ref>
=== Deep stacking networks ===
 
Alternatively, engineers may look for other types of neural networks with more straightforward and convergent training algorithms. CMAC ([[cerebellar model articulation controller]]) is one such kind of neural network. It doesn't require learning rates or randomized initial weights. The training process can be guaranteed to converge in one step with a new batch of data, and the computational complexity of the training algorithm is linear with respect to the number of neurons involved.<ref name=Qin1>Ting Qin, et al. "A learning algorithm of CMAC based on RLS". Neural Processing Letters 19.1 (2004): 49-61.</ref><ref name=Qin2>Ting Qin, et al. "[http://www-control.eng.cam.ac.uk/Homepage/papers/cued_control_997.pdf Continuous CMAC-QRLS and its systolic array]". {{Webarchive|url=https://web.archive.org/web/20181118122850/http://www-control.eng.cam.ac.uk/Homepage/papers/cued_control_997.pdf |date=2018-11-18 }}. Neural Processing Letters 22.1 (2005): 1-16.</ref>
One deep architecture based on a hierarchy of blocks of simplified [[neural network]] modules is a deep convex network, introduced in 2011.<ref name="ref16">{{cite journal
| last1 = Deng
| first1 = Li
| last2 = Yu
| first2 = Dong
| title = Deep Convex Net: A Scalable Architecture for Speech Pattern Classification
| journal = Proceedings of the Interspeech
| pages = 2285–2288
| date = 2011
| url = http://www.truebluenegotiations.com/files/deepconvexnetwork-interspeech2011-pub.pdf}}</ref> Here, the weights learning problem is formulated as a [[convex optimization problem]] with a [[Closed-form expression|closed-form solution]]. This architecture is also called a deep stacking network (DSN),<ref name="ref17">{{cite journal
| last1 = Deng
| first1 = Li
| last2 = Yu
| first2 = Dong
| last3 = Platt
| first3 = John
| title = Scalable stacking and learning for building deep architectures
| journal = 2012 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)
| pages = 2133–2136
| date = 2012
| url = http://research-srv.microsoft.com/pubs/157586/DSN-ICASSP2012.pdf}}</ref> emphasizing the mechanism's similarity to ''stacked generalization''.<ref name="ref18">{{cite journal
| last1 = David
| first1 = Wolpert
| title = Stacked generalization
| journal = Neural Networks
| volume = 5 | issue = 2
| pages = 241–259
| date = 1992
| doi=10.1016/S0893-6080(05)80023-1}}</ref> Each DSN block is a simple module that is easy to train by itself in a [[Supervised learning|supervised]] fashion without [[back-propagation]] for the entire blocks.<ref name="ref12">{{cite journal
| last1 = Bengio
| first1 = Yoshua
| title = Learning deep architectures for AI
| journal = Foundations and Trends in Machine Learning
| volume = 2 | issue = 1
| pages = 1–127
| date = 2009
| url = http://www.nowpublishers.com/product.aspx?product=MAL&doi=2200000006
| doi=10.1561/2200000006}}</ref>
 
== Hardware ==
As designed by Deng and Dong,<ref name="ref16" /> each block consists of a simplified [[multi-layer perceptron]] (MLP) with a single hidden layer. The hidden layer '''''h''''' has logistic [[Sigmoid function|sigmoidal]] [[Artificial neuron|units]], and the output layer has linear units. Connections between these layers are represented by weight matrix '''''U;''''' input-to-hidden-layer connections have weight matrix '''''W'''''. Target vectors '''''t''''' form the columns of matrix '''''T''''', and the input data vectors '''''x''''' form the columns of matrix '''''X.''''' The matrix of hidden units is <math>\boldsymbol{H} = \sigma(\boldsymbol{W}^T\boldsymbol{X})</math>. Modules are trained in order, so lower-layer weights '''''W''''' are known at each stage. The function performs the element-wise logistic sigmoid operation. Each block estimates the same final label class ''y'', and its estimate is concatenated with original input '''''X''''' to form the ''expanded input'' for the next block. Thus, the input to the first block contains the original data only, while downstream blocks' input also has the output of preceding blocks. Then learning the upper-layer weight matrix '''''U''''' given other weights in the network can be formulated as a convex optimization problem:
Since the 2010s, advances in both machine learning algorithms and [[computer hardware]] have led to more efficient methods for training deep neural networks that contain many layers of non-linear hidden units and a very large output layer.<ref>{{cite web|last1=Research|first1=AI|title=Deep Neural Networks for Acoustic Modeling in Speech Recognition|url=http://airesearch.com/ai-research-papers/deep-neural-networks-for-acoustic-modeling-in-speech-recognition/|website=airesearch.com|access-date=23 October 2015|date=23 October 2015|archive-date=1 February 2016|archive-url=https://web.archive.org/web/20160201033801/http://airesearch.com/ai-research-papers/deep-neural-networks-for-acoustic-modeling-in-speech-recognition/|url-status=live}}</ref> By 2019, [[graphics processing unit]]s (GPUs), often with AI-specific enhancements, had displaced CPUs as the dominant method for training large-scale commercial cloud AI .<ref>{{cite news |title=GPUs Continue to Dominate the AI Accelerator Market for Now |url=https://www.informationweek.com/big-data/ai-machine-learning/gpus-continue-to-dominate-the-ai-accelerator-market-for-now/a/d-id/1336475 |access-date=11 June 2020 |work=InformationWeek |date=December 2019 |language=en |archive-date=10 June 2020 |archive-url=https://web.archive.org/web/20200610094310/https://www.informationweek.com/big-data/ai-machine-learning/gpus-continue-to-dominate-the-ai-accelerator-market-for-now/a/d-id/1336475 |url-status=live }}</ref> [[OpenAI]] estimated the hardware computation used in the largest deep learning projects from AlexNet (2012) to AlphaZero (2017) and found a 300,000-fold increase in the amount of computation required, with a doubling-time trendline of 3.4 months.<ref>{{cite news |last1=Ray |first1=Tiernan |title=AI is changing the entire nature of computation |url=https://www.zdnet.com/article/ai-is-changing-the-entire-nature-of-compute/ |access-date=11 June 2020 |work=ZDNet |date=2019 |language=en |archive-date=25 May 2020 |archive-url=https://web.archive.org/web/20200525144635/https://www.zdnet.com/article/ai-is-changing-the-entire-nature-of-compute/ |url-status=live }}</ref><ref>{{cite web |title=AI and Compute |url=https://openai.com/blog/ai-and-compute/ |website=OpenAI |access-date=11 June 2020 |language=en |date=16 May 2018 |archive-date=17 June 2020 |archive-url=https://web.archive.org/web/20200617200602/https://openai.com/blog/ai-and-compute/ |url-status=live }}</ref>
 
Special [[electronic circuit]]s called [[deep learning processor]]s were designed to speed up deep learning algorithms. Deep learning processors include neural processing units (NPUs) in [[Huawei]] cellphones<ref>{{Cite web|url=https://consumer.huawei.com/en/press/news/2017/ifa2017-kirin970/|title=HUAWEI Reveals the Future of Mobile AI at IFA 2017 &#124; HUAWEI Latest News &#124; HUAWEI Global|website=consumer.huawei.com}}</ref> and [[cloud computing]] servers such as [[tensor processing unit]]s (TPU) in the [[Google Cloud Platform]].<ref>{{Cite journal|last1=P|first1=JouppiNorman|last2=YoungCliff|last3=PatilNishant|last4=PattersonDavid|last5=AgrawalGaurav|last6=BajwaRaminder|last7=BatesSarah|last8=BhatiaSuresh|last9=BodenNan|last10=BorchersAl|last11=BoyleRick|date=2017-06-24|title=In-Datacenter Performance Analysis of a Tensor Processing Unit|journal=ACM SIGARCH Computer Architecture News|volume=45|issue=2|pages=1–12|language=EN|doi=10.1145/3140659.3080246|doi-access=free|arxiv=1704.04760}}</ref> [[Cerebras|Cerebras Systems]] has also built a dedicated system to handle large deep learning models, the CS-2, based on the largest processor in the industry, the second-generation Wafer Scale Engine (WSE-2).<ref>{{Cite web |last=Woodie |first=Alex |date=2021-11-01 |title=Cerebras Hits the Accelerator for Deep Learning Workloads |url=https://www.datanami.com/2021/11/01/cerebras-hits-the-accelerator-for-deep-learning-workloads/ |access-date=2022-08-03 |website=Datanami}}</ref><ref>{{Cite web |date=2021-04-20 |title=Cerebras launches new AI supercomputing processor with 2.6 trillion transistors |url=https://venturebeat.com/2021/04/20/cerebras-systems-launches-new-ai-supercomputing-processor-with-2-6-trillion-transistors/ |access-date=2022-08-03 |website=VentureBeat |language=en-US}}</ref>
:<math>\min_{U^T} f = ||\boldsymbol{U}^T \boldsymbol{H} - \boldsymbol{T}||^2_F,</math>
 
Atomically thin [[semiconductors]] are considered promising for energy-efficient deep learning hardware where the same basic device structure is used for both logic operations and data storage.
which has a closed-form solution.
In 2020, Marega et al. published experiments with a large-area active channel material for developing logic-in-memory devices and circuits based on [[floating-gate]] [[field-effect transistor]]s (FGFETs).<ref name="atomthin">{{cite journal|title=Logic-in-memory based on an atomically thin semiconductor|year=2020|doi=10.1038/s41586-020-2861-0|last1=Marega|first1=Guilherme Migliato|last2=Zhao|first2=Yanfei|last3=Avsar|first3=Ahmet|last4=Wang|first4=Zhenyu|last5=Tripati|first5=Mukesh|last6=Radenovic|first6=Aleksandra|last7=Kis|first7=Anras|journal=Nature|volume=587|issue=2|pages=72–77|pmid=33149289|pmc=7116757|bibcode=2020Natur.587...72M }}</ref>
 
In 2021, J. Feldmann et al. proposed an integrated [[photonic]] [[hardware accelerator]] for parallel convolutional processing.<ref name="photonic">{{cite journal |title=Parallel convolutional processing using an integrated photonic tensor |year=2021 |doi=10.1038/s41586-020-03070-1 |last1=Feldmann |first1=J. |last2=Youngblood|first2=N. |last3=Karpov |first3=M. | last4=Gehring |first4=H. | display-authors=3 | journal=Nature |volume=589 |issue=2 |pages=52–58|pmid=33408373 |arxiv=2002.00281 |s2cid=211010976 }}</ref> The authors identify two key advantages of integrated photonics over its electronic counterparts: (1) massively parallel data transfer through [[wavelength]] division [[multiplexing]] in conjunction with [[frequency comb]]s, and (2) extremely high data modulation speeds.<ref name="photonic"/> Their system can execute trillions of multiply-accumulate operations per second, indicating the potential of [[Photonic integrated circuit|integrated]] [[photonics]] in data-heavy AI applications.<ref name="photonic"/>
Unlike other deep architectures, such as [[Deep belief network|DBNs]], the goal is not to discover the transformed [[Feature (machine learning)|feature]] representation. The structure of the hierarchy of this kind of architecture makes parallel learning straightforward, as a batch-mode optimization problem. In purely [[Discriminative model|discriminative tasks]], DSNs perform better than conventional [[Deep belief network|DBN]].<ref name="ref17" />
 
=== Tensor deep stacking networks ===
 
This architecture is an extension of deep stacking networks (DSN). It improves on {{H:title|Deep stacking network|DSN}} in two important ways: it uses higher-order information from [[covariance]] statistics, and it transforms the [[Convex optimization|non-convex problem]] of a lower-layer to a convex sub-problem of an upper-layer.<ref name="ref19">{{cite journal
| last1 = Hutchinson
| first1 = Brian
| last2 = Deng
| first2 = Li
| last3 = Yu
| first3 = Dong
| title = Tensor deep stacking networks
| journal = IEEE Transactions on Pattern Analysis and Machine Intelligence
| volume = 1-15
| date = 2012
| doi=10.1109/tpami.2012.268
| pages=1944–1957}}</ref> TDSNs use covariance statistics of the data by using a [[bilinear map]]ping from each of two distinct sets of hidden units in the same layer to predictions, via a third-order [[tensor]].
 
While parallelization and scalability are not considered seriously in conventional {{H:title|Deep neural networks|DNNs}},<ref name="ref26">{{cite journal
| last1 = Hinton
| first1 = Geoffrey
| last2 = Salakhutdinov
| first2 = Ruslan
| title = Reducing the Dimensionality of Data with Neural Networks
| journal = Science
| volume = 313
| pages = 504–507
| date = 2006
| doi=10.1126/science.1127647
| pmid=16873662}}</ref><ref name="ref27">{{cite journal
| last1 = Dahl
| first1 = G.
| last2 = Yu
| first2 = D.
| last3 = Deng
| first3 = L.
| last4 = Acero
| first4 = A.
| title = Context-Dependent Pre-Trained Deep Neural Networks for Large-Vocabulary Speech Recognition
| journal = IEEE Transactions on Audio, Speech, and Language Processing
| volume = 20 | issue = 1
| pages = 30–42
| date = 2012
| doi=10.1109/tasl.2011.2134090}}</ref><ref name="ref28">{{cite journal
| last1 = Mohamed
| first1 = Abdel-rahman
| last2 = Dahl
| first2 = George
| last3 = Hinton
| first3 = Geoffrey
| title = Acoustic Modeling Using Deep Belief Networks
| journal = IEEE Transactions on Audio, Speech, and Language Processing
| volume = 20 | issue = 1
| pages = 14–22
| date = 2012
| doi=10.1109/tasl.2011.2109382}}</ref> all learning for {{H:title|Deep stacking network|DSN}}s and {{H:title|Tensor deep stacking network|TDSN}}s is done in batch mode, to allow parallelization on a [[Computer cluster|cluster]] of [[CPU]] or [[GPU]] nodes.<ref name="ref16" /><ref name="ref17" /> Parallelization allows scaling the design to larger (deeper) architectures and data sets.
 
The basic architecture is suitable for diverse tasks such as [[Statistical classification|classification]] and [[regression analysis|regression]].
 
=== Spike-and-slab RBMs ===
 
The need for deep learning with [[Real number|real-valued]] inputs, as in Gaussian restricted Boltzmann machines, motivates the ''spike-and-slab'' [[Restricted Boltzmann machine|RBM]] (''ss''[[Restricted Boltzmann machine|RBMs]]), which models continuous-valued inputs with strictly [[Binary variable|binary]] [[latent variable]]s.<ref name="ref30">{{cite journal
| last1 = Courville
| first1 = Aaron
| last2 = Bergstra
| first2 = James
| last3 = Bengio | first3 = Yoshua
| title = A Spike and Slab Restricted Boltzmann Machine
| journal = JMLR: Workshop and Conference Proceeding
| volume = 15
| pages = 233–241
| date = 2011
| url = http://machinelearning.wustl.edu/mlpapers/paper_files/AISTATS2011_CourvilleBB11.pdf}}</ref> Similar to basic [[Restricted Boltzmann machine|RBMs]] and its variants, a spike-and-slab [[Restricted Boltzmann machine|RBM]] is a [[bipartite graph]], while like [[Restricted Boltzmann machine|GRBM]]s, the visible units (input) are real-valued. The difference is in the hidden layer, where each hidden unit has a binary spike variable and a real-valued slab variable. A spike is a discrete [[probability mass]] at zero, while a slab is a [[Probability density|density]] over continuous ___domain;<ref name="ref32">{{cite conference
| last1 = Courville
| first1 = Aaron
| last2 = Bergstra
| first2 = James
| last3 = Bengio
| first3 = Yoshua
| chapter= Unsupervised Models of Images by Spike-and-Slab RBMs
| title = Proceedings of the 28th International Conference on Machine Learning
| volume = 10
| pages = 1–8
| date = 2011
| url = http://machinelearning.wustl.edu/mlpapers/paper_files/ICML2011Courville_591.pdf}}</ref><ref name="ref32" /> their mixture forms a [[Prior probability|prior]]. The terms come from the statistics literature.<ref name="ref31">{{cite journal
| last1 = Mitchell
| first1 = T
| last2 = Beauchamp
| first2 = J
| title = Bayesian Variable Selection in Linear Regression
| journal = Journal of the American Statistical Association
| volume = 83 | issue = 404
| pages = 1023–1032
| date = 1988
| doi=10.1080/01621459.1988.10478694}}</ref>
 
An extension of ss[[Restricted Boltzmann machine|RBM]] called µ-ss[[Restricted Boltzmann machine|RBM]] provides extra modeling capacity using additional terms in the [[energy function]]. One of these terms enables the model to form a [[Conditional probability distribution|conditional distribution]] of the spike variables by [[marginalizing out]] the slab variables given an observation.
 
=== Compound hierarchical-deep models ===
 
Compound hierarchical-deep models compose deep networks with non-parametric [[Bayesian network|Bayesian models]]. [[Feature (machine learning)|Features]] can be learned using deep architectures such as [[Deep belief network|DBNs]],<ref name="hinton2006" /> [[Deep Boltzmann Machines|DBMs]],<ref name="ref3" /> deep auto encoders,<ref name="ref15">{{cite journal
| last1 = Larochelle
| first1 = Hugo
| last2 = Bengio
| first2 = Yoshua
| last3 = Louradour
| first3 = Jerdme
| last4 = Lamblin
| first4 = Pascal
| title = Exploring Strategies for Training Deep Neural Networks
| journal = The Journal of Machine Learning Research
| volume = 10
| pages = 1–40
| date = 2009
| url = http://dl.acm.org/citation.cfm?id=1577070}}</ref> convolutional variants,<ref name="ref39">{{cite journal
| last1 = Coates
| first1 = Adam
| last2 = Carpenter
| first2 = Blake
| title = Text Detection and Character Recognition in Scene Images with Unsupervised Feature Learning
| pages = 440–445
| date = 2011
| url = }}</ref><ref name="ref40">{{cite journal
| last1 = Lee
| first1 = Honglak
| last2 = Grosse
| first2 = Roger
| title = Convolutional deep belief networks for scalable unsupervised learning of hierarchical representations
| journal = Proceedings of the 26th Annual International Conference on Machine Learning
| pages = 1–8
| date = 2009
| url = http://portal.acm.org/citation.cfm?doid=1553374.1553453}}</ref> ssRBMs,<ref name="ref32" /> deep coding networks,<ref name="ref41">{{cite journal
| last1 = Lin
| first1 = Yuanqing
| last2 = Zhang
| first2 = Tong
| title = Deep Coding Network | journal = Advances in Neural . . .
| pages = 1–9
| date = 2010
| url = http://machinelearning.wustl.edu/mlpapers/paper_files/NIPS2010_1077.pdf}}</ref> DBNs with sparse feature learning,<ref name="ref42">{{cite journal
| last1 = Ranzato
| first1 = Marc Aurelio
| last2 = Boureau
| first2 = Y-Lan
| title = Sparse Feature Learning for Deep Belief Networks
| journal = Advances in Neural Information Processing Systems
| volume=23 | pages = 1–8
| date = 2007
| url = http://machinelearning.wustl.edu/mlpapers/paper_files/NIPS2007_1118.pdf}}</ref> recursive neural networks,<ref name="ref43">{{cite journal
| last1 = Socher
| first1 = Richard
| last2 = Lin
| first2 = Clif
| title = Parsing Natural Scenes and Natural Language with Recursive Neural Networks
| journal = Proceedings of the 26th International Conference on Machine Learning
| date = 2011
| url = http://machinelearning.wustl.edu/mlpapers/paper_files/ICML2011Socher_125.pdf}}</ref> conditional DBNs,<ref name="ref44">{{cite journal
| last1 = Taylor
| first1 = Graham
| last2 = Hinton
| first2 = Geoffrey
| title = Modeling Human Motion Using Binary Latent Variables
| journal = Advances in Neural Information Processing Systems
| date = 2006
| url = http://machinelearning.wustl.edu/mlpapers/paper_files/NIPS2006_693.pdf}}</ref> de-noising auto encoders.<ref name="ref45">{{cite journal
| last1 = Vincent
| first1 = Pascal
| last2 = Larochelle
| first2 = Hugo
| title = Extracting and composing robust features with denoising autoencoders
| journal = Proceedings of the 25th international conference on Machine learning - ICML '08
| pages = 1096–1103
| date = 2008
| url = http://portal.acm.org/citation.cfm?doid=1390156.1390294}}</ref> This provides a better representation, allowing faster learning and more accurate classification with high-dimensional data. However, these architectures are poor at learning novel classes with few examples, because all network units are involved in representing the input (a ''distributed representation'') and must be adjusted together (high [[degree of freedom]]). Limiting the degree of freedom reduces the number of parameters to learn, facilitating learning of new classes from few examples. [[Hierarchical Bayesian model|''Hierarchical Bayesian (HB)'' models]] allow learning from few examples, for example<ref name="ref34">{{cite journal
| last1 = Kemp
| first1 = Charles
| last2 = Perfors
| first2 = Amy
| last3 = Tenenbaum
| first3 = Joshua
| title = Learning overhypotheses with hierarchical Bayesian models
| journal = Developmental Science
| volume = 10 | issue = 3
| pages = 307–21
| date = 2007
| pmid=17444972
| doi=10.1111/j.1467-7687.2007.00585.x}}</ref><ref name="ref37">{{cite journal
| last1 = Xu
| first1 = Fei
| last2 = Tenenbaum
| first2 = Joshua
| title = Word learning as Bayesian inference
| journal = Psychol. Rev.
| volume = 114 | issue = 2
| pages = 245–72
| date = 2007
| pmid=17500627
| doi=10.1037/0033-295X.114.2.245}}</ref><ref name="ref46">{{cite journal
| last1 = Chen
| first1 = Bo
| last2 = Polatkan
| first2 = Gungor
| title = The Hierarchical Beta Process for Convolutional Factor Analysis and Deep Learning
| journal = Machine Learning . . .
| date = 2011
| url = http://machinelearning.wustl.edu/mlpapers/paper_files/ICML2011Chen_251.pdf}}</ref><ref name="ref47">{{cite journal
| last1 = Fei-Fei
| first1 = Li
| last2 = Fergus
| first2 = Rob
| title = One-shot learning of object categories
| journal = IEEE Transactions on Pattern Analysis and Machine Intelligence
| volume = 28 | issue = 4
| pages = 594–611
| date = 2006
| pmid=16566508
| doi=10.1109/TPAMI.2006.79}}</ref><ref name="ref48">{{cite journal
| last1 = Rodriguez
| first1 = Abel
| last2 = Dunson
| first2 = David
| title = The Nested Dirichlet Process
| journal = Journal of the American Statistical Association
| volume = 103 | issue = 483
| pages = 1131–1154
| date = 2008
| url = http://amstat.tandfonline.com/doi/full/10.1198/016214508000000553
| doi=10.1198/016214508000000553}}</ref> for [[computer vision]], [[statistics]], and [[cognitive science]].
 
