Editing Neural network (machine learning) (section)

==History==
{{main|History of artificial neural networks}}

=== Early work ===

Today's deep neural networks are based on early work in [[statistics]] over 200 years ago. The simplest kind of [[feedforward neural network]] (FNN) is a linear network, which consists of a single layer of output nodes with linear activation functions; the inputs are fed directly to the outputs via a series of weights. The sum of the products of the weights and the inputs is calculated at each node. The [[mean squared error]]s between these calculated outputs and the given target values are minimized by creating an adjustment to the weights. This technique has been known for over two centuries as the [[method of least squares]] or [[linear regression]]. It was used as a means of finding a good rough linear fit to a set of points by [[Adrien-Marie Legendre|Legendre]] (1805) and [[Gauss]] (1795) for the prediction of planetary movement.<ref name="legendre1805">Mansfield Merriman, "A List of Writings Relating to the Method of Least Squares"</ref><ref name="gauss1795">{{cite journal |first=Stephen M. |last=Stigler |year=1981 |title=Gauss and the Invention of Least Squares |journal=Ann. Stat. |volume=9 |issue=3 |pages=465–474 |doi=10.1214/aos/1176345451 |doi-access=free }}</ref><ref name=brertscher>{{cite book |last=Bretscher |first=Otto |title=Linear Algebra With Applications |edition=3rd |publisher=Prentice Hall |year=1995 |location=Upper Saddle River, NJ}}</ref><ref name=DLhistory/><ref name=stigler>
{{cite book |last=Stigler |first=Stephen M. |author-link=Stephen Stigler |year=1986 |title=The History of Statistics: The Measurement of Uncertainty before 1900 |location=Cambridge |publisher=Harvard |isbn=0-674-40340-1 |url-access=registration |url=https://archive.org/details/historyofstatist00stig}}</ref>

Historically, digital computers such as the [[von Neumann model]] operate via the execution of explicit instructions with access to memory by a number of processors. Some neural networks, on the other hand, originated from efforts to model information processing in biological systems through the framework of [[connectionism]]. Unlike the von Neumann model, connectionist computing does not separate memory and processing.

[[Warren McCulloch]] and [[Walter Pitts]]<ref name=WM /> (1943) considered a non-learning computational model for neural networks.<ref>{{Cite news |last=Kleene |first=S.C. |year=1956 |title=Representation of Events in Nerve Nets and Finite Automata |url=https://www.degruyter.com/view/books/9781400882618/9781400882618-002/9781400882618-002.xml |access-date=17 June 2017 |work=Annals of Mathematics Studies |publisher=Princeton University Press |pages=3–41 |issue=34 |archive-date=19 May 2024 |archive-url=https://web.archive.org/web/20240519081121/https://www.degruyter.com/view/books/9781400882618/9781400882618-002/9781400882618-002.xml |url-status=live }}</ref> This model paved the way for research to split into two approaches. One approach focused on biological processes while the other focused on the application of neural networks to artificial intelligence.

In the late 1940s, [[Donald O. Hebb|D. O. Hebb]]<ref>{{cite book|url={{google books |plainurl=y |id=ddB4AgAAQBAJ}}|title=The Organization of Behavior|last=Hebb|first=Donald|publisher=Wiley|year=1949|isbn=978-1-135-63190-1|location=New York}}</ref> proposed a learning [[hypothesis]] based on the mechanism of [[Neuroplasticity|neural plasticity]] that became known as [[Hebbian learning]]. It was used in many early neural networks, such as Rosenblatt's [[perceptron]] and the [[Hopfield network]]. Farley and [[Wesley A. Clark|Clark]]<ref>{{cite journal|last=Farley|first=B.G.|author2=W.A. Clark|year=1954|title=Simulation of Self-Organizing Systems by Digital Computer|journal=IRE Transactions on Information Theory|volume=4|issue=4|pages=76–84|doi=10.1109/TIT.1954.1057468}}</ref> (1954) used computational machines to simulate a Hebbian network. Other neural network computational machines were created by [[Nathaniel Rochester (computer scientist)|Rochester]], Holland, Habit and Duda (1956).<ref>{{cite journal|last=Rochester|first=N.|author2=J.H. Holland|author3=L.H. Habit|author4=W.L. Duda|year=1956|title=Tests on a cell assembly theory of the action of the brain, using a large digital computer|journal=IRE Transactions on Information Theory|volume=2|issue=3|pages=80–93|doi=10.1109/TIT.1956.1056810}}</ref> 

