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{{machine learning bar}}
'''Deep learning''' ('''deep structured learning''', '''hierarchical learning''' or '''deep machine learning''') is a branch of [[machine learning]] based on a set of [[algorithm]]s that attempt to model high-level abstractions in data by using multiple processing layers, with complex structures or otherwise, composed of multiple non-[[linear transformation]]s.<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 |pages=3–4 |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}}</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="goodfellow2016">Ian Goodfellow, Yoshua Bengio, and Aaron Courville (2016). Deep Learning. MIT Press. [http://www.deeplearningbook.org Online]</ref><ref name="scholarpedia"/>
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, [[Scale-invariant feature transform|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>) from examples. 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>
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=== Definitions ===
There are a number of ways that the field of deep learning has been characterized.
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.
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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"/>
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.
== Interpretations ==
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==History==
Ukrainian mathematicians [[Alexey Grigorevich Ivakhnenko|Ivakhnenko]] and Lapa published the first general, working learning algorithm for supervised deep feedforward multilayer perceptrons.<ref name="ivak1965">{{Cite book|title=Cybernetic Predicting Devices|last=Ivakhnenko|first=Alexey|publisher=Naukova Dumka|year=1965|isbn=|___location=Kiev|pages=}}</ref> A paper from 1971 already described a deep network with 8 layers trained by the [[Group method of data handling]] algorithm which is still popular in the current millennium.<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> 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}}</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 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"/> 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>
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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}}</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
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/> 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"/> Later it was combined with CTC<ref name="graves2006"/> in stacks of LSTM RNNs.<ref name="fernandez2007keyword"/> 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 all smartphone users,<ref name="sak2015"/> and has become a show case of deep learning.
The term "deep learning" gained traction in the mid-2000s after a publication by [[Geoffrey Hinton]] and Ruslan Salakhutdinov showed how a 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."</ref>▼
According to a survey,<ref name="scholarpedia">[[Jürgen Schmidhuber]] (2015). Deep Learning. Scholarpedia, 10(11):32832. [http://www.scholarpedia.org/article/Deep_Learning Online]</ref> the expression "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]</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>http://research.microsoft.com/apps/pubs/default.aspx?id=189004</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"/> however, these are more widely used in computer vision than in ASR.▼
and later to [[Artificial Neural Networks]] 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>
▲
▲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>http://research.microsoft.com/apps/pubs/default.aspx?id=189004</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"/> 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="sak2014"/><ref name="liwu2015"/><ref name="zen2015"/><ref name="sak2015"/>
The real impact of deep learning in industry began with large-scale speech recognition around 2010. In late 2009, Li Deng invited Geoffrey Hinton to work with him and colleagues at Microsoft Research 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/>▼
▲The real impact of deep learning in industry apparently began
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>
Advances in hardware have also been important in enabling the renewed interest in deep learning. 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">Oh, K.-S. and Jung, K. (2004). GPU implementation of neural networks. Pattern Recognition, 37(6):1311–1314.</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> == Artificial neural networks ==
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An obvious need for recognizing general 3-D objects is least shift invariance and tolerance to deformation. 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"/>
With the advent of the [[back-propagation]] algorithm
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.
Another method is the [[long short term memory]] (LSTM) network of [[Sepp Hochreiter|Hochreiter]] & [[Jürgen Schmidhuber|Schmidhuber]] (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> 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>
Sven Behnke in 2003 relied only on the sign of the gradient ([[Rprop]]) when training his Neural Abstraction Pyramid<ref>
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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]].
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"/>
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.
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.