Compound HD architectures aim to integrate characteristics of both HB and deep networks. The compound HDP-DBM architecture, a ''[[hierarchical Dirichlet process]] (HDP)'' as a hierarchical model, incorporated with DBM architecture. It is a full [[generative model]], generalized from abstract concepts flowing through the layers of the model, which is able to synthesize new examples in novel classes that look ''reasonably natural''. All the levels are learned jointly by maximizing a joint [[Log probability|log-probability]] [[Score (statistics)|score]].<ref name="ref38">{{cite journal
| last1 = Ruslan
| first1 = Salakhutdinov
| last2 = Joshua
| first2 = Tenenbaum
| title = Learning with Hierarchical-Deep Models
| journal = IEEE Transactions on Pattern Analysis and Machine Intelligence
| pages = 1958–71
| date = 2012
| doi=10.1109/TPAMI.2012.269
| volume=35}}</ref>
 
In a DBM with three hidden layers, the probability of a visible input '''{{mvar|&nu;}}''' is:
 
:<math>p(\boldsymbol{\nu}, \psi) = \frac{1}{Z}\sum_h e^{\sum_{ij}W_{ij}^{(1)}\nu_i h_j^1 + \sum_{jl}W_{jl}^{(2)}h_j^{1}h_l^{2}+\sum_{lm}W_{lm}^{(3)}h_l^{2}h_m^{3}},</math>
 
where <math>\boldsymbol{h} = \{\boldsymbol{h}^{(1)}, \boldsymbol{h}^{(2)}, \boldsymbol{h}^{(3)} \}</math> is the set of hidden units, and <math>\psi = \{\boldsymbol{W}^{(1)}, \boldsymbol{W}^{(2)}, \boldsymbol{W}^{(3)} \} </math> are the model parameters, representing visible-hidden and hidden-hidden symmetric interaction terms.
 
After a DBM model is learned, we have an undirected model that defines the joint distribution <math>P(\nu, h^1, h^2, h^3)</math>. One way to express what has been learned is the [[Discriminative model|conditional model]] <math>P(\nu, h^1, h^2|h^3)</math> and a prior term <math>P(h^3)</math>.
 
Here <math>P(\nu, h^1, h^2|h^3)</math> represents a ''conditional'' DBM model, which can be viewed as a two-layer DBM but with bias terms given by the states of <math>h^3</math>:
 
:<math>P(\nu, h^1, h^2|h^3) = \frac{1}{Z(\psi, h^3)}e^{\sum_{ij}W_{ij}^{(1)}\nu_i h_j^1 + \sum_{jl}W_{jl}^{(2)}h_j^{1}h_l^{2}+\sum_{lm}W_{lm}^{(3)}h_l^{2}h_m^{3}}.</math>
 
=== Deep coding networks ===
 
There are advantages of a model which can ''actively'' update itself from the context in data. Deep coding network (DPCN) is a [[Predictive modelling|predictive]] coding scheme where top-down information is used to empirically adjust the priors needed for a bottom-up [[inference]] procedure by means of a deep locally connected [[generative model]]. This works by extracting sparse [[Feature (machine learning)|features]] from time-varying observations using a linear dynamical model. Then, a pooling strategy is used to learn invariant feature representations. These units compose to form a deep architecture, and are trained by [[Greedy algorithm|greedy]] layer-wise [[unsupervised learning]]. The layers constitute a kind of [[Markov chain]] such that the states at any layer only depend on the preceding and succeeding layers.
 
Deep predictive coding network (DPCN)<ref name="ref56">{{cite arXiv
| last1 = Chalasani
| first1 = Rakesh
| last2 = Principe
| first2 = Jose
| title = Deep Predictive Coding Networks
| date = 2013
| arxiv=1301.3541
}}</ref> predicts the representation of the layer, by using a top-down approach using the information in upper layer and temporal dependencies from the previous states.
 
DPCNs can be extended to form a [[Convolutional neural network|convolutional network]].<ref name="ref56" />
 
=== Deep Q-networks ===
 
A deep Q-network (DQN) is a type of deep learning model developed at [[Google DeepMind]] which combines a deep [[convolutional neural network]] with [[Q-learning]], a form of [[reinforcement learning]]. Unlike earlier reinforcement learning agents, DQNs can learn directly from high-dimensional sensory inputs. Preliminary results were presented in 2014, with a paper published in February 2015 in Nature<ref name="DQN">{{cite journal
| last1 = Mnih
| first1 = Volodymyr
| title = Human-level control through deep reinforcement learning
| pages = 529–533
| date = 2015
| volume=518|display-authors=etal
| doi=10.1038/nature14236
| journal=Nature
| pmid=25719670}}</ref> The application discussed in this paper is limited to [[Atari 2600]] gaming, although it has implications for other applications. However, much before this work, there had been a number of reinforcement learning models that apply deep learning approaches (e.g.,<ref>
R. Sun and C. Sessions, Self-segmentation of sequences: Automatic formation of hierarchies of sequential behaviors. IEEE Transactions on Systems, Man, and Cybernetics: Part B Cybernetics, Vol.30, No.3, pp.403-418. 2000.
</ref>).
 
===Networks with separate memory structures===
Integrating external memory with [[artificial neural networks]] dates to early research in distributed representations<ref name="Hinton, Geoffrey E 1984">Hinton, Geoffrey E. "Distributed representations." (1984)</ref> and [[Teuvo Kohonen]]'s [[self-organizing map]]s. For example, in [[sparse distributed memory]] or [[hierarchical temporal memory]], the patterns encoded by neural networks are used as addresses for [[content-addressable memory]], with "neurons" essentially serving as address [[encoder]]s and [[Binary decoder|decoder]]s. However, the early controllers of such memories were not differentiable.
 
====LSTM-related differentiable memory structures====
 
Apart from [[long short-term memory]] (LSTM), other approaches of the 1990s and 2000s also added differentiable memory to recurrent functions. For example:
*Differentiable push and pop actions for alternative memory networks called ''neural stack machines''<ref name="S. Das, C.L. Giles p. 79">S. Das, C.L. Giles, G.Z. Sun, "Learning Context Free Grammars: Limitations of a Recurrent Neural Network with an External Stack Memory," Proc. 14th Annual Conf. of the Cog. Sci. Soc., p. 79, 1992.</ref><ref name="Mozer, M. C. 1993 pp. 863-870">Mozer, M. C., & Das, S. (1993). A connectionist symbol manipulator that discovers the structure of context-free languages. NIPS 5 (pp. 863-870).</ref>
*Memory networks where the control network's external differentiable storage is in the fast weights of another network<ref name="ReferenceC">{{cite journal | last1 = Schmidhuber | first1 = J. | year = 1992 | title = Learning to control fast-weight memories: An alternative to recurrent nets | url = | journal = Neural Computation | volume = 4 | issue = 1| pages = 131–139 | doi=10.1162/neco.1992.4.1.131}}</ref>
*LSTM ''"forget gates"''<ref name="F. Gers, N. Schraudolph 2002">{{cite journal | last1 = Gers | first1 = F. | last2 = Schraudolph | first2 = N. | last3 = Schmidhuber | first3 = J. | year = 2002 | title = Learning precise timing with LSTM recurrent networks | url = | journal = JMLR | volume = 3 | issue = | pages = 115–143 }}</ref>
*Self-referential [[recurrent neural networks]] (RNNs) with special output units for addressing and rapidly manipulating each of the RNN's own weights in differentiable fashion (internal storage)<ref name="J. Schmidhuber pages 191-195">{{Cite conference | author = [[Jürgen Schmidhuber]] | title = An introspective network that can learn to run its own weight change algorithm | booktitle= In Proc. of the Intl. Conf. on Artificial Neural Networks, Brighton | pages = 191–195 | publisher = IEE | year = 1993 | url = ftp://ftp.idsia.ch/pub/juergen/iee93self.ps.gz }}</ref><ref name="Hochreiter, Sepp 2001">{{cite journal | last1 = Hochreiter | first1 = Sepp | last2 = Younger | first2 = A. Steven | last3 = Conwell | first3 = Peter R. | year = 2001 | title = Learning to Learn Using Gradient Descent | url = | journal = ICANN | volume = 2130 | issue = | pages = 87–94 }}</ref>
*Learning to transduce with unbounded memory<ref name="Grefenstette, Edward 1506">Grefenstette, Edward, et al. [http://arxiv.org/pdf/1506.02516.pdf "Learning to Transduce with Unbounded Memory."] {{arxiv|1506.02516}} (2015).</ref>
 
====Semantic hashing====
Approaches which represent previous experiences directly and [[Instance-based learning|use a similar experience to form a local model]] are often called [[nearest neighbour]] or [[k-nearest neighbors algorithm|k-nearest neighbors]] methods.<ref>{{cite journal | last1 = Atkeson | first1 = Christopher G. | last2 = Schaal | first2 = Stefan | year = 1995 | title = Memory-based neural networks for robot learning | url = | journal = Neurocomputing | volume = 9 | issue = 3| pages = 243–269 | doi=10.1016/0925-2312(95)00033-6}}</ref> More recently, deep learning was shown to be useful in semantic hashing<ref>Salakhutdinov, Ruslan, and Geoffrey Hinton. [http://www.utstat.toronto.edu/~rsalakhu/papers/sdarticle.pdf "Semantic hashing."] International Journal of Approximate Reasoning 50.7 (2009): 969-978.</ref> where a deep [[graphical model]] the word-count vectors<ref>{{Cite arXiv|last=Le |first=Quoc V. |last2=Mikolov |first2=Tomas |title=Distributed representations of sentences and documents |arxiv=1405.4053 |year=2014}}</ref> obtained from a large set of documents. Documents are mapped to memory addresses in such a way that semantically similar documents are located at nearby addresses. Documents similar to a query document can then be found by simply accessing all the addresses that differ by only a few bits from the address of the query document. Unlike [[sparse distributed memory]] which operates on 1000-bit addresses, semantic hashing works on 32 or 64-bit addresses found in a conventional computer architecture.
 
====Neural Turing machines====
[[Neural Turing machine]]s,<ref name="Graves, Alex 1410">Graves, Alex, Greg Wayne, and Ivo Danihelka. "Neural Turing Machines." {{arxiv|1410.5401}} (2014).</ref> developed by [[Google DeepMind]], couple LSTM networks to external memory resources, which they can interact with by attentional processes. The combined system is analogous to a [[Turing machine]] but is differentiable end-to-end, allowing it to be efficiently trained by [[gradient descent]]. Preliminary results demonstrate that neural Turing machines can infer simple algorithms such as copying, sorting, and associative recall from input and output examples.
 
====Memory networks====
Memory networks<ref name="Weston, Jason 1410">Weston, Jason, Sumit Chopra, and Antoine Bordes. "Memory networks." {{arxiv|1410.3916}} (2014).</ref><ref>Sukhbaatar, Sainbayar, et al. "End-To-End Memory Networks." {{arxiv|1503.08895}} (2015).</ref> are another extension to neural networks incorporating [[long-term memory]], which was developed by the [[Facebook]] research team. The long-term memory can be read and written to, with the goal of using it for prediction. These models have been applied in the context of [[question answering]] (QA) where the long-term memory effectively acts as a (dynamic) knowledge base, and the output is a textual response.<ref>Bordes, Antoine, et al. "Large-scale Simple Question Answering with Memory Networks." {{arxiv|1506.02075}} (2015).</ref>
 
====Pointer networks====
Deep neural networks can be potentially improved if they get deeper and have fewer parameters, while maintaining trainability. While training extremely deep (e.g. 1-million-layer-deep) neural networks might not be practically feasible, [[CPU]]-like architectures such as pointer networks<ref>Vinyals, Oriol, Meire Fortunato, and Navdeep Jaitly. "Pointer networks." {{arxiv|1506.03134}} (2015).</ref> and neural random-access machines<ref>Kurach,Karol, Andrychowicz, Marcin and Sutskever,Ilya. "Neural Random-Access Machines." {{arxiv|1511.06392}} (2015).</ref> developed by [[Google Brain]] researchers overcome this limitation by using external [[random-access memory]] as well as adding other components that typically belong to a [[computer architecture]] such as [[Processor register|registers]], [[Arithmetic logic unit|ALU]] and [[Pointer (computer programming)|pointers]]. Such systems operate on [[probability distribution]] vectors stored in memory cells and registers. Thus, the model is fully differentiable and trains end-to-end. The key characteristic of these models is that their depth, the size of their short-term memory, and the number of parameters can be altered independently — unlike models like [[Long short-term memory]], whose number of parameters grows quadratically with memory size.
 
====Encoder–decoder networks====
An encoder–decoder framework is a framework based on neural networks that aims to map highly [[Structured prediction|structured]] input to highly structured output. It was proposed recently in the context of [[machine translation]],<ref>N. Kalchbrenner and P. Blunsom, "Recurrent continuous translation models," in EMNLP’2013, 2013.</ref><ref>I. Sutskever, O. Vinyals, and Q. V. Le, "Sequence to sequence learning with neural networks," in NIPS’2014, 2014.</ref><ref>K. Cho, B. van Merrienboer, C. Gulcehre, F. Bougares, H. Schwenk, and Y. Bengio, "Learning phrase representations using RNN encoder-decoder for statistical machine translation," in Proceedings of the Empiricial Methods in Natural Language Processing (EMNLP 2014), Oct. 2014</ref> where the input and output are written sentences in two natural languages. In that work, an LSTM [[recurrent neural network]] (RNN) or [[convolutional neural network]] (CNN) was used as an encoder to summarize a source sentence, and the summary was decoded using a conditional recurrent neural network [[language model]] to produce the translation.<ref>Cho, Kyunghyun, Aaron Courville, and Yoshua Bengio. "Describing Multimedia Content using Attention-based Encoder--Decoder Networks." {{arxiv|1507.01053}} (2015).</ref> All these systems have the same building blocks: gated RNNs and CNNs, and trained attention mechanisms.
 
== Multilayer kernel machine ==
 
Multilayer kernel machines (MKM) as introduced in&nbsp;<ref name="ref59">{{cite journal
| last1 = Cho
| first1 = Youngmin
| title = Kernel Methods for Deep Learning
| pages = 1–9
| date = 2012
| url = http://cseweb.ucsd.edu/~yoc002/paper/thesis_youngmincho.pdf}}</ref> are a way of learning highly nonlinear functions by iterative application of weakly nonlinear kernels. They use the [[kernel principal component analysis]] (KPCA), in&nbsp;<ref name="ref60">{{cite journal
| last1 = Scholkopf
| first1 = B
| last2 = Smola
| first2 = Alexander
| title = Nonlinear component analysis as a kernel eigenvalue problem
| journal = Neural computation
| volume = (44)
| date = 1998
| doi=10.1162/089976698300017467
| pages=1299–1319}}</ref> as method for [[Unsupervised learning|unsupervised]] greedy layer-wise pre-training step of the deep learning architecture.
 
Layer <math>l+1</math>-th learns the representation of the previous layer <math>l</math>, extracting the <math>n_l</math> [[Principal component analysis|principal component]] (PC) of the projection layer <math>l</math> output in the feature ___domain induced by the kernel. For the sake of [[dimensionality reduction]] of the updated representation in each layer, a [[Supervised learning|supervised strategy]] is proposed to select the best informative features among features extracted by KPCA. The process is:
 
* rank the <math>n_l</math> features according to their [[mutual information]] with the class labels;
* for different values of ''K'' and <math>m_l \in\{1, \ldots, n_l\}</math>, compute the classification error rate of a ''[[K-nearest neighbor]] (K-NN)'' classifier using only the <math>m_l</math> most informative features on a [[validation set]];
* the value of <math>m_l</math> with which the classifier has reached the lowest error rate determines the number of features to retain.
 
There are some drawbacks in using the KPCA method as the building cells of an MKM.
 
A more straightforward way to use kernel machines for deep learning was developed by Microsoft researchers for spoken language understanding.<ref name="KDCN">L. Deng, G. Tur, X. He, and D. Hakkani-Tur. "Use of Kernel Deep Convex Networks and End-To-End Learning for Spoken Language Understanding," ''Proc. IEEE Workshop on Spoken Language Technologies'', 2012</ref> The main idea is to use a kernel machine to approximate a shallow neural net with an infinite number of hidden units, then use [[#Deep stacking networks|stacking]] to splice the output of the kernel machine and the raw input in building the next, higher level of the kernel machine. The number of levels in the deep convex network is a hyper-parameter of the overall system, to be determined by cross validation.
 