In 1958, psychologist [[Frank Rosenblatt]] described the perceptron, one of the first implemented artificial neural networks,<ref>Haykin (2008) Neural Networks and Learning Machines, 3rd edition</ref><ref>{{cite journal|last=Rosenblatt|first=F.|title=The Perceptron: A Probabilistic Model For Information Storage And Organization in the Brain|journal=Psychological Review|year=1958|volume=65|pages=386–408|doi=10.1037/h0042519|pmid=13602029|issue=6|citeseerx=10.1.1.588.3775|s2cid=12781225 }}</ref><ref name="Werbos 1975">{{cite book|url={{google books |plainurl=y |id=z81XmgEACAAJ}}|title=Beyond Regression: New Tools for Prediction and Analysis in the Behavioral Sciences|last=Werbos|first=P.J.|year=1975}}</ref><ref>{{cite journal |last=Rosenblatt |first=Frank |year=1957 |title=The Perceptron—a perceiving and recognizing automaton |journal=Report 85-460-1 |publisher=Cornell Aeronautical Laboratory }}</ref> funded by the United States [[Office of Naval Research]].<ref name="Olazaran">{{cite journal |first=Mikel |last=Olazaran |title=A Sociological Study of the Official History of the Perceptrons Controversy |journal=Social Studies of Science |volume=26 |issue=3 |year=1996 |jstor=285702|doi=10.1177/030631296026003005 |pages=611–659|s2cid=16786738 }}</ref>
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> mentions an even earlier perceptron-like device by Farley and Clark:<ref name="DLhistory"/> "Farley and Clark of MIT Lincoln Laboratory actually preceded Rosenblatt in the development of a perceptron-like device." However, "they dropped the subject."
The perceptron raised public excitement for research in Artificial Neural Networks, causing the US government to drastically increase funding. This contributed to "the Golden Age of AI" fueled by the optimistic claims made by computer scientists regarding the ability of perceptrons to emulate human intelligence.<ref name=":08">{{Cite book |author=Russel, Stuart |author2=Norvig, Peter |url=https://people.engr.tamu.edu/guni/csce421/files/AI_Russell_Norvig.pdf |title=Artificial Intelligence A Modern Approach |publisher=Pearson Education |year=2010 |isbn=978-0-13-604259-4 |edition=3rd |location=United States of America |pages=16–28 |language=en}}</ref>

The first perceptrons did not have adaptive hidden units. However, Joseph (1960)<ref name="joseph1960"/> also discussed [[multilayer perceptrons]] with an adaptive hidden layer. Rosenblatt (1962)<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}} cited and adopted these ideas, also crediting work by H. D. Block and B. W. Knight. Unfortunately, these early efforts did not lead to a working learning algorithm for hidden units, i.e., [[deep learning]].

=== Deep learning breakthroughs in the 1960s and 1970s===
Fundamental research was conducted on ANNs in the 1960s and 1970s. 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 the [[Soviet Union]] (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.<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 |archive-date=12 August 2024 |access-date=7 August 2024 |archive-url=https://web.archive.org/web/20240812123448/https://linkinghub.elsevier.com/retrieve/pii/0005109870900920 |url-status=live }}</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=5 November 2019|archive-date=29 August 2017|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">{{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>

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"/> Subsequent developments in hardware and hyperparameter tunings have made end-to-end stochastic gradient descent the currently dominant training technique.

In 1969, [[Kunihiko Fukushima]] introduced the [[rectifier (neural networks)|ReLU]] (rectified linear unit) activation function.<ref name="DLhistory" /><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> 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=16 October 2017 |last3=Quoc |first3=V. Le}}</ref>

Nevertheless, research stagnated in the United States following the work of [[Marvin Minsky|Minsky]] and [[Seymour Papert|Papert]] (1969),<ref name=":132">{{cite book |last1=Minsky |first1=Marvin |url={{google books |plainurl=y |id=Ow1OAQAAIAAJ}} |title=Perceptrons: An Introduction to Computational Geometry |last2=Papert |first2=Seymour |publisher=MIT Press |year=1969 |isbn=978-0-262-63022-1}}</ref> who emphasized that basic perceptrons were incapable of processing the exclusive-or circuit. This insight was irrelevant for the deep networks of Ivakhnenko (1965) and Amari (1967).

