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{{Short description|Neural network architecture}}
[[File:TDNN Diagram.png|thumb|right|TDNN diagram]]
'''Time delay neural network''' ('''TDNN''')<ref name="phoneme detection">
Shift-invariant classification means that the classifier does not require explicit segmentation prior to classification. For the classification of a temporal pattern (such as speech), the TDNN thus avoids having to determine the beginning and end points of sounds before classifying them.
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== History ==
The TDNN was introduced in the late 1980s and applied to a task of [[phoneme]] classification for automatic [[speech recognition]] in speech signals where the automatic determination of precise segments or feature boundaries was difficult or impossible. Because the TDNN recognizes phonemes and their underlying acoustic/phonetic features, independent of position in time, it improved performance over static classification.<ref name="phoneme detection" /><ref name=":0">Alexander Waibel, [https://isl.iar.kit.edu/downloads/Pheome_Recognition_Using_Time-Delay_Neural_Networks_SP87-100_6.pdf Phoneme Recognition Using Time-Delay Neural Networks], Procedures of the Institute of Electrical, Information and Communication Engineers (IEICE), December, 1987, Tokyo, Japan.</ref> It was also applied to two-dimensional signals (time-frequency patterns in speech,<ref name=":1">{{cite journal |author=John B. Hampshire |author2=Alex Waibel |url=https://www.researchgate.net/publication/
[[Kunihiko Fukushima]] published the [[neocognitron]] in 1980.<ref name="intro">{{cite journal |last=Fukushima |first=Kunihiko |year=1980 |title=Neocognitron: A Self-organizing Neural Network Model for a Mechanism of Pattern Recognition Unaffected by Shift in Position |url=https://www.cs.princeton.edu/courses/archive/spr08/cos598B/Readings/Fukushima1980.pdf |url-status=live |journal=Biological Cybernetics |volume=36 |issue=4 |pages=193–202 |doi=10.1007/BF00344251 |pmid=7370364 |s2cid=206775608 |archive-url=https://web.archive.org/web/20140603013137/http://www.cs.princeton.edu/courses/archive/spr08/cos598B/Readings/Fukushima1980.pdf |archive-date=3 June 2014 |access-date=16 November 2013}}</ref> [[Max pooling]] appears in a 1982 publication on the neocognitron<ref>{{Cite journal |last1=Fukushima |first1=Kunihiko |last2=Miyake |first2=Sei |date=1982-01-01 |title=Neocognitron: A new algorithm for pattern recognition tolerant of deformations and shifts in position |url=https://www.sciencedirect.com/science/article/abs/pii/0031320382900243 |journal=Pattern Recognition |volume=15 |issue=6 |pages=455–469 |doi=10.1016/0031-3203(82)90024-3 |bibcode=1982PatRe..15..455F |issn=0031-3203|url-access=subscription }}</ref> and was in the 1989 publication in [[LeNet|LeNet-5]].<ref>{{Cite journal |last1=LeCun |first1=Yann |last2=Boser |first2=Bernhard |last3=Denker |first3=John |last4=Henderson |first4=Donnie |last5=Howard |first5=R. |last6=Hubbard |first6=Wayne |last7=Jackel |first7=Lawrence |date=1989 |title=Handwritten Digit Recognition with a Back-Propagation Network |url=https://proceedings.neurips.cc/paper/1989/hash/53c3bce66e43be4f209556518c2fcb54-Abstract.html |journal=Advances in Neural Information Processing Systems |publisher=Morgan-Kaufmann |volume=2}}</ref>
In 1990, Yamaguchi et al. used max pooling in TDNNs in order to realize a speaker independent isolated word recognition system.<ref name="Yamaguchi111990">{{cite conference |title=A Neural Network for Speaker-Independent Isolated Word Recognition |last1=Yamaguchi |first1=Kouichi |last2=Sakamoto |first2=Kenji |last3=Akabane |first3=Toshio |last4=Fujimoto |first4=Yoshiji |date=November 1990 |___location=Kobe, Japan |conference=First International Conference on Spoken Language Processing (ICSLP 90) |url=https://www.isca-speech.org/archive/icslp_1990/i90_1077.html |access-date=2019-09-04 |archive-date=2021-03-07 |archive-url=https://web.archive.org/web/20210307233750/https://www.isca-speech.org/archive/icslp_1990/i90_1077.html |url-status=dead }}</ref>
== Overview ==
=== Architecture ===
In modern language, the design of TDNN is a 1D [[convolutional neural network]], where the direction of convolution is across the dimension of time. In the original design, there are exactly 3 layers.
The input to the network is a continuous speech signal, preprocessed into a 2D array (a [[mel scale]] [[spectrogram]]). One dimension is time at 10 ms per frame, and the other dimension is frequency. The time dimension can be arbitrarily long, but the frequency dimension was only 16-long. In the original experiment, they only considered very short speech signals pronouncing single words like "baa", "daa", "gaa". Because of this, the speech signals could be very short, indeed, only 15 frames long (150 ms in time).
In detail, they processed a voice signal as follows:
* Input speech is sampled at 12 kHz, [[Window function#Hann and Hamming windows|Hamming-windowed]].
* Its [[Fast Fourier transform|FFT]] is computed every 5 ms.
* The mel scale coefficients are computed from the power spectrum by taking log energies in each mel scale energy band.
* Adjacent coefficients in time are soothed over, resulting in one frame every 10 ms.