== Applications ==
 
=== Automatic speech recognition ===
{{Main article|Speech recognition}}
 
Speech recognition has been revolutionised by deep learning, especially by [[Long shortLarge-termscale memory]]automatic (LSTM),speech arecognition [[recurrentis neuralthe network]]first publishedand bymost [[Seppconvincing Hochreiter]]successful &case [[Jürgenof Schmidhuber]]deep in 1997learning.<ref name=lstm/> LSTM RNNs circumvent the [[vanishing gradient problem]] and can learn "Very Deep Learning" tasks<ref name="SCHIDHUB"/> that involve multi-second intervals containing speech events separated by thousands of discrete time steps, where one time step corresponds to about 10 ms. LSTM with forget gates<ref name=":10" /> is competitive with traditional speech recognizers on certain tasks.<ref name="graves2003"/>
In 2003, LSTM with forget gates<ref name="gers2002"/> became competitive with traditional speech recognizers on certain tasks.<ref name="graves2003"/>
In 2007, LSTM trained by Connectionist Temporal Classification (CTC)<ref name="graves2006"/> achieved excellent results in certain applications,<ref name="fernandez2007keyword"/> although computers were much slower than today. In 2015, Google's large scale speech recognition suddenly almost doubled its performance through CTC-trained LSTM, now available to all smartphone users.<ref name="sak2015"/>
 
The initial success of deep learning in speech recognition, however, was based on small-scale TIMITrecognition tasks. The results shown in the table below are for automatic speech recognitionbased on the popular [[TIMIT]] data set. This is a commonThe data set used for initial evaluations of deep learning architectures. The entire set contains 630 speakers from eight major [[dialect]]s of [[American English]], where each speaker reads 10 sentences.<ref name="LDCTIMIT"APC_1>''{{cite book| title=TIMIT Acoustic-Phonetic Continuous Speech Corpus''| author1=Garofolo, J.S.| author2=Lamel, L.F.| author3=Fisher, W.M.| author4=Fiscus, J.G.| author5=Pallett, D.S.| author6=Dahlgren, N.L.| author7=Zue, V.| url=https://catalog.ldc.upenn.edu/LDC93S1| publisher=Linguistic Data Consortium,| Philadelphiadate=1993| access-date=27 December 2023| doi=10.35111/17gk-bn40| isbn=1-58563-019-5}}</ref> Its small size allowslets many configurations to be tried effectively. More importantly, the TIMIT task concerns [[Phone (phonetics)|phone]]-sequence recognition, which, unlike word-sequence recognition, allows very weak "phone [[bigram]] language models". andThis thuslets the weaknessesstrength inof the acoustic modeling aspects of speech recognition can be more easily analyzed. Such analysis on TIMIT by Li Deng and collaborators around 2009-2010, contrasting the GMM (and other generative models of speech) vs. DNN models, stimulated early industrial investment in deep learning for speech recognition from small to large scales,<ref name=ReferenceICASSP2013 /><ref name="NIPS2009"/> eventually leading to pervasive and dominant use in that industry. That analysis was done with comparable performance (less than 1.5% in error rate) between discriminative DNNs and generative models. The error rates listed below, including these early results and measured as percent phone error rates (PER), have been summarized oversince a time span of the past 20 years:1991.
 
{| class="wikitable"
|-
! Method !! Percent phone<br>error rate (PER) (%)
|-
| Randomly Initialized RNN<ref>{{cite journal |last1=Robinson |first1=Tony |author-link=Tony Robinson (speech recognition)|title=Several Improvements to a Recurrent Error Propagation Network Phone Recognition System |journal=Cambridge University Engineering Department Technical Report |date=30 September 1991 |volume=CUED/F-INFENG/TR82 |doi=10.13140/RG.2.2.15418.90567 }}</ref>|| 26.1
| Randomly Initialized RNN || 26.1
|-
| Bayesian Triphone GMM-HMM || 25.6
Line 778 ⟶ 204:
| Monophone DBN-DNN on fbank || 20.7
|-
| Convolutional DNN<ref name="CNN-2014">{{cite journal|last1=Abdel-Hamid|first1=O.|title=Convolutional Neural Networks for Speech Recognition|journal=IEEE/ACM Transactions on Audio, Speech, and Language Processing|date=2014|volume=22|issue=10|pages=1533–1545|doi=10.1109/taslp.2014.2339736|s2cid=206602362|display-authors=etal|bibcode=2014ITASL..22.1533A |url=https://zenodo.org/record/891433|access-date=2018-04-20|archive-date=2020-09-22|archive-url=https://web.archive.org/web/20200922180719/https://zenodo.org/record/891433|url-status=live}}</ref>|| 20.0
|-
| Convolutional DNN w. Heterogeneous Pooling|| 18.7
|-
| Ensemble DNN/CNN/RNN<ref name="EnsembleDL">{{cite journal|last1=Deng|first1=L.|last2=Platt|first2=J.|date=2014|title=Ensemble Deep Learning for Speech Recognition|journal=Proc. Interspeech|datelast1=Deng|first1=L.|pages=1915–1919 |doi=10.21437/Interspeech.2014-433 |s2cid=15641618}}</ref>|| 18.23
|-
| Bidirectional LSTM|| 17.98
|-
| Hierarchical Convolutional Deep Maxout Network<ref name="HCDMM">{{cite journal|last1=Tóth|first1=Laszló|date=2015|title=Phone Recognition with Hierarchical Convolutional Deep Maxout Networks|journal=EURASIP Journal on Audio, Speech, and Music Processing|volume=2015|article-number=25 |doi=10.1186/s13636-015-0068-3|s2cid=217950236|url=http://publicatio.bibl.u-szeged.hu/5976/1/EURASIP2015.pdf|access-date=2019-04-01|archive-date=2020-09-24|archive-url=https://web.archive.org/web/20200924085514/http://publicatio.bibl.u-szeged.hu/5976/1/EURASIP2015.pdf|url-status=live |doi-access=free }}</ref> || 16.5
|}
 
The debut of DNNs for speaker recognition in the late 1990s and speech recognition around 2009-2011 and of LSTM around 2003–2007, accelerated progress in eight major areas:<ref name="BOOK2014" /><ref name="interspeech2014Keynote" /><ref name="ReferenceA" />
In 2010, industrial researchers extended deep learning from TIMIT to large vocabulary speech recognition, by adopting large output layers of the DNN based on context-dependent HMM states constructed by [[decision tree]]s.<ref name="
Roles2010">{{cite journal|last1=Yu|first1=D.|last2=Deng|first2=L.|title=Roles of Pre-Training and Fine-Tuning in Context-Dependent DBN-HMMs for Real-World Speech Recognition|journal=NIPS Workshop on Deep Learning and Unsupervised Feature Learning|date=2010}}</ref><ref>Seide, F., Li, G., Yu, D. Conversational speech transcription using context-dependent deep neural networks. Interspeech, 2011.</ref><ref name="ICASSP2013">Deng L., Li, J., Huang, J., Yao, K., Yu, D., Seide, F. et al. Recent Advances in Deep Learning for Speech Research at Microsoft. ICASSP, 2013.</ref> Comprehensive reviews of this development and of the state of the art as of October 2014 are provided in the recent Springer book from Microsoft Research.<ref name="ReferenceA"/> An earlier article<ref>{{cite journal|last1=Deng|first1=L.|last2=Li|first2=Xiao|title=Machine Learning Paradigms for Speech Recognition: An Overview|journal=IEEE Transactions on Audio, Speech, and Language Processing|date=2013|doi=10.1109/tasl.2013.2244083|volume=21|pages=1060–1089}}</ref> reviewed the background of automatic speech recognition and the impact of various machine learning paradigms, including deep learning.
 
* Scale-up/out and accelerated DNN training and decoding
One fundamental principle of deep learning is to do away with hand-crafted [[feature engineering]] and to use raw features. This principle was first explored successfully in the architecture of deep autoencoder on the "raw" spectrogram or linear filter-bank features at SRI in the late 1990s,<ref name="Heck2000"/> and later at Microsoft,<ref name="interspeech2010">L. Deng, M. Seltzer, D. Yu, A. Acero, A. Mohamed, and G. Hinton (2010) Binary Coding of Speech Spectrograms Using a Deep Auto-encoder. Interspeech.</ref> showing its superiority over the Mel-Cepstral features which contain a few stages of fixed transformation from spectrograms. The true "raw" features of speech, [[waveform]]s, have more recently been shown to produce excellent larger-scale speech recognition results.<ref name="interspeech2014">Z. Tuske, P. Golik, R. Schlüter and H. Ney (2014). Acoustic Modeling with Deep Neural Networks Using Raw Time Signal for LVCSR. Interspeech.</ref>
* Sequence discriminative training
 
* Feature processing by deep models with solid understanding of the underlying mechanisms
Since the initial successful debut of DNNs for speaker recognition in the late 1990s and speech recognition around 2009-2011 and of LSTM around 2003-2007, there have been huge new progresses made. Progress (and future directions) can be summarized into eight major areas:<ref name=BOOK2014 /><ref name="interspeech2014Keynote"/><ref name=ReferenceA />
* Adaptation of DNNs and related deep models
* Scaling up/out and speedup DNN training and decoding;
* [[Multi-task learning|Multi-task]] and [[transfer learning]] by DNNs and related deep models
* Sequence discriminative training of DNNs;
* [[Convolutional neural network|CNNs]] and how to design them to best exploit [[___domain knowledge]] of speech
* Feature processing by deep models with solid understanding of the underlying mechanisms;
* [[Recurrent neural network|RNN]] and its rich LSTM variants
* Adaptation of DNNs and of related deep models;
* [[Multi-task learning|Multi-task]] and [[Inductive transfer|transfer learning]] by DNNs and related deep models;
* Convolution neural networks and how to design them to best exploit ___domain knowledge of speech;
* Recurrent neural network and its rich LSTM variants;
* Other types of deep models including tensor-based models and integrated deep generative/discriminative models.
 
More recent speech recognition models use [[Transformer (deep learning architecture)|Transformers]] or [[Time delay neural network|Temporal Convolution Networks]] with significant success and widespread applications.<ref>{{cite arXiv | author1=Aaron van den Oord | last2=Dieleman | first2=Sander | last3=Zen | first3=Heiga | last4=Simonyan | first4=Karen | last5=Vinyals | first5=Oriol | last6=Graves | first6=Alex | last7=Kalchbrenner | first7=Nal | last8=Senior | first8=Andrew | last9=Kavukcuoglu | first9=Koray | title=WaveNet: A Generative Model for Raw Audio | date=2016 | class=cs.SD | eprint=1609.03499 }}</ref><ref>{{Cite web |date=2016-09-08 |title=WaveNet: A generative model for raw audio |url=https://deepmind.google/discover/blog/wavenet-a-generative-model-for-raw-audio/ |access-date=2025-07-31 |website=Google DeepMind |language=en}}</ref><ref>{{cite arXiv | last1=Latif | first1=Siddique | last2=Zaidi | first2=Aun | last3=Cuayahuitl | first3=Heriberto | last4=Shamshad | first4=Fahad | last5=Shoukat | first5=Moazzam | last6=Usama | first6=Muhammad | last7=Qadir | first7=Junaid | title=Transformers in Speech Processing: A Survey | date=2023 | class=cs.CL | eprint=2303.11607 }}</ref> All major commercial speech recognition systems (e.g., Microsoft [[Cortana (software)|Cortana]], [[Xbox]], [[Skype Translator]], [[Amazon Alexa]], [[Google Now]], [[Siri|Apple Siri]], [[Baidu]] and [[IFlytek|iFlyTek]] voice search, and a range of [[Nuance Communications|Nuance]] speech products, etc.) are based on deep learning.<ref name=BOOK2014 /><ref>{{Cite magazine|url=https://www.wired.com/2014/12/skype-used-ai-build-amazing-new-language-translator/|title=How Skype Used AI to Build Its Amazing New Language Translator {{!}} WIRED|magazine=Wired|access-date=14 June 2017|date=17 December 2014|last1=McMillan|first1=Robert|archive-date=8 June 2017|archive-url=https://web.archive.org/web/20170608062106/https://www.wired.com/2014/12/skype-used-ai-build-amazing-new-language-translator/|url-status=live}}</ref><ref name="Baidu">{{cite arXiv |eprint=1412.5567|last1=Hannun|first1=Awni|title=Deep Speech: Scaling up end-to-end speech recognition|last2=Case|first2=Carl|last3=Casper|first3=Jared|last4=Catanzaro|first4=Bryan|last5=Diamos|first5=Greg|last6=Elsen|first6=Erich|last7=Prenger|first7=Ryan|last8=Satheesh|first8=Sanjeev|last9=Sengupta|first9=Shubho|last10=Coates|first10=Adam|last11=Ng|first11=Andrew Y|class=cs.CL|year=2014}}</ref>
Large-scale automatic speech recognition is the first and most convincing successful case of deep learning in the recent history, embraced by both industry and academia across the board. Between 2010 and 2014, the two major conferences on signal processing and speech recognition, IEEE-ICASSP and Interspeech, have seen a large increase in the numbers of accepted papers in their respective annual conference papers on the topic of deep learning for speech recognition. More importantly, all major commercial speech recognition systems (e.g., Microsoft Cortana, Xbox, Skype Translator, Amazon Alexa, Google Now, Apple Siri, Baidu and iFlyTek voice search, and a range of Nuance speech products, etc.) are all based on deep learning methods.<ref name=BOOK2014 /><ref name="Wire">McMillan, R. "How Skype Used AI to Build Its Amazing New Language Translator", Wire, Dec. 2014.</ref><ref name="Baidu">Hannun et al. (2014) "Deep Speech: Scaling up end-to-end speech recognition", {{arxiv|1412.5567}}.</ref><ref>{{Cite web|url=http://research.microsoft.com/en-US/people/deng/ieee-icassp-plenary-2016-mar24-lideng-posted.pdf|title=Plenary presentation at ICASSP-2016|date=|website=|publisher=|access-date=}}</ref> See also the recent media interview with the CTO of Nuance Communications.<ref name="SPM2015">Ron Schneiderman (2015) "Accuracy, Apps Advance Speech Recognition --- Interviews with Vlad Sejnoha and Li Deng", IEEE Signal Processing Magazine, Jan, 2015.</ref>
 
=== Image recognition ===
{{Main|Computer vision}}
A common evaluation set for image classification is the [[MNIST database]] data set. MNIST is composed of handwritten digits and includes 60,000 training examples and 10,000 test examples. As with TIMIT, its small size allows multiple configurations to be tested. A comprehensive list of results on this set can be found in.<ref name="YANNMNIST">http://yann.lecun.com/exdb/mnist/.</ref> The current best result on MNIST is an error rate of 0.23%, achieved by Ciresan et al. in 2012.<ref name="CIRESAN2012">D. Ciresan, U. Meier, J. Schmidhuber., "Multi-column Deep Neural Networks for Image Classification," ''Technical Report No. IDSIA-04-12'', 2012.</ref>
[[File:Deep Learning in mussel farming.webm|thumb|Richard Green explains how deep learning is used with a [[Remotely operated underwater vehicle|remotely operated vehicle]] in [[Mussel#Aquaculture|mussel aquaculture]].]]
A common evaluation set for image classification is the [[MNIST database]] data set. MNIST is composed of handwritten digits and includes 60,000 training examples and 10,000 test examples. As with TIMIT, its small size lets users test multiple configurations. A comprehensive list of results on this set is available.<ref name="YANNMNIST">{{cite web|url=http://yann.lecun.com/exdb/mnist/.|title=MNIST handwritten digit database, Yann LeCun, Corinna Cortes and Chris Burges|website=yann.lecun.com|access-date=2014-01-28|archive-date=2014-01-13|archive-url=https://web.archive.org/web/20140113175237/http://yann.lecun.com/exdb/mnist/|url-status=live}}</ref>
 
Deep learning-based image recognition has become "superhuman", producing more accurate results than human contestants. This first occurred in 2011 in recognition of traffic signs, and in 2014, with recognition of human faces.<ref name=":7">{{Cite journal|last1=Cireşan|first1=Dan|last2=Meier|first2=Ueli|last3=Masci|first3=Jonathan|last4=Schmidhuber|first4=Jürgen|date=August 2012|title=Multi-column deep neural network for traffic sign classification|journal=Neural Networks|series=Selected Papers from IJCNN 2011|volume=32|pages=333–338|doi=10.1016/j.neunet.2012.02.023|pmid=22386783|citeseerx=10.1.1.226.8219}}</ref><ref name=surpass1>{{cite arXiv|title=Surpassing Human Level Face Recognition|author1=Chaochao Lu |author2= Xiaoou Tang |year=2014 |class=cs.CV |eprint=1404.3840 }}</ref>
According to LeCun,<ref name="lecun2016slides"/> in the early 2000s, in an industrial application CNNs already processed an estimated 10% to 20% of all the checks written in the US in the early 2000s.
Significant additional impact of deep learning in image or object recognition was felt in the years 2011–2012. Although CNNs trained by backpropagation had been around for decades,<ref name="LECUN1989"/> and GPU implementations of NNs for years,<ref name="jung2004"/> including CNNs,<ref name="chellapilla2006"/> fast implementations of CNNs with max-pooling on GPUs in the style of Dan Ciresan and colleagues<ref name="ciresan2011"/> were needed to make a dent in computer vision.<ref name="SCHIDHUB"/> In 2011, this approach achieved for the first time superhuman performance in a visual pattern recognition contest.<ref name="ciresan2011NN"/> Also in 2011, it won the ICDAR Chinese handwriting contest, and in May 2012, it won the ISBI image segmentation contest.<ref name="ciresan2012NIPS"/>
Until 2011, CNNs did not play a major role at computer vision conferences, but in June 2012, a paper by Dan Ciresan et al. at the leading conference CVPR<ref name="ciresan2011CVPR"/> showed how max-pooling CNNs on GPU can dramatically improve many vision benchmark records, sometimes with human-competitive or even superhuman performance. In October 2012, a similar system by Alex Krizhevsky in the team of Geoff Hinton<ref name="krizhevsky2012">
{{cite journal|last1=Krizhevsky|first1=Alex|last2=Sutskever|first2=Ilya|last3=Hinton|first3=Geoffry|title=ImageNet Classification with Deep Convolutional Neural Networks|journal=NIPS 2012: Neural Information Processing Systems, Lake Tahoe, Nevada|date=2012|url=https://www.cs.toronto.edu/~kriz/imagenet_classification_with_deep_convolutional.pdf}}
</ref> won the large-scale [[ImageNet competition]] by a significant margin over shallow machine learning methods. In November 2012, Ciresan et al.'s system also won the ICPR contest on analysis of large medical images for cancer detection, and in the following year also the MICCAI Grand Challenge on the same topic.<ref name="ciresan2013miccai">D. Ciresan, A. Giusti, L.M. Gambardella, J. Schmidhuber (2013). Mitosis Detection in Breast Cancer Histology Images using Deep Neural Networks. Proceedings MICCAI, 2013.</ref>
In 2013 and 2014, the error rate on the ImageNet task using deep learning was further reduced quickly, following a similar trend in large-scale speech recognition. Releases like the Wolfram Image Identification project continue to bring improvements in the technology to the public eye.<ref>{{Cite web|url=https://www.imageidentify.com/|title=The Wolfram Language Image Identification Project|website=www.imageidentify.com|access-date=2017-03-22}}</ref>
As in the ambitious moves from automatic speech recognition toward automatic speech translation and understanding, image classification has recently been extended to the more challenging task of automatic image captioning, in which deep learning (often as a combination of CNNs and LSTMs) is the essential underlying technology<ref name="1411.4555">Vinyals et al. (2014)."Show and Tell: A Neural Image Caption Generator," {{arxiv|1411.4555}}.</ref><ref name="1411.4952">Fang et al. (2014)."From Captions to Visual Concepts and Back," {{arxiv|1411.4952}}.</ref><ref name="1411.2539">Kiros et al. (2014). "Unifying Visual-Semantic Embeddings with Multimodal Neural Language Models," {{arxiv|1411.2539}}.</ref><ref>{{cite journal|last1=Zhong|first1=S.|last2=Liu|first2=Y.|last3=Liu|first3=Y.|title=Bilinear Deep Learning for Image Classification|journal=Proceedings of the 19th ACM International Conference on Multimedia|volume=11|pages=343–352}}</ref>
 
One example application is a car computer said to beDeep learning-trained with deep learning, which may enable carsvehicles tonow interpret 360° camera views.<ref>[http://www.technologyreview.com/news/533936/nvidia-demos-a-car-computer-trained-with-deep-learning/ Nvidia Demos a Car Computer Trained with "Deep Learning"] (6 January 2015-01-06), David Talbot, ''[[MIT Technology Review]]''</ref> Another example is the technology known as [[Facial Dysmorphology Novel Analysis|Facial Dysmorphology Novel Analysis (FDNA)]] used to analyze cases of human malformation connected to a large database of genetic syndromes.
 