In 1976 transfer learning was introduced in neural networks learning.<ref>Bozinovski S. and Fulgosi A. (1976). "The influence of pattern similarity and transfer learning on the base perceptron training" (original in Croatian) Proceedings of Symposium Informatica 3-121-5, Bled.</ref><ref>Bozinovski S.(2020) "Reminder of the first paper on transfer learning in neural networks, 1976". Informatica 44: 291–302.</ref>

Deep learning architectures for [[convolutional neural network]]s (CNNs) with convolutional layers and downsampling layers and weight replication 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><ref name="SCHIDHUB4"/>

=== Backpropagation ===
[[Backpropagation]] is an efficient application of the [[chain rule]] derived by [[Gottfried Wilhelm Leibniz]] in 1673<ref name="leibniz16762">{{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="kelley19602">{{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> In 1970, [[Seppo Linnainmaa]] published the modern form of backpropagation in his Master's [[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><ref name=":1">{{Cite book |url=https://direct.mit.edu/books/book/4886/Talking-NetsAn-Oral-History-of-Neural-Networks |title=Talking Nets: An Oral History of Neural Networks |date=2000 |publisher=The MIT Press |isbn=978-0-262-26715-1 |editor-last=Anderson |editor-first=James A. |language=en |doi=10.7551/mitpress/6626.003.0016 |editor-last2=Rosenfeld |editor-first2=Edward |archive-date=12 October 2024 |access-date=7 August 2024 |archive-url=https://archive.today/20241012223136/https://direct.mit.edu/books/book/4886/Talking-NetsAn-Oral-History-of-Neural-Networks |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 October 2014 | access-date = 14 September 2024 | archive-url = https://web.archive.org/web/20240730110408/https://people.idsia.ch/~juergen/who-invented-backpropagation.html | archive-date = 30 July 2024 | quote =  | url-status = live }}</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 |archive-date=8 March 2021 |access-date=17 March 2021 |archive-url=https://web.archive.org/web/20210308045630/https://www.nature.com/articles/323533a0 |url-status=live }}</ref>

=== Convolutional neural networks ===
Kunihiko Fukushima's [[convolutional neural network]] (CNN) architecture of 1979<ref name="FUKU1979"/> also introduced [[max pooling]],<ref>{{Cite journal |last1=Fukushima |first1=Kunihiko |last2=Miyake |first2=Sei |date=1 January 1982 |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 |archive-date=12 October 2024 |access-date=9 September 2024 |archive-url=https://archive.today/20241012232918/https://www.sciencedirect.com/science/article/abs/pii/0031320382900243 |url-status=live }}</ref> a popular downsampling procedure for CNNs. CNNs have become an essential tool for [[computer vision]].

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 |access-date=20 September 2024 |archive-date=17 September 2024 |archive-url=https://web.archive.org/web/20240917173146/https://isl.anthropomatik.kit.edu/pdf/Waibel1987a.pdf |url-status=live }}</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] {{Webarchive|url=https://web.archive.org/web/20241211184304/https://www.inf.ufrgs.br/~engel/data/media/file/cmp121/waibel89_TDNN.pdf |date=11 December 2024 }}'' 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 |archive-date=23 June 2020 |access-date=12 April 2023 |archive-url=https://web.archive.org/web/20200623051222/https://drive.google.com/file/d/1nN_5odSG_QVae54EsQN_qSz-0ZsX6wA0/view?usp=sharing |url-status=live }}</ref>
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 |archive-date=6 February 2017 |access-date=12 April 2023 |archive-url=https://web.archive.org/web/20170206111407/https://drive.google.com/file/d/0B65v6Wo67Tk5ODRzZmhSR29VeDg/view?usp=sharing |url-status=live }}</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 |archive-date=19 June 2024 |access-date=20 September 2024 |archive-url=https://web.archive.org/web/20240619084309/https://drive.google.com/file/d/0B65v6Wo67Tk5cm5DTlNGd0NPUmM/view?usp=sharing |url-status=live }}</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 |archive-date=20 June 2024 |access-date=20 September 2024 |archive-url=https://web.archive.org/web/20240620055642/https://drive.google.com/file/d/0B65v6Wo67Tk5Ml9qeW5nQ3poVTQ/view?usp=sharing |url-status=live }}</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 32×32 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=7 October 2016 |archive-date=30 October 2023 |archive-url=https://web.archive.org/web/20231030100650/http://yann.lecun.com/exdb/publis/pdf/lecun-01a.pdf |url-status=dead }}</ref>