* For each signal, a human manually detect the onset of the vowel, and the entire speech signal is cut off except 7 frames before and 7 frames after, leaving just 15 frames in total, centered at the onset of the vowel.
* The coefficients are normalized by subtracting the mean, then scaling, so that the signals fall between -1 and +1.
The first layer of the TDNN is a 1D convolutional layer. The layer contains 8 kernels of shape <math>3 \times 16 </math>. It outputs a tensor of shape <math>8 \times 13</math>.
The second layer of the TDNN is a 1D convolutional layer. The layer contains 3 kernels of shape <math>5 \times 8</math>. It outputs a tensor of shape <math>3 \times 9</math>.
The third layer of the TDNN is not a convolutional layer. Instead, it is simply a fixed layer with 3 neurons. Let the output from the second layer be <math>x_{i,j}</math> where <math>i \in 1:3</math> and <math>j \in 1:9</math>. The <math>i</math>-th neuron in the third layer computes <math>\sigma(\sum_{j\in 1:9} x_{i,j})</math>, where <math>\sigma</math> is the [[sigmoid function]]. Essentially, it can be thought of as a convolution layer with 3 kernels of shape <math>1 \times 9</math>.
It was trained on ~800 samples for 20000--50000 [[backpropagation]] steps. Each steps was computed in a [[Batch processing|batch]] over the entire training dataset, i.e. not [[Stochastic gradient descent|stochastic]]. It required the use of an [[Alliant Computer Systems|Alliant supercomputer]] with 4 processors.
=== Example ===
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=== Implementation ===
The precise architecture of TDNNs (time-delays, number of layers) is mostly determined by the designer depending on the classification problem and the most useful context sizes. The delays or context windows are chosen specific to each application. Work has also been done to create adaptable time-delay TDNNs<ref>
=== State of the art ===
TDNN-based phoneme recognizers compared favourably in early comparisons with HMM-based phone models.<ref name="phoneme detection" /><ref name=":3" /> Modern deep TDNN architectures include many more hidden layers and sub-sample or pool connections over broader contexts at higher layers. They achieve up to 50% word error reduction over [[Mixture model|GMM]]-based acoustic models.<ref name=":4">
== Applications ==
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=== Large vocabulary speech recognition ===
Large vocabulary speech recognition requires recognizing sequences of phonemes that make up words subject to the constraints of a large pronunciation vocabulary. Integration of TDNNs into large vocabulary speech recognizers is possible by introducing state transitions and search between phonemes that make up a word. The resulting Multi-State Time-Delay Neural Network (MS-TDNN) can be trained discriminative from the word level, thereby optimizing the entire arrangement toward word recognition instead of phoneme classification.<ref name=":6" /><ref name=":7">
=== Speaker independence ===
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=== Handwriting recognition ===
TDNNs have been used effectively in compact and high-performance [[handwriting recognition]] systems.<ref>{{Cite journal |last=Guyon |first=I. |last2=Albrecht |first2=P. |last3=Le Cun |first3=Y. |last4=Denker |first4=J. |last5=Hubbard |first5=W. |date=1991-01-01 |title=Design of a neural network character recognizer for a touch terminal |url=https://www.sciencedirect.com/science/article/pii/003132039190081F |journal=Pattern Recognition |volume=24 |issue=2 |pages=105–119 |doi=10.1016/0031-3203(91)90081-F |issn=0031-3203|url-access=subscription }}</ref> Shift-invariance was also adapted to spatial patterns (x/y-axes) in image offline handwriting recognition.<ref name=":2" />
=== Video analysis ===
Video has a temporal dimension that makes a TDNN an ideal solution to analysing motion patterns. An example of this analysis is a combination of vehicle detection and recognizing pedestrians.<ref>
=== Image recognition ===
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* TDNNs can be implemented in virtually all machine-learning frameworks using one-dimensional [[convolutional neural network]]s, due to the equivalence of the methods.
* [[Matlab]]: The neural network toolbox has explicit functionality designed to produce a time delay neural network give the step size of time delays and an optional training function. The default training algorithm is a Supervised Learning back-propagation algorithm that updates filter weights based on the Levenberg-Marquardt optimizations. The function is timedelaynet(delays, hidden_layers, train_fnc) and returns a time-delay neural network architecture that a user can train and provide inputs to.<ref>''"[https://www.mathworks.com/help/deeplearning/time-series-and-dynamic-systems.html Time Series and Dynamic Systems - MATLAB & Simulink]".'' mathworks.com. Retrieved 21 June 2016.</ref>
* The [[Kaldi (software)|Kaldi ASR Toolkit]] has an implementation of TDNNs with several optimizations for speech recognition.<ref>
== See also ==
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== References ==
{{reflist}}
* {{Cite journal |last1=Hampshire |first1=John |last2=Waibel |first2=Alex |orig-date=November 30, 1989 |editor-last=Touretzky |editor-first=David |title=Connectionist Architectures for Multi-Speaker Phoneme Recognition |url=http://papers.nips.cc/paper/213-connectionist-architectures-for-multi-speaker-phoneme-recognition |journal=Advances in Neural Information Processing Systems 2 |date=1990 |page=203-210}}
* {{Cite journal |last=Waibel |first=Alex |date=1987 |orig-date=December |title=Phoneme Recognition Using Time-Delay Neural Networks |url=https://www.researchgate.net/publication/391037926 |journal=Conference: Meeting of the Institute of Electrical, Information and Communication Engineers (IEICE) |___location=Japan}}
[[Category:Neural network architectures]]
[[Category:1987 in artificial intelligence]]
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