=== Visual art processing ===
[[File:Jimmy Wales in France, with the style of Munch's "The Scream" applied using neural style transfer.jpg|thumb|164x164px|Visual art processing of Jimmy Wales in France, with the style of Munch's "[[The Scream]]" applied using neural style transfer]]
Closely related to the progress that has been made in image recognition is the increasing application of deep learning techniques to various visual art tasks. DNNs have proven themselves capable, for example, of
*identifying the style period of a given painting<ref name = art1/><ref name = art2/>
*[[Neural Style Transfer]]{{snd}} capturing the style of a given artwork and applying it in a visually pleasing manner to an arbitrary photograph or video<ref name = art1/><ref name = art2/>
*generating striking imagery based on random visual input fields.<ref name = art1 >{{cite journal |author1=G. W. Smith|author2=Frederic Fol Leymarie|date=10 April 2017|title=The Machine as Artist: An Introduction|journal=Arts|volume=6|issue=4|pages=5|doi=10.3390/arts6020005|doi-access=free}}</ref><ref name = art2>{{cite journal |author=Blaise Agüera y Arcas|date=29 September 2017|title=Art in the Age of Machine Intelligence|journal=Arts|volume=6|issue=4|pages=18|doi=10.3390/arts6040018|doi-access=free}}</ref>
 
=== Natural language processing ===
{{Main|Natural language processing}}
Neural networks have been used for implementing language models since the early 2000s.<ref name="gers2001" /> LSTM helped to improve machine translation and language modeling.<ref name="NIPS2014" /><ref name="vinyals2016" /><ref name="gillick2015" />
 
Other key techniques in this field are negative sampling<ref name="GoldbergLevy2014">{{cite arXiv|last1=Goldberg|first1=Yoav|last2=Levy|first2=Omar|title=word2vec Explained: Deriving Mikolov et al.'s Negative-Sampling Word-Embedding Method|eprint=1402.3722|class=cs.CL|year=2014}}</ref> and [[word embedding]]. Word embedding, such as ''[[word2vec]]'', can be thought of as a representational layer in a deep learning architecture that transforms an atomic word into a positional representation of the word relative to other words in the dataset; the position is represented as a point in a [[vector space]]. Using word embedding as an RNN input layer allows the network to parse sentences and phrases using an effective compositional vector grammar. A compositional vector grammar can be thought of as [[probabilistic context free grammar]] (PCFG) implemented by an RNN.<ref name="SocherManning2014">{{cite web|last1=Socher|first1=Richard|last2=Manning|first2=Christopher|title=Deep Learning for NLP|url=http://nlp.stanford.edu/courses/NAACL2013/NAACL2013-Socher-Manning-DeepLearning.pdf|access-date=26 October 2014|archive-date=6 July 2014|archive-url=https://web.archive.org/web/20140706040227/http://nlp.stanford.edu/courses/NAACL2013/NAACL2013-Socher-Manning-DeepLearning.pdf|url-status=live}}</ref> Recursive auto-encoders built atop word embeddings can assess sentence similarity and detect paraphrasing.<ref name="SocherManning2014" /> Deep neural architectures provide the best results for constituency parsing,<ref>{{Cite journal|url = http://aclweb.org/anthology/P/P13/P13-1045.pdf|title = Parsing With Compositional Vector Grammars|last1 = Socher|first1 = Richard|date = 2013|journal = Proceedings of the ACL 2013 Conference|last2 = Bauer|first2 = John|last3 = Manning|first3 = Christopher|last4 = Ng|first4 = Andrew|access-date = 2014-09-03|archive-date = 2014-11-27|archive-url = https://web.archive.org/web/20141127005912/http://www.aclweb.org/anthology/P/P13/P13-1045.pdf|url-status = live}}</ref> [[sentiment analysis]],<ref name=RDM_1>{{cite book| title=Proceedings of the 2013 Conference on Empirical Methods in Natural Language Processing| author1=Socher, R.| author2=Perelygin, A.| author3=Wu, J.| author4=Chuang, J.| author5=Manning, C.D.| author6=Ng, A.| author7=Potts, C.| chapter=Recursive Deep Models for Semantic Compositionality over a Sentiment Treebank| chapter-url=https://nlp.stanford.edu/~socherr/EMNLP2013_RNTN.pdf| publisher=Association for Computational Linguistics| date=October 2013| pages=1631–1642| doi=10.18653/v1/D13-1170| access-date=21 December 2023| url-status = live| archive-url=https://web.archive.org/web/20161228100300/http://nlp.stanford.edu/%7Esocherr/EMNLP2013_RNTN.pdf| archive-date=28 December 2016}}</ref> information retrieval,<ref>{{Cite journal| last1=Shen| first1=Yelong| last2=He| first2=Xiaodong| last3=Gao| first3=Jianfeng|last4=Deng|first4=Li|last5=Mesnil|first5=Gregoire|date=1 November 2014|title=A Latent Semantic Model with Convolutional-Pooling Structure for Information Retrieval|url=https://www.microsoft.com/en-us/research/publication/a-latent-semantic-model-with-convolutional-pooling-structure-for-information-retrieval/|journal=Microsoft Research|access-date=14 June 2017|archive-date=27 October 2017|archive-url=https://web.archive.org/web/20171027050418/https://www.microsoft.com/en-us/research/publication/a-latent-semantic-model-with-convolutional-pooling-structure-for-information-retrieval/|url-status=live}}</ref><ref>{{Cite journal|last1=Huang|first1=Po-Sen|last2=He|first2=Xiaodong|last3=Gao|first3=Jianfeng|last4=Deng|first4=Li|last5=Acero|first5=Alex|last6=Heck|first6=Larry|date=1 October 2013|title=Learning Deep Structured Semantic Models for Web Search using Clickthrough Data|url=https://www.microsoft.com/en-us/research/publication/learning-deep-structured-semantic-models-for-web-search-using-clickthrough-data/|journal=Microsoft Research|access-date=14 June 2017|archive-date=27 October 2017|archive-url=https://web.archive.org/web/20171027050414/https://www.microsoft.com/en-us/research/publication/learning-deep-structured-semantic-models-for-web-search-using-clickthrough-data/|url-status=live}}</ref> spoken language understanding,<ref name="IEEE-TASL2015">{{cite journal | last1 = Mesnil | first1 = G. | last2 = Dauphin | first2 = Y. | last3 = Yao | first3 = K. | last4 = Bengio | first4 = Y. | last5 = Deng | first5 = L. | last6 = Hakkani-Tur | first6 = D.|author6-link=Dilek Hakkani-Tür | last7 = He | first7 = X. | last8 = Heck | first8 = L. | last9 = Tur | first9 = G. | last10 = Yu | first10 = D. | last11 = Zweig | first11 = G. | s2cid = 1317136 | year = 2015 | title = Using recurrent neural networks for slot filling in spoken language understanding | journal = IEEE Transactions on Audio, Speech, and Language Processing | volume = 23 | issue = 3| pages = 530–539 | doi=10.1109/taslp.2014.2383614 | bibcode = 2015ITASL..23..530M }}</ref> machine translation,<ref name="NIPS2014">{{Cite journal|last1=Sutskever|first1=L.|last2=Vinyals|first2=O.|last3=Le|first3=Q.|date=2014|title=Sequence to Sequence Learning with Neural Networks|url=https://papers.nips.cc/paper/5346-sequence-to-sequence-learning-with-neural-networks.pdf|journal=Proc. NIPS|bibcode=2014arXiv1409.3215S|arxiv=1409.3215|access-date=2017-06-13|archive-date=2021-05-09|archive-url=https://web.archive.org/web/20210509123145/https://papers.nips.cc/paper/2014/file/a14ac55a4f27472c5d894ec1c3c743d2-Paper.pdf|url-status=live}}</ref><ref name="auto">{{Cite journal|last1=Gao|first1=Jianfeng|last2=He|first2=Xiaodong|last3=Yih|first3=Scott Wen-tau|last4=Deng|first4=Li|date=1 June 2014|title=Learning Continuous Phrase Representations for Translation Modeling|url=https://www.microsoft.com/en-us/research/publication/learning-continuous-phrase-representations-for-translation-modeling/|journal=Microsoft Research|access-date=14 June 2017|archive-date=27 October 2017|archive-url=https://web.archive.org/web/20171027050403/https://www.microsoft.com/en-us/research/publication/learning-continuous-phrase-representations-for-translation-modeling/|url-status=live}}</ref> contextual entity linking,<ref name="auto"/> writing style recognition,<ref name="BROC2017">{{Cite journal |doi = 10.1002/dac.3259|title = Authorship verification using deep belief network systems|journal = International Journal of Communication Systems|volume = 30|issue = 12|pages = e3259|year = 2017|last1 = Brocardo|first1 = Marcelo Luiz|last2 = Traore|first2 = Issa|last3 = Woungang|first3 = Isaac|last4 = Obaidat|first4 = Mohammad S.| s2cid=40745740 }}</ref> [[named-entity recognition]] (token classification),<ref>{{Cite journal |last1=Kariampuzha |first1=William |last2=Alyea |first2=Gioconda |last3=Qu |first3=Sue |last4=Sanjak |first4= Jaleal |last5=Mathé |first5=Ewy |last6=Sid |first6=Eric |last7= Chatelaine |first7=Haley |last8=Yadaw |first8=Arjun |last9=Xu |first9=Yanji |last10=Zhu |first10=Qian |date=2023 |title=Precision information extraction for rare disease epidemiology at scale |journal=Journal of Translational Medicine |language=en |volume=21 |issue=1 |page=157 |doi=10.1186/s12967-023-04011-y |pmid=36855134 |pmc=9972634 |doi-access=free }}</ref> text classification, and others.<ref>{{Cite news|url=https://www.microsoft.com/en-us/research/project/deep-learning-for-natural-language-processing-theory-and-practice-cikm2014-tutorial/|title=Deep Learning for Natural Language Processing: Theory and Practice (CIKM2014 Tutorial) - Microsoft Research|work=Microsoft Research|access-date=14 June 2017|archive-date=13 March 2017|archive-url=https://web.archive.org/web/20170313184253/https://www.microsoft.com/en-us/research/project/deep-learning-for-natural-language-processing-theory-and-practice-cikm2014-tutorial/|url-status=live}}</ref>
 
Recent developments generalize [[word embedding]] to [[sentence embedding]].
Neural networks have been used for implementing [[language model]]s since the early 2000s.<ref name="gers2001"/><ref name="BENGIO2003">Y. Bengio, R. Ducharme, P. Vincent, C. Jauvin., "A Neural Probabilistic Language Model," ''Journal of Machine Learning Research'' 3 (2003) 1137–1155, 2003.</ref>
[[Recurrent neural networks]], especially LSTM,<ref name=lstm/> are most appropriate for sequential data such as language.
LSTM helped to improve machine translation<ref name="NIPS2014"/> and Language Modeling.<ref name="vinyals2016"/><ref name="gillick2015"/> LSTM combined with CNNs also improved automatic image captioning<ref name="vinyals2015"/> and a plethora of other applications.<ref name="SCHIDHUB"/>
 
[[Google Translate]] (GT) uses a large end-to-end [[long short-term memory]] (LSTM) network.<ref name="GT_Turovsky_2016">{{cite web|url=https://blog.google/products/translate/found-translation-more-accurate-fluent-sentences-google-translate/|title=Found in translation: More accurate, fluent sentences in Google Translate|last=Turovsky|first=Barak|date=15 November 2016|website=The Keyword Google Blog|access-date=23 March 2017|archive-date=7 April 2017|archive-url=https://web.archive.org/web/20170407071226/https://blog.google/products/translate/found-translation-more-accurate-fluent-sentences-google-translate/|url-status=live}}</ref><ref name="googleblog_GNMT_2016">{{cite web|url=https://research.googleblog.com/2016/11/zero-shot-translation-with-googles.html|title=Zero-Shot Translation with Google's Multilingual Neural Machine Translation System|last1=Schuster|first1=Mike|last2=Johnson|first2=Melvin|date=22 November 2016|website=Google Research Blog|access-date=23 March 2017|last3=Thorat|first3=Nikhil|archive-date=10 July 2017|archive-url=https://web.archive.org/web/20170710183732/https://research.googleblog.com/2016/11/zero-shot-translation-with-googles.html|url-status=live}}</ref><ref name="GoogleTranslate">{{cite arXiv |eprint=1609.08144|last1=Wu|first1=Yonghui|title=Google's Neural Machine Translation System: Bridging the Gap between Human and Machine Translation|last2=Schuster|first2=Mike|last3=Chen|first3=Zhifeng|last4=Le|first4=Quoc V|last5=Norouzi|first5=Mohammad|last6=Macherey|first6=Wolfgang|last7=Krikun|first7=Maxim|last8=Cao|first8=Yuan|last9=Gao|first9=Qin|last10=Macherey|first10=Klaus|last11=Klingner|first11=Jeff|last12=Shah|first12=Apurva|last13=Johnson|first13=Melvin|last14=Liu|first14=Xiaobing|last15=Kaiser|first15=Łukasz|last16=Gouws|first16=Stephan|last17=Kato|first17=Yoshikiyo|last18=Kudo|first18=Taku|last19=Kazawa|first19=Hideto|last20=Stevens|first20=Keith|last21=Kurian|first21=George|last22=Patil|first22=Nishant|last23=Wang|first23=Wei|last24=Young|first24=Cliff|last25=Smith|first25=Jason|last26=Riesa|first26=Jason|last27=Rudnick|first27=Alex|last28=Vinyals|first28=Oriol|last29=Corrado|first29=Greg|last30=Hughes|first30=Macduff|display-authors=29|class=cs.CL|year=2016}}</ref><ref name="WiredGoogleTranslate">{{cite magazine |title=An Infusion of AI Makes Google Translate More Powerful Than Ever |first=Cade |last=Metz |magazine=[[Wired (magazine)|Wired]] |date=27 September 2016 |url=https://www.wired.com/2016/09/google-claims-ai-breakthrough-machine-translation/ |access-date=12 October 2017 |archive-date=8 November 2020 |archive-url=https://web.archive.org/web/20201108101324/https://www.wired.com/2016/09/google-claims-ai-breakthrough-machine-translation/ |url-status=live }}</ref> [[Google Neural Machine Translation|Google Neural Machine Translation (GNMT)]] uses an [[example-based machine translation]] method in which the system "learns from millions of examples".<ref name="googleblog_GNMT_2016" /> It translates "whole sentences at a time, rather than pieces". Google Translate supports over one hundred languages.<ref name="googleblog_GNMT_2016" /> The network encodes the "semantics of the sentence rather than simply memorizing phrase-to-phrase translations".<ref name="googleblog_GNMT_2016" /><ref name="Biotet">{{cite web|url=http://www-clips.imag.fr/geta/herve.blanchon/Pdfs/NLP-KE-10.pdf|title=MT on and for the Web|last1=Boitet|first1=Christian|last2=Blanchon|first2=Hervé|date=2010|access-date=1 December 2016|last3=Seligman|first3=Mark|last4=Bellynck|first4=Valérie|archive-date=29 March 2017|archive-url=https://web.archive.org/web/20170329125916/http://www-clips.imag.fr/geta/herve.blanchon/Pdfs/NLP-KE-10.pdf|url-status=dead}}</ref> GT uses English as an intermediate between most language pairs.<ref name="Biotet" />
Other key techniques in this field are [[negative sampling]]<ref name=GoldbergLevy2014>{{cite arXiv|last1=Goldberg|first1=Yoav|last2=Levy|first2=Omar|title=word2vec Explained: Deriving Mikolov et al.’s Negative-Sampling Word-Embedding Method|arxiv=1402.3722}}</ref> and [[word embedding]]. Word embedding, such as ''word2vec'', can be thought of as a representational layer in a deep learning architecture, that transforms an atomic word into a positional representation of the word relative to other words in the dataset; the position is represented as a point in a [[vector space]]. Using word embedding as an input layer to a recursive neural network (RNN) allows the training of the network to parse sentences and phrases using an effective ''compositional vector grammar''. A compositional vector grammar can be thought of as [[probabilistic context free grammar]] (PCFG) implemented by a recursive neural network.<ref name=SocherManning2014>{{cite web|last1=Socher|first1=Richard|last2=Manning|first2=Christopher|title=Deep Learning for NLP|url=http://nlp.stanford.edu/courses/NAACL2013/NAACL2013-Socher-Manning-DeepLearning.pdf|accessdate=26 October 2014}}</ref> Recursive auto-encoders built atop word embeddings have been trained to assess sentence similarity and detect paraphrasing.<ref name=SocherManning2014 /> Deep neural architectures have achieved state-of-the-art results in many natural language processing tasks such as [[Statistical parsing|constituency parsing]],<ref>{{Cite journal|url = http://aclweb.org/anthology/P/P13/P13-1045.pdf|title = Parsing With Compositional Vector Grammars|last = Socher|first = Richard|date = 2013|journal = Proceedings of the ACL 2013 conference|accessdate = |doi = |pmid = |last2 = Bauer|first2 = John|last3 = Manning|first3 = Christopher|last4 = Ng|first4 = Andrew}}</ref> [[sentiment analysis]],<ref>{{Cite journal|url = http://nlp.stanford.edu/~socherr/EMNLP2013_RNTN.pdf|title = Recursive Deep Models for Semantic Compositionality Over a Sentiment Treebank|last = Socher|first = Richard|date = 2013|journal = EMNLP 2013|accessdate = |doi = |pmid = }}</ref> information retrieval,<ref name="CIKM2014">Y. Shen, X. He, J. Gao, L. Deng, and G. Mesnil (2014) " A Latent Semantic Model with Convolutional-Pooling Structure for Information Retrieval," Proc. CIKM.</ref><ref name="CIKM2013">P. Huang, X. He, J. Gao, L. Deng, A. Acero, and L. Heck (2013) "Learning Deep Structured Semantic Models for Web Search using Clickthrough Data," Proc. CIKM.</ref> spoken language understanding,<ref name="IEEE-TASL2015">{{cite journal | last1 = Mesnil | first1 = G. | last2 = Dauphin | first2 = Y. | last3 = Yao | first3 = K. | last4 = Bengio | first4 = Y. | last5 = Deng | first5 = L. | last6 = Hakkani-Tur | first6 = D. | last7 = He | first7 = X. | last8 = Heck | first8 = L. | last9 = Tur | first9 = G. | last10 = Yu | first10 = D. | last11 = Zweig | first11 = G. | year = 2015 | title = Using recurrent neural networks for slot filling in spoken language understanding | url = | journal = IEEE Transactions on Audio, Speech, and Language Processing | volume = 23 | issue = 3| pages = 530–539 | doi=10.1109/taslp.2014.2383614}}</ref> machine translation,<ref name="NIPS2014">I. Sutskever, O. Vinyals, Q. Le (2014) "Sequence to Sequence Learning with Neural Networks," Proc. NIPS.</ref><ref name="ACL2014">J. Gao, X. He, W. Yih, and L. Deng(2014) "Learning Continuous Phrase Representations for Translation Modeling," Proc. ACL.</ref> contextual entity linking,<ref name="EMNLP2014">J. Gao, P. Pantel, M. Gamon, X. He, L. Deng (2014) "Modeling Interestingness with Deep Neural Networks," Proc. EMNLP.</ref> writing style recognition <ref name="BROC2017">Brocardo ML, Traore I, Woungang I, Obaidat MS. "[http://onlinelibrary.wiley.com/doi/10.1002/dac.3259/full Authorship verification using deep belief network systems]". Int J Commun Syst. 2017. doi:10.1002/dac.3259</ref> and others.<ref name="Tutorial2014">J. Gao, X. He, L. Deng (2014) "Deep Learning for Natural Language Processing: Theory and Practice (Tutorial)," CIKM.</ref>{{overcite|date=March 2017}}
 