From 1988 onward,<ref name="Qian1988">Qian, Ning, and Terrence J. Sejnowski. "Predicting the secondary structure of globular proteins using neural network models." ''Journal of molecular biology'' 202, no. 4 (1988): 865–884.</ref><ref name="Bohr1988">Bohr, Henrik, Jakob Bohr, Søren Brunak, Rodney MJ Cotterill, Benny Lautrup, Leif Nørskov, Ole H. Olsen, and Steffen B. Petersen. "Protein secondary structure and homology by neural networks The α-helices in rhodopsin." ''FEBS letters'' 241, (1988): 223–228</ref> the use of neural networks transformed the field of [[protein structure prediction]], in particular when the first cascading networks were trained on ''profiles'' (matrices) produced by multiple [[sequence alignment]]s.<ref name="Rost1993">Rost, Burkhard, and Chris Sander. "Prediction of protein secondary structure at better than 70% accuracy." ''Journal of molecular biology'' 232, no. 2 (1993): 584–599.</ref>

=== Recurrent neural networks ===
One origin of RNN was [[statistical mechanics]]. In 1972, [[Shun'ichi Amari]] proposed to modify the weights of an [[Ising model]] by [[Hebbian theory|Hebbian learning]] rule as a model of [[Hopfield network|associative memory]], adding in the component of learning.<ref>{{Cite journal |last=Amari |first=S.-I. |date=November 1972 |title=Learning Patterns and Pattern Sequences by Self-Organizing Nets of Threshold Elements |url=https://ieeexplore.ieee.org/document/1672070 |journal=IEEE Transactions on Computers |volume=C-21 |issue=11 |pages=1197–1206 |doi=10.1109/T-C.1972.223477 |issn=0018-9340 |archive-date=12 October 2024 |access-date=7 August 2024 |archive-url=https://archive.today/20241012222852/https://ieeexplore.ieee.org/document/1672070 |url-status=live }}</ref> This was popularized as the Hopfield network by [[John Hopfield]] (1982).<ref name="Hopfield19822">{{cite journal |last1=Hopfield |first1=J. J. |date=1982 |title=Neural networks and physical systems with emergent collective computational abilities |journal=Proceedings of the National Academy of Sciences |volume=79 |issue=8 |pages=2554–2558 |bibcode=1982PNAS...79.2554H |doi=10.1073/pnas.79.8.2554 |pmc=346238 |pmid=6953413 |doi-access=free}}</ref> Another origin of RNN was neuroscience. The word "recurrent" is used to describe loop-like structures in anatomy. In 1901, [[Santiago Ramón y Cajal|Cajal]] observed "recurrent semicircles" in the [[Cerebellum|cerebellar cortex]].<ref>{{Cite journal |last1=Espinosa-Sanchez |first1=Juan Manuel |last2=Gomez-Marin |first2=Alex |last3=de Castro |first3=Fernando |date=5 July 2023 |title=The Importance of Cajal's and Lorente de Nó's Neuroscience to the Birth of Cybernetics |url=http://journals.sagepub.com/doi/10.1177/10738584231179932 |journal=The Neuroscientist |volume=31 |issue=1 |pages=14–30 |language=en |doi=10.1177/10738584231179932 |issn=1073-8584 |pmid=37403768 |hdl=10261/348372 |hdl-access=free |archive-date=12 October 2024 |access-date=7 August 2024 |archive-url=https://archive.today/20241012221924/http://journals.sagepub.com/doi/10.1177/10738584231179932 |url-status=live }}</ref> [[Donald O. Hebb|Hebb]] considered "reverberating circuit" as an explanation for short-term memory.<ref>{{Cite web |title=reverberating circuit |url=https://www.oxfordreference.com/display/10.1093/oi/authority.20110803100417461 |access-date=27 July 2024 |website=Oxford Reference |archive-date=12 October 2024 |archive-url=https://archive.today/20241012222600/https://www.oxfordreference.com/display/10.1093/oi/authority.20110803100417461 |url-status=live }}</ref> The McCulloch and Pitts paper (1943) considered neural networks that contain cycles, and noted that the current activity of such networks can be affected by activity indefinitely far in the past.<ref name=WM>{{Cite journal |last1=McCulloch |first1=Warren S. |last2=Pitts |first2=Walter |date=December 1943 |title=A logical calculus of the ideas immanent in nervous activity |url=http://link.springer.com/10.1007/BF02478259 |journal=The Bulletin of Mathematical Biophysics |volume=5 |issue=4 |pages=115–133 |doi=10.1007/BF02478259 |issn=0007-4985 |archive-date=12 October 2024 |access-date=7 August 2024 |archive-url=https://archive.today/20241012221923/http://link.springer.com/10.1007/BF02478259 |url-status=live }}</ref>