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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" />
DNNs are typically designed as [[feedforward neural network|feedforward]] networks, but
==== Backpropagation ====
A DNN can be [[discriminative model|discriminatively]] trained with the standard [[backpropagation]] algorithm. The weight updates can be done via [[stochastic gradient descent]] using the following equation:▼
A DNN can be [[discriminative model|discriminatively]] trained with the standard [[backpropagation]] algorithm. According to various sources,<ref name="dreyfus1990">[[Stuart Dreyfus]] (1990). Artificial Neural Networks, Back Propagation and the Kelley-Bryson Gradient Procedure. J. Guidance, Control and Dynamics, 1990. </ref><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><ref name="SCHIDHUB"/><ref name="scholarpedia"/>
basics of continuous backpropagation were derived in the context of [[control theory]] by [[Henry J. Kelley]]<ref name="kelley1960">[[Henry J. Kelley]] (1960). Gradient theory of optimal flight paths. Ars Journal, 30(10), 947-954. [http://arc.aiaa.org/doi/abs/10.2514/8.5282?journalCode=arsj Online]</ref> in 1960 and by [[Arthur E. Bryson]] in 1961,<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> using principles of [[dynamic programming]]. In 1962, [[Stuart Dreyfus]] published a simpler derivation based only on the [[chain rule]].<ref name="dreyfus1962">[[Stuart Dreyfus]] (1962). The numerical solution of variational problems. Journal of Mathematical Analysis and Applications, 5(1), 30-45. [https://www.researchgate.net/publication/256244271_The_numerical_solution_of_variational_problems Online]</ref> [[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">[[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="lin1976">[[Seppo Linnainmaa]] (1976). Taylor expansion of the accumulated rounding error. BIT Numerical Mathematics, 16(2), 146-160.</ref> This corresponds to the modern version of backpropagation which is efficient even when the networks are sparse.<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="grie2008">Griewank, Andreas and Walther, A.. Principles and Techniques of Algorithmic Differentiation, Second Edition. SIAM, 2008.</ref><ref name="SCHIDHUB"/><ref name="scholarpedia"/>
In 1973, [[Stuart Dreyfus]] used backpropagation to adapt [[parameter]]s of controllers in proportion to error gradients.<ref name="dreyfus1973">[[Stuart Dreyfus]] (1973). The computational solution of optimal control problems with time lag. IEEE Transactions on Automatic Control, 18(4):383–385.</ref> 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="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><ref name="scholarpedia"/>
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>
▲
:<math> w_{ij}(t + 1) = w_{ij}(t) + \eta\frac{\partial C}{\partial w_{ij}} </math>
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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">[[Alexey Grigorevich Ivakhnenko]] (1968). The [[group method of data handling]] – a rival of the method of stochastic approximation. Soviet Automatic Control, 13(3):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]]. The size and depth of the resulting network depends on the problem. Variants of this method are still being used today.<ref name="kondo2008">T. Kondo and J. Ueno (2008). Multi-layered GMDH-type neural network self-selecting optimum neural network architecture and its application to 3-dimensional medical image recognition of blood vessels. International Journal of Innovative Computing,Information and Control, 4(1):175–187.</ref>
=== Convolutional neural networks ===▼
{{main|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
===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">[[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>
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"/>
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|distributed representations]] 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]]===
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">Felix Gers, Nicholas Schraudolph, and [[Jürgen Schmidhuber]] (2002). Learning precise timing with LSTM recurrent networks. Journal of Machine Learning Research 3:115–143.</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">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> 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="graves2009"/><ref name="SCHIDHUB"/> Already 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> In 2007, the combination with CTC achieved first good results on speech data.<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>. 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">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> 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="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><ref name="scholarpedia"/> 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">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>
LSTM has also become very popular in the field of [[Natural Language Processing]].
Unlike previous models based on HMMs and similar concepts, LSTM can learn to recognise [[context-sensitive languages]].<ref name="gers2001">Felix A. Gers and [[Jürgen Schmidhuber]]. LSTM Recurrent Networks Learn Simple Context Free and Context Sensitive Languages. IEEE TNN 12(6):1333–1340, 2001.</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 ===
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Although the approximation of CD to maximum likelihood is very crude (CD 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 neural networks ===
▲{{main|Convolutional neural network}}
▲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. This architecture allows CNNs to take advantage of the 2D structure of input data. In comparison with other deep architectures, convolutional neural networks are starting to show 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">http://ufldl.stanford.edu/tutorial/supervised/ConvolutionalNeuralNetwork/</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>
=== Convolutional deep belief networks ===
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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" />
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" />
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" />
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=== Deep q-networks ===
This is
| last1 = Mnih
| first1 = Volodymyr
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| journal=Nature}}</ref> The application discussed in this paper is limited to [[Atari 2600]] gaming, but the implications for other applications are profound.