=== Drug discovery and toxicology ===
{{For|more information|Drug discovery|Toxicology}}
The [[pharmaceutical industry]] faces the problem that a large percentage of candidate drugs fail to reach the market. These failures of [[chemical compounds]] are caused by insufficient efficacy on the [[Biological target|biomolecular target]] (on-target effect), undetected and undesired interactions with other [[biomolecules]] (off-target effects), or unanticipated [[cytotoxicity|toxic effects]].<ref name="ARROWSMITH2013">{{Cite journal
A large percentage of candidate drugs fail to win regulatory approval. These failures are caused by insufficient efficacy (on-target effect), undesired interactions (off-target effects), or unanticipated [[Toxicity|toxic effects]].<ref name="ARROWSMITH2013">{{Cite journal
| pmid = 23903212
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| year = 2013
| author1last1 = Arrowsmith
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| title = Trial watch: Phase II and phase III attrition rates 2011-2012
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| doi = 10.1038/nrd4090
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}}</ref><ref name="VERBIEST2015">{{Cite journal
| pmid = 25582842
| year = 2015
| author1last1 = Verbist
| first1 = B
| title = Using transcriptomics to guide lead optimization in drug discovery projects: Lessons learned from the QSTAR project
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| first10 = S
| doi = 10.1016/j.drudis.2014.12.014
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}}</ref> In 2012, a team led by George Dahl won the "Merck Molecular Activity Challenge" using multi-task deep neural networks to predict the biomolecular target of a compound.<ref name="MERCK2012">"Announcement of the winners of the Merck Molecular Activity Challenge" https://www.kaggle.com/c/MerckActivity/details/winners.</ref><ref name="DAHL2014">Dahl, G. E.; Jaitly, N.; & Salakhutdinov, R. (2014) "Multi-task Neural Networks for QSAR Predictions," ArXiv, 2014.</ref> In 2014, Sepp Hochreiter's group used Deep Learning to detect off-target and [[cytotoxicity|toxic effects]] of environmental chemicals in nutrients, household products and drugs and won the "Tox21 Data Challenge" of [[NIH]], [[FDA]] and [[National Center for Advancing Translational Sciences|NCATS]].<ref name="TOX21">"Toxicology in the 21st century Data Challenge" https://tripod.nih.gov/tox21/challenge/leaderboard.jsp</ref><ref name="TOX21Data">"NCATS Announces Tox21 Data Challenge Winners" http://www.ncats.nih.gov/news-and-events/features/tox21-challenge-winners.html</ref> These impressive successes show that deep learning may be superior to other [[virtual screening]] methods.<ref name="Unterthiner2014">Unterthiner, T.; Mayr, A.; Klambauer, G.; Steijaert, M.; Ceulemans, H.; Wegner, J. K.; & Hochreiter, S. (2014) [http://www.bioinf.jku.at/publications/2014/NIPS2014a.pdf "Deep Learning as an Opportunity in Virtual Screening"]. Workshop on Deep Learning and Representation Learning (NIPS2014).</ref><ref name="Unterthiner2015">Unterthiner, T.; Mayr, A.; Klambauer, G.; & Hochreiter, S. (2015) [http://arxiv.org/pdf/1503.01445v1 "Toxicity Prediction using Deep Learning"]. ArXiv, 2015.</ref> Researchers from [[Google]] and [[Stanford University|Stanford]] enhanced deep learning for drug discovery by combining data from a variety of sources.<ref name="Ramsudar2015">Ramsundar, B.; Kearnes, S.; Riley, P.; Webster, D.; Konerding, D.;& Pande, V. (2015) "Massively Multitask Networks for Drug Discovery". ArXiv, 2015.</ref> In 2015, Atomwise introduced AtomNet, the first deep learning neural networks for structure-based rational drug design.<ref>{{cite arXiv|title = AtomNet: A Deep Convolutional Neural Network for Bioactivity Prediction in Structure-based Drug Discovery|arxiv= 1510.02855|date = 2015-10-09|first = Izhar|last = Wallach|first2 = Michael|last2 = Dzamba|first3 = Abraham|last3 = Heifets}}</ref> Subsequently, AtomNet was used to predict novel candidate biomolecules for several disease targets, most notably treatments for the Ebola virus<ref>{{Cite web|title = Toronto startup has a faster way to discover effective medicines|url = http://www.theglobeandmail.com/report-on-business/small-business/starting-out/toronto-startup-has-a-faster-way-to-discover-effective-medicines/article25660419/|website = The Globe and Mail|accessdate = 2015-11-09}}</ref> and multiple sclerosis.<ref>{{Cite web|title = Startup Harnesses Supercomputers to Seek Cures|url = http://ww2.kqed.org/futureofyou/2015/05/27/startup-harnesses-supercomputers-to-seek-cures/|website = KQED Future of You|accessdate = 2015-11-09}}</ref><ref>{{cite web|url=http://www.theglobeandmail.com/report-on-business/small-business/starting-out/toronto-startup-has-a-faster-way-to-discover-effective-medicines/article25660419/%5D%20and%20multiple%20sclerosis%20%5B/|title=Toronto startup has a faster way to discover effective medicines|publisher=}}</ref>
| doi-access = free
| hdl = 1942/18723
| hdl-access = free
}}</ref> Research has explored use of deep learning to predict the [[biomolecular target]]s,<ref name="MERCK2012">{{Cite web |title=Merck Molecular Activity Challenge |url=https://kaggle.com/c/MerckActivity |url-status=live |archive-url=https://web.archive.org/web/20200716190808/https://www.kaggle.com/c/MerckActivity |archive-date=2020-07-16 |access-date=2020-07-16 |website=kaggle.com}}</ref><ref name=":5">{{Cite web |title=Multi-task Neural Networks for QSAR Predictions {{!}} Data Science Association |url=http://www.datascienceassn.org/content/multi-task-neural-networks-qsar-predictions |url-status=live |archive-url=https://web.archive.org/web/20170430142049/http://www.datascienceassn.org/content/multi-task-neural-networks-qsar-predictions |archive-date=30 April 2017 |access-date=14 June 2017 |website=www.datascienceassn.org}}</ref> [[off-target]]s, and [[Toxicity|toxic effects]] of environmental chemicals in nutrients, household products and drugs.<ref name="TOX21">"Toxicology in the 21st century Data Challenge"</ref><ref name="TOX21Data">{{cite web |title=NCATS Announces Tox21 Data Challenge Winners |url=https://tripod.nih.gov/tox21/challenge/leaderboard.jsp |url-status=live |archive-url=https://web.archive.org/web/20150908025122/https://tripod.nih.gov/tox21/challenge/leaderboard.jsp |archive-date=2015-09-08 |access-date=2015-03-05}}</ref><ref name=":11">{{cite web |title=NCATS Announces Tox21 Data Challenge Winners |url=http://www.ncats.nih.gov/news-and-events/features/tox21-challenge-winners.html |url-status=dead |archive-url=https://web.archive.org/web/20150228225709/http://www.ncats.nih.gov/news-and-events/features/tox21-challenge-winners.html |archive-date=28 February 2015 |access-date=5 March 2015}}</ref>
 
AtomNet is a deep learning system for structure-based [[Drug design|rational drug design]].<ref>{{cite arXiv|title = AtomNet: A Deep Convolutional Neural Network for Bioactivity Prediction in Structure-based Drug Discovery|eprint= 1510.02855|date = 9 October 2015|first1 = Izhar|last1 = Wallach|first2 = Michael|last2 = Dzamba|first3 = Abraham|last3 = Heifets|class= cs.LG}}</ref> AtomNet was used to predict novel candidate biomolecules for disease targets such as the [[Ebola virus]]<ref name="Toronto">{{Cite news |title = Toronto startup has a faster way to discover effective medicines |url = https://www.theglobeandmail.com/report-on-business/small-business/starting-out/toronto-startup-has-a-faster-way-to-discover-effective-medicines/article25660419/ |website = [[The Globe and Mail]] |access-date = 9 November 2015 |archive-date = 20 October 2015 |archive-url = https://web.archive.org/web/20151020040115/http://www.theglobeandmail.com/report-on-business/small-business/starting-out/toronto-startup-has-a-faster-way-to-discover-effective-medicines/article25660419/ |url-status = live }}</ref> and [[multiple sclerosis]].<ref>{{Cite web|title = Startup Harnesses Supercomputers to Seek Cures|url = http://ww2.kqed.org/futureofyou/2015/05/27/startup-harnesses-supercomputers-to-seek-cures/|website = KQED Future of You| date=27 May 2015 |access-date = 9 November 2015|archive-date = 24 December 2015|archive-url = https://web.archive.org/web/20151224104721/http://ww2.kqed.org/futureofyou/2015/05/27/startup-harnesses-supercomputers-to-seek-cures/|url-status = live}}</ref><ref name="Toronto" />
 
In 2017 [[graph neural network]]s were used for the first time to predict various properties of molecules in a large toxicology data set.<ref>{{cite arXiv|last1=Gilmer|first1=Justin|last2=Schoenholz|first2=Samuel S.|last3=Riley|first3=Patrick F.|last4=Vinyals|first4=Oriol|last5=Dahl|first5=George E.|date=2017-06-12|title=Neural Message Passing for Quantum Chemistry|class=cs.LG|eprint=1704.01212}}</ref> In 2019, generative neural networks were used to produce molecules that were validated experimentally all the way into mice.<ref>{{cite journal |last1=Zhavoronkov |first1=Alex|s2cid=201716327|date=2019|title=Deep learning enables rapid identification of potent DDR1 kinase inhibitors |journal=Nature Biotechnology |volume=37|issue=9|pages=1038–1040|doi=10.1038/s41587-019-0224-x |pmid=31477924}}</ref><ref>{{cite magazine |last1=Gregory |first1=Barber |title=A Molecule Designed By AI Exhibits 'Druglike' Qualities |url=https://www.wired.com/story/molecule-designed-ai-exhibits-druglike-qualities/ |magazine=Wired |access-date=2019-09-05 |archive-date=2020-04-30 |archive-url=https://web.archive.org/web/20200430143244/https://www.wired.com/story/molecule-designed-ai-exhibits-druglike-qualities/ |url-status=live }}</ref>
 
=== Customer relationship management ===
{{Main|Customer relationship management}}
Recently success has been reported with application of deep reinforcement learning in direct marketing settings, illustrating suitability of the method for [[Customer relationship management|CRM]] automation. A neural network was used to approximate the value of possible direct marketing actions over the customer state space, defined in terms of [[RFM (customer value)|RFM]] variables. The estimated value function was shown to have a natural interpretation as [[customer lifetime value]].<ref>Tkachenko, Yegor. Autonomous CRM Control via CLV Approximation with Deep Reinforcement Learning in Discrete and Continuous Action Space. (April 8, 2015). arXiv.org: http://arxiv.org/abs/1504.01840</ref>
[[Deep reinforcement learning]] has been used to approximate the value of possible [[direct marketing]] actions, defined in terms of [[RFM (customer value)|RFM]] variables. The estimated value function was shown to have a natural interpretation as [[customer lifetime value]].<ref>{{cite arXiv|last=Tkachenko |first=Yegor |title=Autonomous CRM Control via CLV Approximation with Deep Reinforcement Learning in Discrete and Continuous Action Space |date=8 April 2015 |eprint=1504.01840|class=cs.LG }}</ref>
 
=== Recommendation systems ===
{{Main|Recommender system}}
[[Recommendation systems]] have used deep learning to extract meaningful deep features for latent factor model for content-based recommendation for music.<ref>Van den Oord, Aaron, Sander Dieleman, and Benjamin Schrauwen. "Deep content-based music recommendation." Advances in Neural Information Processing Systems. 2013.</ref> Recently, a more general approach for learning user preferences from multiple domains using multiview deep learning has been introduced.<ref>Elkahky, Ali Mamdouh, Yang Song, and Xiaodong He. "A Multi-View Deep Learning Approach for Cross Domain User Modeling in Recommendation Systems." Proceedings of the 24th International Conference on World Wide Web. International World Wide Web Conferences Steering Committee, 2015.</ref> The model uses a hybrid collaborative and content-based approach and enhances recommendations in multiple tasks.
Recommendation systems have used deep learning to extract meaningful features for a latent factor model for content-based music and journal recommendations.<ref>{{Cite book|url=http://papers.nips.cc/paper/5004-deep-content-based-music-recommendation.pdf|title=Advances in Neural Information Processing Systems 26|last1=van den Oord|first1=Aaron|last2=Dieleman|first2=Sander|last3=Schrauwen|first3=Benjamin|date=2013|publisher=Curran Associates, Inc.|editor-last=Burges|editor-first=C. J. C.|pages=2643–2651|editor-last2=Bottou|editor-first2=L.|editor-last3=Welling|editor-first3=M.|editor-last4=Ghahramani|editor-first4=Z.|editor-last5=Weinberger|editor-first5=K. Q.|access-date=2017-06-14|archive-date=2017-05-16|archive-url=https://web.archive.org/web/20170516185259/http://papers.nips.cc/paper/5004-deep-content-based-music-recommendation.pdf|url-status=live}}</ref><ref>{{cite journal | last1 = Feng | first1 = X.Y. | last2 = Zhang | first2 = H. | last3 = Ren | first3 = Y.J. | last4 = Shang | first4 = P.H. | last5 = Zhu | first5 = Y. | last6 = Liang | first6 = Y.C. | last7 = Guan | first7 = R.C. | last8 = Xu | first8 = D. | year = 2019 | title = The Deep Learning–Based Recommender System "Pubmender" for Choosing a Biomedical Publication Venue: Development and Validation Study | journal = [[Journal of Medical Internet Research]] | volume = 21 | issue = 5| page = e12957 | doi = 10.2196/12957 | pmid = 31127715 | pmc = 6555124 | doi-access = free }}</ref> Multi-view deep learning has been applied for learning user preferences from multiple domains.<ref>{{Cite journal|last1=Elkahky|first1=Ali Mamdouh|last2=Song|first2=Yang|last3=He|first3=Xiaodong|date=1 May 2015|title=A Multi-View Deep Learning Approach for Cross Domain User Modeling in Recommendation Systems|url=https://www.microsoft.com/en-us/research/publication/a-multi-view-deep-learning-approach-for-cross-___domain-user-modeling-in-recommendation-systems/|journal=Microsoft Research|access-date=14 June 2017|archive-date=25 January 2018|archive-url=https://web.archive.org/web/20180125134534/https://www.microsoft.com/en-us/research/publication/a-multi-view-deep-learning-approach-for-cross-___domain-user-modeling-in-recommendation-systems/|url-status=live}}</ref> The model uses a hybrid collaborative and content-based approach and enhances recommendations in multiple tasks.
 
=== Biomedical informaticsBioinformatics ===
{{Main|Bioinformatics}}
Recently, a deep-learning approach based on an [[autoencoder]] [[artificial neural network]] has been used in [[bioinformatics]], to predict [[Gene Ontology]] annotations and gene-function relationships.<ref>{{cite journal|url=http://doi.acm.org/10.1145/2649387.2649442|title=Deep Autoencoder Neural Networks for Gene Ontology Annotation Predictions|first1=Davide|last1=Chicco|first2=Peter|last2=Sadowski|first3=Pierre|last3=Baldi|date=1 January 2014|publisher=ACM|pages=533–540|via=ACM Digital Library|doi=10.1145/2649387.2649442|journal=Proceedings of the 5th ACM Conference on Bioinformatics, Computational Biology, and Health Informatics - BCB '14}}</ref>
An [[autoencoder]] ANN was used in [[bioinformatics]], to predict [[Gene Ontology|gene ontology]] annotations and gene-function relationships.<ref>{{cite book|first1=Davide|last1=Chicco|first2=Peter|last2=Sadowski|first3=Pierre|last3=Baldi|title=Proceedings of the 5th ACM Conference on Bioinformatics, Computational Biology, and Health Informatics |chapter=Deep autoencoder neural networks for gene ontology annotation predictions |s2cid=207217210|date=1 January 2014|publisher=ACM|pages=533–540|doi=10.1145/2649387.2649442|isbn=9781450328944|hdl=11311/964622|url=http://dl.acm.org/citation.cfm?id=2649442|access-date=23 November 2015|archive-date=9 May 2021|archive-url=https://web.archive.org/web/20210509123140/https://dl.acm.org/doi/10.1145/2649387.2649442|url-status=live}}</ref>
 
In medical informatics, deep learning has also beenwas used into the health ___domain, including the prediction ofpredict sleep quality based on wearabledata datafrom wearables<ref>{{Cite journal|last=Sathyanarayana|first=Aarti|s2cid=3821594|date=1 January 2016-01-01|title=Sleep Quality Prediction From Wearable Data Using Deep Learning|url=http://doi.org/10.2196/mhealth.6562|journal=JMIR mHealth and uHealth|language=en|volume=4|issue=4|doi=10.2196/mhealth.6562|pmid=27815231|pmc=5116102|pages=e125 |doi-access=free }}</ref> and predictions of health complications from Electronic[[electronic Healthhealth Recordrecord]] data.<ref>{{Cite journal|lastlast1=Choi|firstfirst1=Edward|last2=Schuetz|first2=Andy|last3=Stewart|first3=Walter F.|last4=Sun|first4=Jimeng|date=2016-08-13 August 2016|title=Using recurrent neural network models for early detection of heart failure onset|url=http://jamia.oxfordjournals.org/content/early/2016/08/13/jamia.ocw112|journal=Journal of the American Medical Informatics Association|languagevolume=24|issue=en2|pages=ocw112361–370|doi=10.1093/jamia/ocw112|issn=1067-5027|pmid=27521897|pmc=5391725}}</ref>
 
Deep neural networks have shown unparalleled performance in [[Protein structure prediction|predicting protein structure]], according to the sequence of the amino acids that make it up. In 2020, [[AlphaFold]], a deep-learning based system, achieved a level of accuracy significantly higher than all previous computational methods.<ref>{{Cite web |title=DeepMind's protein-folding AI has solved a 50-year-old grand challenge of biology |url=https://www.technologyreview.com/2020/11/30/1012712/deepmind-protein-folding-ai-solved-biology-science-drugs-disease/ |access-date=2024-05-10 |website=MIT Technology Review |language=en}}</ref><ref>{{Cite web |last=Shead |first=Sam |date=2020-11-30 |title=DeepMind solves 50-year-old 'grand challenge' with protein folding A.I. |url=https://www.cnbc.com/2020/11/30/deepmind-solves-protein-folding-grand-challenge-with-alphafold-ai.html |access-date=2024-05-10 |website=CNBC |language=en}}</ref>
== Theories of the human brain ==
 
=== Deep Neural Network Estimations ===
Computational deep learning is closely related to a class of theories of [[brain development]] (specifically, neocortical development) proposed by [[cognitive neuroscientist]]s in the early 1990s.<ref name="UTGOFF">{{cite journal | last1 = Utgoff | first1 = P. E. | last2 = Stracuzzi | first2 = D. J. | year = 2002 | title = Many-layered learning | url = | journal = Neural Computation | volume = 14 | issue = | pages = 2497–2529 | doi=10.1162/08997660260293319}}</ref> An approachable summary of this work is Elman, et al.'s 1996 book "Rethinking Innateness"<ref name="ELMAN">J. Elman et al., "Rethinking Innateness," 1996.</ref> (see also: Shrager and Johnson;<ref name="SHRAGER">{{cite journal | last1 = Shrager | first1 = J. | last2 = Johnson | first2 = MH | year = 1996 | title = Dynamic plasticity influences the emergence of function in a simple cortical array | url = | journal = Neural Networks | volume = 9 | issue = 7| pages = 1119–1129 | doi=10.1016/0893-6080(96)00033-0}}</ref> Quartz and Sejnowski<ref name="QUARTZ">{{cite journal | last1 = Quartz | first1 = SR | last2 = Sejnowski | first2 = TJ | year = 1997 | title = The neural basis of cognitive development: A constructivist manifesto | url = | journal = Behavioral and Brain Sciences | volume = 20 | issue = 4| pages = 537–556 | doi=10.1017/s0140525x97001581}}</ref>). As these developmental theories were also instantiated in computational models, they are technical predecessors of purely computationally motivated deep learning models. These developmental models share the interesting property that various proposed learning dynamics in the brain (e.g., a wave of [[nerve growth factor]]) conspire to support the [[self-organization]] of just the sort of inter-related neural networks utilized in the later, purely computational deep learning models; and such computational neural networks seem analogous to a view of the brain's neocortex as a hierarchy of filters in which each layer captures some of the information in the operating environment, and then passes the remainder, as well as modified base signal, to other layers further up the hierarchy. This process yields a self-organizing stack of [[transducer]]s, well-tuned to their operating environment. As described in The [[New York Times]] in 1995: "...the infant's brain seems to organize itself under the influence of waves of so-called trophic-factors ... different regions of the brain become connected sequentially, with one layer of tissue maturing before another and so on until the whole brain is mature."<ref name="BLAKESLEE">S. Blakeslee., "In brain's early growth, timetable may be critical," ''The New York Times, Science Section'', pp. B5–B6, 1995.</ref>
Deep neural networks can be used to estimate the entropy of a [[stochastic process]] and called Neural Joint Entropy Estimator (NJEE).<ref name="SPB22">{{Cite journal |last1=Shalev |first1=Y. |last2=Painsky |first2=A. |last3=Ben-Gal |first3=I. |title=Neural Joint Entropy Estimation |journal=IEEE Transactions on Neural Networks and Learning Systems |language=en |date=2022 |volume=PP |issue=4 |pages=5488–5500 |url=https://www.iradbengal.sites.tau.ac.il/_files/ugd/901879_d51bc0a620734585b5d3154488b3ae84.pdf |doi=10.1109/TNNLS.2022.3204919 |pmid=36155469 |arxiv=2012.11197 |s2cid=229339809 }}</ref> Such an estimation provides insights on the effects of input [[random variables]] on an independent [[random variable]]. Practically, the DNN is trained as a [[Classifier (machine learning)|classifier]] that maps an input [[Vector (mathematics and physics)|vector]] or [[Matrix (mathematics)|matrix]] X to an output [[probability distribution]] over the possible classes of random variable Y, given input X. For example, in [[image classification]] tasks, the NJEE maps a vector of [[pixels]]' color values to probabilities over possible image classes. In practice, the probability distribution of Y is obtained by a [[Softmax]] layer with number of nodes that is equal to the [[alphabet]] size of Y. NJEE uses continuously differentiable [[activation function]]s, such that the conditions for the [[universal approximation theorem]] holds. It is shown that this method provides a strongly [[consistent estimator]] and outperforms other methods in case of large alphabet sizes.<ref name="SPB22" />
 
=== Medical image analysis ===
The importance of deep learning with respect to the evolution and development of human [[cognition]] did not escape the attention of these researchers. One aspect of human development that distinguishes us from our nearest primate neighbors may be changes in the timing of development.<ref name="BUFILL">{BUFILL} E. Bufill, J. Agusti, R. Blesa., "Human neoteny revisited: The case of synaptic plasticity," ''American Journal of Human Biology'', 23 (6), pp. 729–739, 2011.</ref> Among [[primate]]s, the human brain remains relatively plastic until late in the post-natal period, whereas the brains of our closest relatives are more completely formed by birth. Thus, humans have greater access to the complex experiences afforded by being out in the world during the most formative period of brain development. This may enable us to "tune in" to rapidly changing features of the environment that other animals, more constrained by evolutionary structuring of their brains, are unable to take account of. To the extent that these changes are reflected in similar timing changes in hypothesized wave of cortical development, they may also lead to changes in the extraction of information from the stimulus environment during the early self-organization of the brain. Of course, along with this flexibility comes an extended period of immaturity, during which we are dependent upon our caretakers and our community for both support and training. The theory of deep learning therefore sees the coevolution of culture and cognition as a fundamental condition of human evolution.<ref name="SHRAGER2">J. Shrager and M. H. Johnson., "Timing in the development of cortical function: A computational approach," ''In B. Julesz and I. Kovacs (Eds.), Maturational windows and adult cortical plasticity'', 1995.</ref>
Deep learning has been shown to produce competitive results in medical application such as cancer cell classification, lesion detection, organ segmentation and image enhancement.<ref>{{Cite journal|last1=Litjens|first1=Geert|last2=Kooi|first2=Thijs|last3=Bejnordi|first3=Babak Ehteshami|last4=Setio|first4=Arnaud Arindra Adiyoso|last5=Ciompi|first5=Francesco|last6=Ghafoorian|first6=Mohsen|last7=van der Laak|first7=Jeroen A.W.M.|last8=van Ginneken|first8=Bram|last9=Sánchez|first9=Clara I.|s2cid=2088679|date=December 2017|title=A survey on deep learning in medical image analysis|journal=Medical Image Analysis|volume=42|pages=60–88|doi=10.1016/j.media.2017.07.005|pmid=28778026|arxiv=1702.05747|bibcode=2017arXiv170205747L}}</ref><ref>{{Cite book|doi=10.1109/ICCVW.2017.18|isbn=9781538610343|chapter=Deep Convolutional Neural Networks for Detecting Cellular Changes Due to Malignancy|title=2017 IEEE International Conference on Computer Vision Workshops (ICCVW)|pages=82–89|year=2017|last1=Forslid|first1=Gustav|last2=Wieslander|first2=Hakan|last3=Bengtsson|first3=Ewert|last4=Wahlby|first4=Carolina|last5=Hirsch|first5=Jan-Michael|last6=Stark|first6=Christina Runow|last7=Sadanandan|first7=Sajith Kecheril|s2cid=4728736|chapter-url=http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-326160|access-date=2019-11-12|archive-date=2021-05-09|archive-url=https://web.archive.org/web/20210509123157/https://d1bxh8uas1mnw7.cloudfront.net/assets/embed.js|url-status=live}}</ref> Modern deep learning tools demonstrate the high accuracy of detecting various diseases and the helpfulness of their use by specialists to improve the diagnosis efficiency.<ref>{{Cite journal |last1=Dong |first1=Xin |last2=Zhou |first2=Yizhao |last3=Wang |first3=Lantian |last4=Peng |first4=Jingfeng |last5=Lou |first5=Yanbo |last6=Fan |first6=Yiqun |date=2020 |title=Liver Cancer Detection Using Hybridized Fully Convolutional Neural Network Based on Deep Learning Framework |journal=IEEE Access |volume=8 |pages=129889–129898 |doi=10.1109/ACCESS.2020.3006362 |bibcode=2020IEEEA...8l9889D |s2cid=220733699 |issn=2169-3536|doi-access=free }}</ref><ref>{{Cite journal |last1=Lyakhov |first1=Pavel Alekseevich |last2=Lyakhova |first2=Ulyana Alekseevna |last3=Nagornov |first3=Nikolay Nikolaevich |date=2022-04-03 |title=System for the Recognizing of Pigmented Skin Lesions with Fusion and Analysis of Heterogeneous Data Based on a Multimodal Neural Network |journal=Cancers |language=en |volume=14 |issue=7 |pages=1819 |doi=10.3390/cancers14071819 |pmid=35406591 |pmc=8997449 |issn=2072-6694|doi-access=free }}</ref>
 
=== CommercialMobile activitiesadvertising ===
Finding the appropriate mobile audience for [[mobile advertising]] is always challenging, since many data points must be considered and analyzed before a target segment can be created and used in ad serving by any ad server.<ref>{{cite book |doi=10.1109/CSCITA.2017.8066548 |isbn=978-1-5090-4381-1|chapter=Predicting the popularity of instagram posts for a lifestyle magazine using deep learning|title=2017 2nd International Conference on Communication Systems, Computing and IT Applications (CSCITA)|pages=174–177|year=2017|last1=De|first1=Shaunak|last2=Maity|first2=Abhishek|last3=Goel|first3=Vritti|last4=Shitole|first4=Sanjay|last5=Bhattacharya|first5=Avik|s2cid=35350962}}</ref> Deep learning has been used to interpret large, many-dimensioned advertising datasets. Many data points are collected during the request/serve/click internet advertising cycle. This information can form the basis of machine learning to improve ad selection.
Deep learning is often presented as a step towards realising [[Artificial general intelligence|strong AI]]<ref name="HERN2013">D. Hernandez., "The Man Behind the Google Brain: Andrew Ng and the Quest for the New AI," ''http://www.wired.com/wiredenterprise/2013/05/neuro-artificial-intelligence/all/. Wired'', 10 May 2013.</ref> and thus many organizations have become interested in its use for particular applications. In December 2013, [[Facebook]] hired [[Yann LeCun]] to head its new [[artificial intelligence]] (AI) lab that was to have operations in California, London, and New York. The AI lab will develop deep learning techniques to help Facebook do tasks such as [[Automatic image annotation|automatically tagging uploaded pictures]] with the names of the people in them.<ref name="METZ2013">C. Metz., "Facebook's 'Deep Learning' Guru Reveals the Future of AI," ''http://www.wired.com/wiredenterprise/2013/12/facebook-yann-lecun-qa/. Wired'', 12 December 2013.</ref> Late in 2014, Facebook also hired [[Vladimir Vapnik]], a main developer of the Vapnik–Chervonenkis theory of statistical learning, and co-inventor of the [[support vector machine]] method.<ref name="Vapnik2014">V. Vapnik., [https://research.facebook.com/researchers/1566384816909948/vladimir-vapnik/ "research.facebook.com"] .</ref>
 
=== Image restoration ===
In 2014, Google also bought [[DeepMind Technologies]], a British start-up that developed a system capable of learning how to play [[Atari]] video games using only raw pixels as data input. In 2015 they demonstrated [[AlphaGo]] system which achieved one of the long-standing "grand challenges" of AI by learning the game of [[Go (game)|Go]] well enough to beat a human professional Go player.<ref>{{Cite web|title = Google AI algorithm masters ancient game of Go|url = http://www.nature.com/news/google-ai-algorithm-masters-ancient-game-of-go-1.19234|website = Nature News & Comment|access-date = 2016-01-30}}</ref><ref>{{Cite journal|title = Mastering the game of Go with deep neural networks and tree search|url = http://www.nature.com/nature/journal/v529/n7587/full/nature16961.html|journal = Nature|date = 2016-01-28|issn = 0028-0836|pages = 484–489|volume = 529|issue = 7587|doi = 10.1038/nature16961|first = David|last = Silver|first2 = Aja|last2 = Huang|first3 = Chris J.|last3 = Maddison|first4 = Arthur|last4 = Guez|first5 = Laurent|last5 = Sifre|first6 = George|last6 = van den Driessche|first7 = Julian|last7 = Schrittwieser|first8 = Ioannis|last8 = Antonoglou|first9 = Veda|last9 = Panneershelvam|pmid=26819042}}</ref><ref>{{Cite web|title = A Google DeepMind Algorithm Uses Deep Learning and More to Master the Game of Go {{!}} MIT Technology Review|url = http://www.technologyreview.com/news/546066/googles-ai-masters-the-game-of-go-a-decade-earlier-than-expected/|website = MIT Technology Review|access-date = 2016-01-30}}</ref>
Deep learning has been successfully applied to [[inverse problems]] such as [[denoising]], [[super-resolution]], [[inpainting]], and [[film colorization]].<ref>{{Cite news|url=https://blog.floydhub.com/colorizing-and-restoring-old-images-with-deep-learning/|title=Colorizing and Restoring Old Images with Deep Learning|date=13 November 2018|website=FloydHub Blog|language=en|access-date=11 October 2019|archive-date=11 October 2019|archive-url=https://web.archive.org/web/20191011162814/https://blog.floydhub.com/colorizing-and-restoring-old-images-with-deep-learning/|url-status=live}}</ref> These applications include learning methods such as "Shrinkage Fields for Effective Image Restoration"<ref>{{cite conference |url= http://research.uweschmidt.org/pubs/cvpr14schmidt.pdf |first1= Uwe |last1= Schmidt |first2= Stefan |last2= Roth |conference= Computer Vision and Pattern Recognition (CVPR), 2014 IEEE Conference on |title= Shrinkage Fields for Effective Image Restoration |access-date= 2018-01-01 |archive-date= 2018-01-02 |archive-url= https://web.archive.org/web/20180102013217/http://research.uweschmidt.org/pubs/cvpr14schmidt.pdf |url-status= live }}</ref> which trains on an image dataset, and [[Deep Image Prior]], which trains on the image that needs restoration.
 
=== Financial fraud detection ===
In 2015, [[Blippar]] demonstrated a new mobile [[augmented reality]] application that makes use of deep learning to recognize objects in real time.<ref>{{Cite web|title=Blippar Demonstrates New Real-Time Augmented Reality App|url=http://techcrunch.com/2015/12/08/blippar-demonstrates-new-real-time-augmented-reality-app/|website=TechCrunch}}</ref>
Deep learning is being successfully applied to financial [[fraud detection]], tax evasion detection,<ref>{{cite journal
|first1=Christos |last1=Kleanthous
|first2=Sotirios |last2=Chatzis
|title=Gated Mixture Variational Autoencoders for Value Added Tax audit case selection
|journal=Knowledge-Based Systems
|volume=188
|year=2020
|article-number=105048
|doi=10.1016/j.knosys.2019.105048
|s2cid=204092079
}}</ref> and anti-money laundering.<ref>{{cite journal
|first=Tomasz
|last=Czech
|title=Deep learning: the next frontier for money laundering detection
|url=https://www.globalbankingandfinance.com/deep-learning-the-next-frontier-for-money-laundering-detection/
|journal=Global Banking and Finance Review
|date=28 June 2018
|access-date=2018-07-15
|archive-date=2018-11-16
|archive-url=https://web.archive.org/web/20181116082711/https://www.globalbankingandfinance.com/deep-learning-the-next-frontier-for-money-laundering-detection/
|url-status=live
}}</ref>
 
=== Materials science ===
In November 2023, researchers at [[Google DeepMind]] and [[Lawrence Berkeley National Laboratory]] announced that they had developed an AI system known as GNoME. This system has contributed to [[materials science]] by discovering over 2 million new materials within a relatively short timeframe. GNoME employs deep learning techniques to efficiently explore potential material structures, achieving a significant increase in the identification of stable inorganic [[crystal structure]]s. The system's predictions were validated through autonomous robotic experiments, demonstrating a noteworthy success rate of 71%. The data of newly discovered materials is publicly available through the [[Materials Project]] database, offering researchers the opportunity to identify materials with desired properties for various applications. This development has implications for the future of scientific discovery and the integration of AI in material science research, potentially expediting material innovation and reducing costs in product development. The use of AI and deep learning suggests the possibility of minimizing or eliminating manual lab experiments and allowing scientists to focus more on the design and analysis of unique compounds.<ref>{{Cite web |last=Nuñez |first=Michael |date=2023-11-29 |title=Google DeepMind's materials AI has already discovered 2.2 million new crystals |url=https://venturebeat.com/ai/google-deepminds-materials-ai-has-already-discovered-2-2-million-new-crystals/ |access-date=2023-12-19 |website=VentureBeat |language=en-US}}</ref><ref>{{Cite journal |last1=Merchant |first1=Amil |last2=Batzner |first2=Simon |last3=Schoenholz |first3=Samuel S. |last4=Aykol |first4=Muratahan |last5=Cheon |first5=Gowoon |last6=Cubuk |first6=Ekin Dogus |date=December 2023 |title=Scaling deep learning for materials discovery |journal=Nature |language=en |volume=624 |issue=7990 |pages=80–85 |doi=10.1038/s41586-023-06735-9 |issn=1476-4687|doi-access=free |pmid=38030720 |pmc=10700131 |bibcode=2023Natur.624...80M }}</ref><ref>{{Cite journal |last=Peplow |first=Mark |date=2023-11-29 |title=Google AI and robots join forces to build new materials |url=https://www.nature.com/articles/d41586-023-03745-5 |journal=Nature |language=en |doi=10.1038/d41586-023-03745-5|pmid=38030771 |s2cid=265503872 }}</ref>
 
=== Military ===
 
The United States Department of Defense applied deep learning to train robots in new tasks through observation.<ref name=":12">{{Cite web|url=https://www.eurekalert.org/pub_releases/2018-02/uarl-ard020218.php|title=Army researchers develop new algorithms to train robots|website=EurekAlert!|access-date=29 August 2018|archive-date=28 August 2018|archive-url=https://web.archive.org/web/20180828035608/https://www.eurekalert.org/pub_releases/2018-02/uarl-ard020218.php|url-status=live}}</ref>
 
=== Partial differential equations ===
Physics informed neural networks have been used to solve [[partial differential equation]]s in both forward and inverse problems in a data driven manner.<ref>{{Cite journal|last1=Raissi|first1=M.|last2=Perdikaris|first2=P.|last3=Karniadakis|first3=G. E.|date=2019-02-01|title=Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations|journal=Journal of Computational Physics|language=en|volume=378|pages=686–707|doi=10.1016/j.jcp.2018.10.045|bibcode=2019JCoPh.378..686R|osti=1595805|s2cid=57379996|issn=0021-9991|doi-access=free}}</ref> One example is the reconstructing fluid flow governed by the [[Navier–Stokes equations|Navier-Stokes equations]]. Using physics informed neural networks does not require the often expensive mesh generation that conventional [[Computational fluid dynamics|CFD]] methods rely on.<ref>{{Cite journal|last1=Mao|first1=Zhiping|last2=Jagtap|first2=Ameya D.|last3=Karniadakis|first3=George Em|date=2020-03-01|title=Physics-informed neural networks for high-speed flows|journal=Computer Methods in Applied Mechanics and Engineering|language=en|volume=360|article-number=112789|doi=10.1016/j.cma.2019.112789|bibcode=2020CMAME.360k2789M|s2cid=212755458|issn=0045-7825|doi-access=free}}</ref><ref>{{Cite journal|last1=Raissi|first1=Maziar|last2=Yazdani|first2=Alireza|last3=Karniadakis|first3=George Em|date=2020-02-28|title=Hidden fluid mechanics: Learning velocity and pressure fields from flow visualizations|journal=Science|volume=367|issue=6481|pages=1026–1030|doi=10.1126/science.aaw4741|pmc=7219083|pmid=32001523|bibcode=2020Sci...367.1026R}}</ref>
 
=== Deep backward stochastic differential equation method ===
[[Deep backward stochastic differential equation method]] is a numerical method that combines deep learning with [[Backward stochastic differential equation]] (BSDE). This method is particularly useful for solving high-dimensional problems in financial mathematics. By leveraging the powerful function approximation capabilities of [[deep neural networks]], deep BSDE addresses the computational challenges faced by traditional numerical methods in high-dimensional settings. Specifically, traditional methods like finite difference methods or Monte Carlo simulations often struggle with the curse of dimensionality, where computational cost increases exponentially with the number of dimensions. Deep BSDE methods, however, employ deep neural networks to approximate solutions of high-dimensional partial differential equations (PDEs), effectively reducing the computational burden.<ref name="Han2018">{{cite journal | last1=Han | first1=J. | last2=Jentzen | first2=A. | last3=E | first3=W. | title=Solving high-dimensional partial differential equations using deep learning | journal=Proceedings of the National Academy of Sciences | volume=115 | issue=34 | pages=8505–8510 | year=2018 | doi=10.1073/pnas.1718942115 | doi-access=free | pmid=30082389 | pmc=6112690 | arxiv=1707.02568 | bibcode=2018PNAS..115.8505H }}</ref>
 
In addition, the integration of [[Physics-informed neural networks]] (PINNs) into the deep BSDE framework enhances its capability by embedding the underlying physical laws directly into the neural network architecture. This ensures that the solutions not only fit the data but also adhere to the governing stochastic differential equations. PINNs leverage the power of deep learning while respecting the constraints imposed by the physical models, resulting in more accurate and reliable solutions for financial mathematics problems.
 