===Networks with seperate memory structures===
▲===Memory networks ===
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.
====
*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>
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====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
====Memory networks====
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====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.
== Other architectures ==
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=== Automatic speech recognition ===
{{Main|Speech recognition}}
Speech recognition has been revolutionised by deep learning, especially by [[Long short term memory]] (LSTM), a [[recurrent neural network]] published by [[Sepp Hochreiter]] & [[Jürgen Schmidhuber]] in 1997.<ref name=lstm/> LSTM RNNs circumvent the [[vanishing gradient problem]] and can learn "Very Deep Learning" tasks<ref name="SCHIDHUB"/> that involve speech events sepearated by thousands of discrete time steps, where one time step corresponds to about 10 ms.
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 results shown in the table below are for automatic speech recognition on the popular [[TIMIT]] data set. This is a common 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">''TIMIT Acoustic-Phonetic Continuous Speech Corpus'' Linguistic Data Consortium, Philadelphia.</ref> Its small size allows many configurations to be tried effectively. More importantly, the TIMIT task concerns phone-sequence recognition, which, unlike word-sequence recognition, allows very weak "language models" and thus the weaknesses in 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">NIPS Workshop: Deep Learning for Speech Recognition and Related Applications, Whistler, BC, Canada, Dec. 2009 (Organizers: Li Deng, Geoff Hinton, D. Yu).</ref> 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 over a time span of the past 20 years:
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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,<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>
Since the initial successful debut of DNNs for speech recognition around 2009-2011 and of LSTM around 2003-2007,
* Scaling up/out and speedup DNN training and decoding;
* Sequence discriminative training of DNNs;
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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, Google Now, Apple Siri, Baidu and iFlyTek voice search, and a range of Nuance speech products, etc.) are 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> 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 ===
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>
According to LeCun,<ref name="lecun2016slides">[[Yann LeCun]] (2016). Slides on Deep Learning [https://indico.cern.ch/event/510372/ Online]</ref> 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">Krizhevsky, A., Sutskever, I. and Hinton, G. E. (2012). ImageNet Classification with Deep Convolutional Neural Networks.
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 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|accessdate=5 April 2015}}</ref>▼
NIPS 2012: Neural Information Processing Systems, Lake Tahoe, Nevada</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.
▲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
One example application is a car computer said to be trained with deep learning, which may enable cars to 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"] (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.
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=== Natural language processing ===
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>
Neural networks have been used for implementing [[language model]]s since the early 2000s.<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> Key techniques in this field are [[negative sampling]]<ref name=GoldbergLevy2014>{{cite web|last1=Goldberg|first1=Yoav|last2=Levy|first2=Omar|title=word2vec Explained: Deriving Mikolov et al.’s Negative-Sampling Word-Embedding Method|url=http://arxiv.org/pdf/1402.3722v1.pdf|website=Arxiv|accessdate=26 October 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 a 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">Mesnil, G., Dauphin, Y., Yao, K., Bengio, Y., Deng, L., Hakkani-Tur, D., He, X., Heck, L., Tur, G., Yu, D. and Zweig, G., 2015. Using recurrent neural networks for slot filling in spoken language understanding. IEEE Transactions on Audio, Speech, and Language Processing, 23(3), pp.530-539.</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> and others.<ref name="Tutorial2014">J. Gao, X. He, L. Deng (2014) "Deep Learning for Natural Language Processing: Theory and Practice (Tutorial)," CIKM.</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"/>
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=== Drug discovery and toxicology ===
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