=== Image reconstruction ===
Image reconstruction is the reconstruction of the underlying images from the image-related measurements. Several works showed the better and superior performance of the deep learning methods compared to analytical methods for various applications, e.g., spectral imaging <ref>{{Cite journal |last1=Oktem |first1=Figen S. |last2=Kar |first2=Oğuzhan Fatih |last3=Bezek |first3=Can Deniz |last4=Kamalabadi |first4=Farzad |date=2021 |title=High-Resolution Multi-Spectral Imaging With Diffractive Lenses and Learned Reconstruction |journal=IEEE Transactions on Computational Imaging |volume=7 |pages=489–504 |doi=10.1109/TCI.2021.3075349 |arxiv=2008.11625 |bibcode=2021ITCI....7..489O |s2cid=235340737 |issn=2333-9403}}</ref> and ultrasound imaging.<ref>{{Cite journal |last1=Bernhardt |first1=Melanie |last2=Vishnevskiy |first2=Valery |last3=Rau |first3=Richard |last4=Goksel |first4=Orcun |date=December 2020 |title=Training Variational Networks With Multidomain Simulations: Speed-of-Sound Image Reconstruction |journal=IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control |volume=67 |issue=12 |pages=2584–2594 |doi=10.1109/TUFFC.2020.3010186 |pmid=32746211 |arxiv=2006.14395 |bibcode=2020ITUFF..67.2584B |s2cid=220055785 |issn=1525-8955}}</ref>
 
=== Weather prediction ===
Traditional weather prediction systems solve a very complex system of partial differential equations. GraphCast is a deep learning based model, trained on a long history of weather data to predict how weather patterns change over time. It is able to predict weather conditions for up to 10 days globally, at a very detailed level, and in under a minute, with precision similar to state of the art systems.<ref>{{Cite journal |last1=Lam |first1=Remi |last2=Sanchez-Gonzalez |first2=Alvaro |last3=Willson |first3=Matthew |last4=Wirnsberger |first4=Peter |last5=Fortunato |first5=Meire |last6=Alet |first6=Ferran |last7=Ravuri |first7=Suman |last8=Ewalds |first8=Timo |last9=Eaton-Rosen |first9=Zach |last10=Hu |first10=Weihua |last11=Merose |first11=Alexander |last12=Hoyer |first12=Stephan |last13=Holland |first13=George |last14=Vinyals |first14=Oriol |last15=Stott |first15=Jacklynn |date=2023-12-22 |title=Learning skillful medium-range global weather forecasting |journal=Science |language=en |volume=382 |issue=6677 |pages=1416–1421 |doi=10.1126/science.adi2336 |issn=0036-8075|doi-access=free |pmid=37962497 |arxiv=2212.12794 |bibcode=2023Sci...382.1416L }}</ref><ref>{{Cite web |last=Sivakumar |first=Ramakrishnan |date=2023-11-27 |title=GraphCast: A breakthrough in Weather Forecasting |url=https://ramkrishna2910.medium.com/graphcast-a-breakthrough-in-weather-forecasting-d70fae9ac365 |access-date=2024-05-19 |website=Medium |language=en}}</ref>
 
=== Epigenetic clock ===
{{Main|Epigenetic clock}}
 
An epigenetic clock is a [[Biomarkers of aging|biochemical test]] that can be used to measure age. Galkin et al. used deep neural networks to train an epigenetic aging clock of unprecedented accuracy using >6,000 blood samples.<ref>{{cite journal | last1 = Galkin | first1 = F. | last2 = Mamoshina | first2 = P. | last3 = Kochetov | first3 = K. | last4 = Sidorenko | first4 = D. | last5 = Zhavoronkov | first5 = A. | year = 2020 | title = DeepMAge: A Methylation Aging Clock Developed with Deep Learning | journal = Aging and Disease | doi = 10.14336/AD | doi-access = free }}</ref> The clock uses information from 1000 [[CpG site]]s and predicts people with certain conditions older than healthy controls: [[Inflammatory bowel disease|IBD]], [[frontotemporal dementia]], [[ovarian cancer]], [[obesity]]. The aging clock was planned to be released for public use in 2021 by an [[Insilico Medicine]] spinoff company Deep Longevity.
 
== Relation to human cognitive and brain development ==
Deep learning is closely related to a class of theories of [[brain development]] (specifically, neocortical development) proposed by [[cognitive neuroscientist]]s in the early 1990s.<ref name="UTGOFF">{{cite journal | last1 = Utgoff | first1 = P. E. | last2 = Stracuzzi | first2 = D. J. | s2cid = 1119517 | year = 2002 | title = Many-layered learning | journal = Neural Computation | volume = 14 | issue = 10| pages = 2497–2529 | doi=10.1162/08997660260293319| pmid = 12396572 }}</ref><ref name="ELMAN">{{cite book|url={{google books |plainurl=y |id=vELaRu_MrwoC}}|title=Rethinking Innateness: A Connectionist Perspective on Development|last=Elman|first=Jeffrey L.|publisher=MIT Press|year=1998|isbn=978-0-262-55030-7}}</ref><ref name="SHRAGER">{{cite journal | last1 = Shrager | first1 = J. | last2 = Johnson | first2 = MH | year = 1996 | title = Dynamic plasticity influences the emergence of function in a simple cortical array | journal = Neural Networks | volume = 9 | issue = 7| pages = 1119–1129 | doi=10.1016/0893-6080(96)00033-0| pmid = 12662587 }}</ref><ref name="QUARTZ">{{cite journal | last1 = Quartz | first1 = SR | last2 = Sejnowski | first2 = TJ | year = 1997 | title = The neural basis of cognitive development: A constructivist manifesto | journal = Behavioral and Brain Sciences | volume = 20 | issue = 4| pages = 537–556 | doi=10.1017/s0140525x97001581| pmid = 10097006 | citeseerx = 10.1.1.41.7854 | s2cid = 5818342 }}</ref> These developmental theories were instantiated in computational models, making them predecessors of deep learning systems. These developmental models share the property that various proposed learning dynamics in the brain (e.g., a wave of [[nerve growth factor]]) support the [[self-organization]] somewhat analogous to the neural networks utilized in deep learning models. Like the [[neocortex]], neural networks employ a hierarchy of layered filters in which each layer considers information from a prior layer (or the operating environment), and then passes its output (and possibly the original input), to other layers. This process yields a self-organizing stack of [[transducer]]s, well-tuned to their operating environment. A 1995 description stated, "...the infant's brain seems to organize itself under the influence of waves of so-called trophic-factors ... different regions of the brain become connected sequentially, with one layer of tissue maturing before another and so on until the whole brain is mature".<ref name="BLAKESLEE">S. Blakeslee, "In brain's early growth, timetable may be critical", ''The New York Times, Science Section'', pp. B5–B6, 1995.</ref>
 
A variety of approaches have been used to investigate the plausibility of deep learning models from a neurobiological perspective. On the one hand, several variants of the [[backpropagation]] algorithm have been proposed in order to increase its processing realism.<ref>{{Cite journal|last1=Mazzoni|first1=P.|last2=Andersen|first2=R. A.|last3=Jordan|first3=M. I.|date=15 May 1991|title=A more biologically plausible learning rule for neural networks.|journal=Proceedings of the National Academy of Sciences|volume=88|issue=10|pages=4433–4437|doi=10.1073/pnas.88.10.4433|issn=0027-8424|pmid=1903542|pmc=51674|bibcode=1991PNAS...88.4433M|doi-access=free}}</ref><ref>{{Cite journal|last=O'Reilly|first=Randall C.|s2cid=2376781|date=1 July 1996|title=Biologically Plausible Error-Driven Learning Using Local Activation Differences: The Generalized Recirculation Algorithm|journal=Neural Computation|volume=8|issue=5|pages=895–938|doi=10.1162/neco.1996.8.5.895|issn=0899-7667}}</ref> Other researchers have argued that unsupervised forms of deep learning, such as those based on hierarchical [[generative model]]s and [[deep belief network]]s, may be closer to biological reality.<ref>{{Cite journal|last1=Testolin|first1=Alberto|last2=Zorzi|first2=Marco|s2cid=9868901|date=2016|title=Probabilistic Models and Generative Neural Networks: Towards an Unified Framework for Modeling Normal and Impaired Neurocognitive Functions|journal=Frontiers in Computational Neuroscience|volume=10|pages=73|doi=10.3389/fncom.2016.00073|pmid=27468262|pmc=4943066|issn=1662-5188|doi-access=free}}</ref><ref>{{Cite journal|last1=Testolin|first1=Alberto|last2=Stoianov|first2=Ivilin|last3=Zorzi|first3=Marco|s2cid=24504018|date=September 2017|title=Letter perception emerges from unsupervised deep learning and recycling of natural image features|journal=Nature Human Behaviour|volume=1|issue=9|pages=657–664|doi=10.1038/s41562-017-0186-2|pmid=31024135|issn=2397-3374}}</ref> In this respect, generative neural network models have been related to neurobiological evidence about sampling-based processing in the cerebral cortex.<ref>{{Cite journal|last1=Buesing|first1=Lars|last2=Bill|first2=Johannes|last3=Nessler|first3=Bernhard|last4=Maass|first4=Wolfgang|s2cid=7504633|date=3 November 2011|title=Neural Dynamics as Sampling: A Model for Stochastic Computation in Recurrent Networks of Spiking Neurons|journal=PLOS Computational Biology|volume=7|issue=11|pages=e1002211|doi=10.1371/journal.pcbi.1002211|pmid=22096452|pmc=3207943|issn=1553-7358|bibcode=2011PLSCB...7E2211B |doi-access=free }}</ref>
 
Although a systematic comparison between the human brain organization and the neuronal encoding in deep networks has not yet been established, several analogies have been reported. For example, the computations performed by deep learning units could be similar to those of actual neurons<ref>{{Cite journal|last1=Cash|first1=S.|last2=Yuste|first2=R.|date=February 1999|title=Linear summation of excitatory inputs by CA1 pyramidal neurons|journal=Neuron|volume=22|issue=2|pages=383–394|issn=0896-6273|pmid=10069343|doi=10.1016/s0896-6273(00)81098-3|s2cid=14663106|doi-access=free}}</ref> and neural populations.<ref>{{Cite journal|date=1 August 2004|title=Sparse coding of sensory inputs|journal=Current Opinion in Neurobiology|volume=14|issue=4|pages=481–487|doi=10.1016/j.conb.2004.07.007|pmid=15321069|issn=0959-4388 | last1 = Olshausen | first1 = B | last2 = Field | first2 = D|s2cid=16560320}}</ref> Similarly, the representations developed by deep learning models are similar to those measured in the primate visual system<ref>{{Cite journal|last1=Yamins|first1=Daniel L K|last2=DiCarlo|first2=James J|s2cid=16970545|date=March 2016|title=Using goal-driven deep learning models to understand sensory cortex|journal=Nature Neuroscience|volume=19|issue=3|pages=356–365|doi=10.1038/nn.4244|pmid=26906502|issn=1546-1726}}</ref> both at the single-unit<ref>{{Cite journal|last1=Zorzi|first1=Marco|last2=Testolin|first2=Alberto|s2cid=39281431|date=19 February 2018|title=An emergentist perspective on the origin of number sense|journal=Phil. Trans. R. Soc. B|volume=373|issue=1740|pages=20170043|doi=10.1098/rstb.2017.0043|issn=0962-8436|pmid=29292348|pmc=5784047}}</ref> and at the population<ref>{{Cite journal|last1=Güçlü|first1=Umut|last2=van Gerven|first2=Marcel A. J.|date=8 July 2015|title=Deep Neural Networks Reveal a Gradient in the Complexity of Neural Representations across the Ventral Stream|journal=Journal of Neuroscience|volume=35|issue=27|pages=10005–10014|doi=10.1523/jneurosci.5023-14.2015|pmid=26157000|pmc=6605414|arxiv=1411.6422}}</ref> levels.
 
== Commercial activity ==
[[Facebook]]'s AI lab performs tasks such as [[Automatic image annotation|automatically tagging uploaded pictures]] with the names of the people in them.<ref name="METZ2013">{{cite magazine |first=C. |last=Metz |title=Facebook's 'Deep Learning' Guru Reveals the Future of AI |url=https://www.wired.com/wiredenterprise/2013/12/facebook-yann-lecun-qa/ |magazine=Wired |date=12 December 2013 |access-date=26 August 2017 |archive-date=28 March 2014 |archive-url=https://web.archive.org/web/20140328071226/http://www.wired.com/wiredenterprise/2013/12/facebook-yann-lecun-qa/ |url-status=live }}</ref>
 
Google's [[DeepMind Technologies]] developed a system capable of learning how to play [[Atari]] video games using only pixels as data input. In 2015 they demonstrated their [[AlphaGo]] system, which learned the game of [[Go (game)|Go]] well enough to beat a professional Go player.<ref>{{Cite journal|title = Google AI algorithm masters ancient game of Go|journal = Nature|year = 2016|doi = 10.1038/529445a|last1 = Gibney|first1 = Elizabeth|volume = 529|issue = 7587|pages = 445–446|pmid = 26819021|bibcode = 2016Natur.529..445G|s2cid = 4460235|doi-access = free}}</ref><ref>{{Cite journal|title = Mastering the game of Go with deep neural networks and tree search|journal = [[Nature (journal)|Nature]]| issn= 0028-0836|pages = 484–489|volume = 529|issue = 7587|doi = 10.1038/nature16961|pmid = 26819042|first1 = David|last1 = Silver|author-link1=David Silver (programmer)|first2 = Aja|last2 = Huang|author-link2=Aja Huang|first3 = Chris J.|last3 = Maddison|first4 = Arthur|last4 = Guez|first5 = Laurent|last5 = Sifre|first6 = George van den|last6 = Driessche|first7 = Julian|last7 = Schrittwieser|first8 = Ioannis|last8 = Antonoglou|first9 = Veda|last9 = Panneershelvam|first10= Marc|last10= Lanctot|first11= Sander|last11= Dieleman|first12=Dominik|last12= Grewe|first13= John|last13= Nham|first14= Nal|last14= Kalchbrenner|first15= Ilya|last15= Sutskever|author-link15=Ilya Sutskever|first16= Timothy|last16= Lillicrap|first17= Madeleine|last17= Leach|first18= Koray|last18= Kavukcuoglu|first19= Thore|last19= Graepel|first20= Demis |last20=Hassabis|s2cid = 515925|author-link20=Demis Hassabis|date= 28 January 2016|bibcode = 2016Natur.529..484S}}{{closed access}}</ref><ref>{{Cite web|title = A Google DeepMind Algorithm Uses Deep Learning and More to Master the Game of Go {{!}} MIT Technology Review|url = http://www.technologyreview.com/news/546066/googles-ai-masters-the-game-of-go-a-decade-earlier-than-expected/|website = MIT Technology Review|access-date = 30 January 2016|archive-date = 1 February 2016|archive-url = https://web.archive.org/web/20160201140636/http://www.technologyreview.com/news/546066/googles-ai-masters-the-game-of-go-a-decade-earlier-than-expected/|url-status = dead}}</ref> [[Google Translate]] uses a neural network to translate between more than 100 languages.
 
In 2017, Covariant.ai was launched, which focuses on integrating deep learning into factories.<ref>{{Cite news|url=https://www.nytimes.com/2017/11/06/technology/artificial-intelligence-start-up.html|title=A.I. Researchers Leave Elon Musk Lab to Begin Robotics Start-Up|first=Cade|last=Metz|newspaper=The New York Times|date=6 November 2017|access-date=5 July 2019|archive-date=7 July 2019|archive-url=https://web.archive.org/web/20190707161547/https://www.nytimes.com/2017/11/06/technology/artificial-intelligence-start-up.html|url-status=live}}</ref>
 
As of 2008,<ref>{{Cite book|author1=Bradley Knox, W.|author2=Stone, Peter|title=2008 7th IEEE International Conference on Development and Learning |chapter=TAMER: Training an Agent Manually via Evaluative Reinforcement |year=2008|pages = 292–297|doi=10.1109/devlrn.2008.4640845|isbn = 978-1-4244-2661-4|s2cid = 5613334}}</ref> researchers at [[University of Texas at Austin|The University of Texas at Austin]] (UT) developed a machine learning framework called Training an Agent Manually via Evaluative Reinforcement, or TAMER, which proposed new methods for robots or computer programs to learn how to perform tasks by interacting with a human instructor.<ref name=":12" /> First developed as TAMER, a new algorithm called Deep TAMER was later introduced in 2018 during a collaboration between [[U.S. Army Research Laboratory]] (ARL) and UT researchers. Deep TAMER used deep learning to provide a robot with the ability to learn new tasks through observation.<ref name=":12" /> Using Deep TAMER, a robot learned a task with a human trainer, watching video streams or observing a human perform a task in-person. The robot later practiced the task with the help of some coaching from the trainer, who provided feedback such as "good job" and "bad job".<ref>{{Cite web|url=https://governmentciomedia.com/talk-algorithms-ai-becomes-faster-learner|title=Talk to the Algorithms: AI Becomes a Faster Learner|website=governmentciomedia.com|date=16 May 2018 |access-date=29 August 2018|archive-date=28 August 2018|archive-url=https://web.archive.org/web/20180828001727/https://governmentciomedia.com/talk-algorithms-ai-becomes-faster-learner|url-status=live}}</ref>
 
== Criticism and comment ==
Deep learning has attracted both criticism and comment, in some cases from outside the field of computer science.
 
=== Theory ===
{{see also|Explainable artificial intelligence}}
A main criticism concerns the lack of theory surrounding some methods.<ref>{{Cite web|url=https://medium.com/@GaryMarcus/in-defense-of-skepticism-about-deep-learning-6e8bfd5ae0f1|title=In defense of skepticism about deep learning|last=Marcus|first=Gary|date=14 January 2018|website=Gary Marcus|access-date=11 October 2018|archive-date=12 October 2018|archive-url=https://web.archive.org/web/20181012035405/https://medium.com/@GaryMarcus/in-defense-of-skepticism-about-deep-learning-6e8bfd5ae0f1|url-status=live}}</ref> Learning in the most common deep architectures is implemented using well-understood gradient descent. However, the theory surrounding other algorithms, such as contrastive divergence is less clear.{{citation needed|date=July 2016}} (e.g., Does it converge? If so, how fast? What is it approximating?) Deep learning methods are often looked at as a [[black box]], with most confirmations done empirically, rather than theoretically.<ref name="Knight 2017">{{cite web | last=Knight | first=Will | title=DARPA is funding projects that will try to open up AI's black boxes | website=MIT Technology Review | date=14 March 2017 | url=https://www.technologyreview.com/s/603795/the-us-military-wants-its-autonomous-machines-to-explain-themselves/ | access-date=2 November 2017 | archive-date=4 November 2019 | archive-url=https://web.archive.org/web/20191104033107/https://www.technologyreview.com/s/603795/the-us-military-wants-its-autonomous-machines-to-explain-themselves/ | url-status=live }}</ref>
 
In further reference to the idea that artistic sensitivity might be inherent in relatively low levels of the cognitive hierarchy, a published series of graphic representations of the internal states of deep (20-30 layers) neural networks attempting to discern within essentially random data the images on which they were trained<ref>{{cite web |url=http://googleresearch.blogspot.co.uk/2015/06/inceptionism-going-deeper-into-neural.html |author1=Alexander Mordvintsev |author2=Christopher Olah |author3=Mike Tyka |date=17 June 2015 |title=Inceptionism: Going Deeper into Neural Networks |publisher=Google Research Blog |access-date=20 June 2015 |archive-date=3 July 2015 |archive-url=https://web.archive.org/web/20150703064823/http://googleresearch.blogspot.co.uk/2015/06/inceptionism-going-deeper-into-neural.html |url-status=live }}</ref> demonstrate a visual appeal: the original research notice received well over 1,000 comments, and was the subject of what was for a time the most frequently accessed article on ''[[The Guardian]]'s''<ref>{{cite news|url=https://www.theguardian.com/technology/2015/jun/18/google-image-recognition-neural-network-androids-dream-electric-sheep|title=Yes, androids do dream of electric sheep|date=18 June 2015|newspaper=The Guardian|author=Alex Hern|access-date=20 June 2015|archive-date=19 June 2015|archive-url=https://web.archive.org/web/20150619200845/http://www.theguardian.com/technology/2015/jun/18/google-image-recognition-neural-network-androids-dream-electric-sheep|url-status=live}}</ref> website.
 
Furthermore, some researchers have argued that standard loss functions and differentiable architectures in deep learning may limit the discovery of deeper causal or generative mechanisms.<ref>{{cite journal |last1=Zenil |first1=Hector |last2=Kiani |first2=Narsis A. |last3=Zea |first3=Allan A. |last4=Tegnér |first4=Jesper |title=Causal deconvolution by algorithmic generative models |journal=Nature Machine Intelligence |volume=1 |issue=1 |year=2019 |pages=58–66 |doi=10.1038/s42256-018-0005-0 }}</ref> Building on [[Algorithmic information theory]] (AIT), Hernández-Orozco et al. (2021)<ref name="HernandezOrozco2021">{{Cite journal|last1=Hernández-Orozco|first1=Santiago|last2=Zenil|first2=Hector|last3=Riedel|first3=Jürgen|last4=Uccello|first4=Adam|last5=Kiani|first5=Narsis A.|last6=Tegnér|first6=Jesper|date=2021|title=Algorithmic Probability-Guided Machine Learning on Non-Differentiable Spaces|journal=Frontiers in Artificial Intelligence|volume=3|pages=1–20|article-number=567356 |doi=10.3389/frai.2020.567356|doi-access=free |pmid=33733213 |pmc=7944352 }}</ref> proposed an algorithmic loss function to measure the discrepancy between predicted and observed system behavior. Their approach integrates AIT with [[Machine learning]] to formulate a framework for learning generative rules in non-differentiable spaces, bridging discrete algorithmic theory with continuous optimization techniques. This framework provides a new perspective on generalization and model interpretability by grounding learning dynamics in algorithmic complexity.<ref>{{cite book | last1=Zenil | first1=Hector | last2=Kiani | first2=Narsis A. | last3=Tegner | first3=Jesper | title=Algorithmic Information Dynamics: A Computational Approach to Causality with Applications to Living Systems | publisher=Cambridge University Press | year=2023 | doi=10.1017/9781108596619 | isbn=978-1-108-59661-9 | url=https://doi.org/10.1017/9781108596619}}</ref><ref>{{cite journal | last=Zenil | first=Hector | title=Algorithmic Information Dynamics | journal=Scholarpedia | date=25 July 2020 | volume=15 | issue=7 | doi=10.4249/scholarpedia.53143 | doi-access=free | bibcode=2020SchpJ..1553143Z | hdl=10754/666314 | hdl-access=free }}</ref>
 
=== Errors ===
Some deep learning architectures display problematic behaviors,<ref name=goertzel>{{cite web |first=Ben |last=Goertzel |title=Are there Deep Reasons Underlying the Pathologies of Today's Deep Learning Algorithms? |year=2015 |url=http://goertzel.org/DeepLearning_v1.pdf |access-date=2015-05-10 |archive-date=2015-05-13 |archive-url=https://web.archive.org/web/20150513053107/http://goertzel.org/DeepLearning_v1.pdf |url-status=live }}</ref> such as confidently classifying unrecognizable images as belonging to a familiar category of ordinary images (2014)<ref>{{cite arXiv |eprint=1412.1897|last1=Nguyen|first1=Anh|title=Deep Neural Networks are Easily Fooled: High Confidence Predictions for Unrecognizable Images|last2=Yosinski|first2=Jason|last3=Clune|first3=Jeff|class=cs.CV|year=2014}}</ref> and misclassifying minuscule perturbations of correctly classified images (2013).<ref>{{cite arXiv |eprint=1312.6199|last1=Szegedy|first1=Christian|title=Intriguing properties of neural networks|last2=Zaremba|first2=Wojciech|last3=Sutskever|first3=Ilya|last4=Bruna|first4=Joan|last5=Erhan|first5=Dumitru|last6=Goodfellow|first6=Ian|last7=Fergus|first7=Rob|class=cs.CV|year=2013}}</ref> [[Ben Goertzel|Goertzel]] hypothesized that these behaviors are due to limitations in their internal representations and that these limitations would inhibit integration into heterogeneous multi-component [[artificial general intelligence]] (AGI) architectures.<ref name="goertzel" /> These issues may possibly be addressed by deep learning architectures that internally form states homologous to image-grammar<ref>{{cite journal | last1 = Zhu | first1 = S.C. | last2 = Mumford | first2 = D. | year = 2006| title = A stochastic grammar of images | journal = Found. Trends Comput. Graph. Vis. | volume = 2 | issue = 4| pages = 259–362 | doi = 10.1561/0600000018| citeseerx = 10.1.1.681.2190 }}</ref> decompositions of observed entities and events.<ref name="goertzel"/> [[Grammar induction|Learning a grammar]] (visual or linguistic) from training data would be equivalent to restricting the system to [[commonsense reasoning]] that operates on concepts in terms of grammatical [[Production (computer science)|production rules]] and is a basic goal of both human language acquisition<ref>Miller, G. A., and N. Chomsky. "Pattern conception". Paper for Conference on pattern detection, University of Michigan. 1957.</ref> and [[artificial intelligence]] (AI).<ref>{{cite web |first=Jason |last=Eisner |title=Deep Learning of Recursive Structure: Grammar Induction |url=http://techtalks.tv/talks/deep-learning-of-recursive-structure-grammar-induction/58089/ |access-date=2015-05-10 |archive-date=2017-12-30 |archive-url=https://web.archive.org/web/20171230010335/http://techtalks.tv/talks/deep-learning-of-recursive-structure-grammar-induction/58089/ |url-status=dead }}</ref>
 
=== Cyber threat ===
Given the far-reaching implications of artificial intelligence coupled with the realization that deep learning is emerging as one of its most powerful techniques, the subject is understandably attracting both criticism and comment, and in some cases from outside the field of computer science itself.
As deep learning moves from the lab into the world, research and experience show that artificial neural networks are vulnerable to hacks and deception.<ref>{{Cite web|url=https://gizmodo.com/hackers-have-already-started-to-weaponize-artificial-in-1797688425|title=Hackers Have Already Started to Weaponize Artificial Intelligence|website=Gizmodo|date=11 September 2017 |access-date=11 October 2019|archive-date=11 October 2019|archive-url=https://web.archive.org/web/20191011162231/https://gizmodo.com/hackers-have-already-started-to-weaponize-artificial-in-1797688425|url-status=live}}</ref> By identifying patterns that these systems use to function, attackers can modify inputs to ANNs in such a way that the ANN finds a match that human observers would not recognize. For example, an attacker can make subtle changes to an image such that the ANN finds a match even though the image looks to a human nothing like the search target. Such manipulation is termed an "[[Adversarial machine learning|adversarial attack]]".<ref>{{Cite web|url=https://www.dailydot.com/debug/adversarial-attacks-ai-mistakes/|title=How hackers can force AI to make dumb mistakes|date=18 June 2018|website=The Daily Dot|language=en|access-date=11 October 2019|archive-date=11 October 2019|archive-url=https://web.archive.org/web/20191011162230/https://www.dailydot.com/debug/adversarial-attacks-ai-mistakes/|url-status=live}}</ref>
 
In 2016 researchers used one ANN to doctor images in trial and error fashion, identify another's focal points, and thereby generate images that deceived it. The modified images looked no different to human eyes. Another group showed that printouts of doctored images then photographed successfully tricked an image classification system.<ref name=":4">{{Cite news|url=https://singularityhub.com/2017/10/10/ai-is-easy-to-fool-why-that-needs-to-change|title=AI Is Easy to Fool—Why That Needs to Change|date=10 October 2017|work=Singularity Hub|access-date=11 October 2017|archive-date=11 October 2017|archive-url=https://web.archive.org/web/20171011233017/https://singularityhub.com/2017/10/10/ai-is-easy-to-fool-why-that-needs-to-change/|url-status=live}}</ref> One defense is reverse image search, in which a possible fake image is submitted to a site such as [[TinEye]] that can then find other instances of it. A refinement is to search using only parts of the image, to identify images from which that piece may have been taken'''.'''<ref>{{Cite journal|last=Gibney|first=Elizabeth|title=The scientist who spots fake videos|url=https://www.nature.com/news/the-scientist-who-spots-fake-videos-1.22784|journal=Nature|doi=10.1038/nature.2017.22784|year=2017|access-date=2017-10-11|archive-date=2017-10-10|archive-url=https://web.archive.org/web/20171010011017/http://www.nature.com/news/the-scientist-who-spots-fake-videos-1.22784|url-status=live}}</ref>
A main criticism of deep learning concerns the lack of theory surrounding many of the methods.{{citation needed|date=July 2016}} Learning in the most common deep architectures is implemented using [[gradient descent]]; while gradient descent has been understood for a while now, the theory surrounding other algorithms, such as contrastive divergence is less clear.{{citation needed|date=July 2016}} (i.e., Does it converge? If so, how fast? What is it approximating?) Deep learning methods are often looked at as a black box, with most confirmations done empirically, rather than theoretically.{{citation needed|date=July 2016}}
 
Another group showed that certain [[Psychedelic art|psychedelic]] spectacles could fool a [[facial recognition system]] into thinking ordinary people were celebrities, potentially allowing one person to impersonate another. In 2017 researchers added stickers to [[stop sign]]s and caused an ANN to misclassify them.<ref name=":4" />
Others point out that deep learning should be looked at as a step towards realizing strong AI, not as an all-encompassing solution. Despite the power of deep learning methods, they still lack much of the functionality needed for realizing this goal entirely. Research psychologist [[Gary Marcus]] has noted that:<blockquote>"Realistically, deep learning is only part of the larger challenge of building intelligent machines. Such techniques lack ways of representing [[causality|causal relationships]] (...) have no obvious ways of performing [[inference|logical inferences]], and they are also still a long way from integrating abstract knowledge, such as information about what objects are, what they are for, and how they are typically used. The most powerful A.I. systems, like [[Watson (computer)|Watson]] (...) use techniques like deep learning as just one element in a very complicated ensemble of techniques, ranging from the statistical technique of [[Bayesian inference]] to [[deductive reasoning]]."<ref name="MARCUS">G. Marcus., "Is "Deep Learning" a Revolution in Artificial Intelligence?" ''The New Yorker'', 25 November 2012.</ref></blockquote>To the extent that such a viewpoint implies, without intending to, that deep learning will ultimately constitute nothing more than the primitive discriminatory levels of a comprehensive future machine intelligence, a recent pair of speculations regarding art and artificial intelligence<ref>{{cite web |url=http://artent.net/2015/03/27/art-and-artificial-intelligence-by-g-w-smith/|author=Smith, G. W.|date=March 27, 2015|title=Art and Artificial Intelligence|publisher=ArtEnt|accessdate=March 27, 2015}}</ref> offers an alternative and more expansive outlook. The first such speculation is that it might be possible to train a machine vision stack to perform the sophisticated task of discriminating between "old master" and amateur figure drawings; and the second is that such a sensitivity might in fact represent the rudiments of a non-trivial machine empathy. It is suggested, moreover, that such an eventuality would be in line with anthropology, which identifies a concern with aesthetics as a key element of [[behavioral modernity]].<ref>{{cite web |url=http://repositriodeficheiros.yolasite.com/resources/Texto%2028.pdf |author=Mellars, Paul |date=February 1, 2005 |title=The Impossible Coincidence: A Single-Species Model for the Origins of Modern Human Behavior in Europe|publisher=Evolutionary Anthropology: Issues, News, and Reviews |accessdate=April 5, 2017 }}</ref>
 
ANNs can however be further trained to detect attempts at [[deception]], potentially leading attackers and defenders into an arms race similar to the kind that already defines the [[malware]] defense industry. ANNs have been trained to defeat ANN-based anti-[[malware]] software by repeatedly attacking a defense with malware that was continually altered by a [[genetic algorithm]] until it tricked the anti-malware while retaining its ability to damage the target.<ref name=":4" />
In further reference to the idea that a significant degree of artistic sensitivity might inhere within relatively low levels, whether biological or digital, of the cognitive hierarchy, a published series of graphic representations of the internal states of deep (20-30 layers) neural networks attempting to discern within essentially random data the images on which they were trained<ref>{{cite web|url=http://googleresearch.blogspot.co.uk/2015/06/inceptionism-going-deeper-into-neural.html |author1=Alexander Mordvintsev |author2=Christopher Olah |author3=Mike Tyka |date=June 17, 2015 |title=Inceptionism: Going Deeper into Neural Networks |publisher=Google Research Blog |accessdate=June 20, 2015 }}</ref> seem to demonstrate a striking visual appeal in light of the remarkable level of public attention which this work captured: the original research notice received well over 1,000 comments, and the coverage by [[The Guardian]]<ref>{{cite web |url=https://www.theguardian.com/technology/2015/jun/18/google-image-recognition-neural-network-androids-dream-electric-sheep|author=Alex Hern|date=June 18, 2015|title=Yes, androids do dream of electric sheep|publisher=The Guardian|accessdate=June 20, 2015}}</ref> was for a time the most frequently accessed article on that newspaper's web site.
 
In 2016, another group demonstrated that certain sounds could make the [[Google Now]] voice command system open a particular web address, and hypothesized that this could "serve as a stepping stone for further attacks (e.g., opening a web page hosting drive-by malware)".<ref name=":4" />
Some currently popular and successful deep learning architectures display certain problematic behaviors,<ref name=goertzel>Ben Goertzel. Are there Deep Reasons Underlying the Pathologies of Today's Deep Learning Algorithms? (2015) Url: http://goertzel.org/DeepLearning_v1.pdf</ref> such as confidently classifying unrecognizable images as belonging to a familiar category of ordinary images<ref>Nguyen, Anh, Jason Yosinski, and Jeff Clune. "Deep Neural Networks are Easily Fooled: High Confidence Predictions for Unrecognizable Images." {{arxiv|1412.1897}} (2014).</ref> and misclassifying minuscule perturbations of correctly classified images.<ref>Szegedy, Christian, et al. "Intriguing properties of neural networks." {{arxiv|1312.6199}} (2013).</ref> The creator of [[OpenCog]], [[Ben Goertzel]], hypothesized<ref name="goertzel"/> that these behaviors are due to limitations in the internal representations learned by these architectures, and that these limitations would inhibit integration of these architectures into heterogeneous multi-component [[Artificial general intelligence|AGI]] architectures. It is suggested that these issues can be worked around by developing deep learning architectures that internally form states homologous to image-grammar<ref>{{cite journal | last1 = Zhu | first1 = S.C. | last2 = Mumford | first2 = D. | year = | title = A stochastic grammar of images | url = | journal = Found. Trends Comput. Graph. Vis. | volume = 2 | issue = 4| pages = 259–362 | doi = 10.1561/0600000018 }}</ref> decompositions of observed entities and events.<ref name="goertzel"/> Learning a [[grammar]] (visual or linguistic) from training data would be equivalent to restricting the system to [[commonsense reasoning]] which operates on concepts in terms of [[Production (computer science)|production rules]] of the grammar, and is a basic goal of both human language acquisition<ref>Miller, G. A., and N. Chomsky. "Pattern conception." Paper for Conference on pattern detection, University of Michigan. 1957.</ref> and AI. (See also [[Grammar induction]].<ref>Jason Eisner, Deep Learning of Recursive Structure: Grammar Induction, http://techtalks.tv/talks/deep-learning-of-recursive-structure-grammar-induction/58089/</ref>)
 
In "[[Adversarial machine learning#Data poisoning|data poisoning]]", false data is continually smuggled into a machine learning system's training set to prevent it from achieving mastery.<ref name=":4" />
== Software libraries ==
{{main article|Comparison of deep learning software}}
 
=== Data collection ethics ===
* [[Deeplearning4j]] — An open-source deep-learning library written for Java/C++ with LSTMs and convolutional networks. It provides parallelization with Spark on CPUs and GPUs.
The deep learning systems that are trained using supervised learning often rely on data that is created or annotated by humans, or both.<ref>{{Cite journal |last=Tubaro |first=Paola |date=2020 |title=Whose intelligence is artificial intelligence? |url=https://hal.science/hal-03029735 |journal=Global Dialogue |language=en |pages=38–39}}</ref> It has been argued that not only low-paid [[Clickworkers|clickwork]] (such as on [[Amazon Mechanical Turk]]) is regularly deployed for this purpose, but also implicit forms of human [[microwork]] that are often not recognized as such.<ref name=":13">{{Cite journal|last=Mühlhoff|first=Rainer|date=6 November 2019|title=Human-aided artificial intelligence: Or, how to run large computations in human brains? Toward a media sociology of machine learning|journal=New Media & Society|language=en|volume=22|issue=10|pages=1868–1884|doi=10.1177/1461444819885334|s2cid=209363848|issn=1461-4448|url=https://depositonce.tu-berlin.de/handle/11303/12510|doi-access=free}}</ref> The philosopher [[Rainer Mühlhoff]] distinguishes five types of "machinic capture" of human microwork to generate training data: (1) [[gamification]] (the embedding of annotation or computation tasks in the flow of a game), (2) "trapping and tracking" (e.g. [[CAPTCHA]]s for image recognition or click-tracking on Google [[Search engine results page|search results pages]]), (3) exploitation of social motivations (e.g. [[Tag (Facebook)|tagging faces]] on [[Facebook]] to obtain labeled facial images), (4) [[information mining]] (e.g. by leveraging [[Quantified self|quantified-self]] devices such as [[activity tracker]]s) and (5) [[Clickworkers|clickwork]].<ref name=":13" />
* [[Gensim]] — A toolkit for natural language processing implemented in the Python programming language.
* [[Keras]] — An open-source deep learning framework for the Python programming language.
* Microsoft [[CNTK]] (Computational Network Toolkit) — Microsoft's open-source deep-learning toolkit for Windows and Linux. It provides parallelization with CPUs and GPUs across multiple servers.
* [[MXNet]] — An open source deep learning framework that allows you to define, train, and deploy deep neural networks.
* [[OpenNN]] — An open source C++ library which implements deep neural networks and provides parallelization with CPUs.
* [http://www.paddlepaddle.org PaddlePaddle] — An open source C++ /CUDA library with Python API for scalable deep learning platform with CPUs and GPUs, originally developed by Baidu.
* [[TensorFlow]] — Google's open source machine learning library in C++ and Python with APIs for both. It provides parallelization with CPUs and GPUs.
* [[Theano (software)|Theano]] — An open source machine learning library for Python supported by the University of Montreal and Yoshua Bengio's team.
* [[Torch (machine learning)|Torch]] — An open source software library for machine learning based on the Lua programming language and used by Facebook.
* [http://caffe.berkeleyvision.org Caffe] - Caffe is a deep learning framework made with expression, speed, and modularity in mind. It is developed by the Berkeley Vision and Learning Center (BVLC) and by community contributors.
* [http://dianne.intec.ugent.be DIANNE] - A modular open-source deep learning framework in Java / OSGi developed at Ghent University, Belgium. It provides parallelization with CPUs and GPUs across multiple servers.
 
== See also ==
* [[Applications of artificial intelligence]]
* [[Comparison of deep learning software]]
*[[Artificial neural networks]]
* [[BoltzmannCompressed machinesensing]]
* [[CompressedDifferentiable Sensingprogramming]]
* [[Connectionism]]
* [[Echo state network]]
* [[List of artificial intelligence projects]]
* [[Liquid state machine]]
* [[List of datasets for machine -learning research]]
* [[Reservoir computing]]
* [[Scale space#Deep learning and scale space|Scale space and deep learning]]
* [[Sparse coding]]
* [[Stochastic parrot]]
* [[Topological deep learning]]
 
== References ==
{{Reflist|30em}}
 
== Further reading ==
==External links==
{{refbegin}}
* [http://www.teglor.com/b/deep-learning-libraries-language-cm569/ Deep Learning Libraries by Language]
* {{cite book |last1=Bishop |first1=Christopher M. |last2=Bishop |first2=Hugh |title=Deep learning: foundations and concepts |date=2024 |publisher=Springer |isbn=978-3-031-45467-7}}
* [https://mitprofessionalx.mit.edu/courses/course-v1:MITProfessionalX+DSx+2016_T1/about Data Science: Data to Insights from MIT (deep learning)]
* {{cite book |last1=Prince |first1=Simon J. D. |title=Understanding deep learning |date=2023 |publisher=The MIT Press |isbn=9780262048644}}
{{Prone to spam|date=June 2015}}{{Z148}}
* {{cite book
|title=Deep Learning
|year=2016
|first1=Ian
|last1=Goodfellow
|author-link1=Ian Goodfellow
|first2=Yoshua
|last2=Bengio
|author-link2=Yoshua Bengio
|first3=Aaron
|last3=Courville
|publisher=MIT Press
|url=http://www.deeplearningbook.org
|isbn=978-0-26203561-3
|postscript=, introductory textbook.
|access-date=2021-05-09
|archive-date=2016-04-16
|archive-url=https://web.archive.org/web/20160416111010/http://www.deeplearningbook.org/
|url-status=live
}}
 
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