In 1982 a recurrent neural network with an array architecture (rather than a multilayer perceptron architecture), namely a Crossbar Adaptive Array,<ref name="CAA1982"> Bozinovski, S. (1982). "A self-learning system using secondary reinforcement". In Trappl, Robert (ed.). Cybernetics and Systems Research: Proceedings of the Sixth European Meeting on Cybernetics and Systems Research. North-Holland. pp. 397–402. ISBN 978-0-444-86488-8</ref><ref name="" "caa1995"="">Bozinovski S. (1995) "Neuro genetic agents and structural theory of self-reinforcement learning systems". CMPSCI Technical Report 95-107, University of Massachusetts at Amherst [https://web.cs.umass.edu/publication/docs/1995/UM-CS-1995-107.pdf] {{Webarchive|url=https://web.archive.org/web/20241008120651/https://web.cs.umass.edu/publication/docs/1995/UM-CS-1995-107.pdf |date=8 October 2024 }}</ref> used direct recurrent connections from the output to the supervisor (teaching) inputs. In addition of computing actions (decisions), it computed internal state evaluations (emotions) of the consequence situations. Eliminating the external supervisor, it introduced the self-learning method in neural networks.  

In cognitive psychology, the journal American Psychologist in early 1980's carried out a debate on the relation between cognition and emotion. Zajonc in 1980 stated that emotion is computed first and is independent from cognition, while Lazarus in 1982 stated that cognition is computed first and is inseparable from emotion.<ref>R. Zajonc (1980) "Feeling and thinking: Preferences need no inferences". American Psychologist 35 (2): 151-175</ref><ref>Lazarus R. (1982) "Thoughts on the relations between emotion and cognition" American Psychologist 37 (9): 1019-1024</ref> In 1982 the Crossbar Adaptive Array gave a neural network model of cognition-emotion relation.<ref name = "CAA1982" /><ref>Bozinovski, S. (2014) "Modeling mechanisms of cognition-emotion interaction in artificial neural networks, since 1981" Procedia Computer Science p. 255-263 (https://core.ac.uk/download/pdf/81973924.pdf {{Webarchive|url=https://web.archive.org/web/20190323204838/https://core.ac.uk/download/pdf/81973924.pdf |date=23 March 2019 }})</ref> It was an example of a debate where an AI system, a recurrent neural network, contributed to an issue in the same time addressed by cognitive psychology.

Two early influential works were the [[Recurrent neural network#Jordan network|Jordan network]] (1986) and the [[Recurrent neural network#Elman network|Elman network]] (1990), which applied RNN to study [[cognitive psychology]]. 

In the 1980s, backpropagation did not work well for deep RNNs. To overcome this problem, in 1991, [[Jürgen Schmidhuber]] proposed the "neural sequence chunker" or "neural history compressor"<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 |archive-date=14 September 2024 |access-date=21 September 2024 |archive-url=https://web.archive.org/web/20240914162750/https://people.idsia.ch/~juergen/FKI-148-91ocr.pdf |url-status=live }}</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 |archive-date=14 September 2024 |access-date=21 September 2024 |archive-url=https://web.archive.org/web/20240914162750/https://sferics.idsia.ch/pub/juergen/chunker.pdf |url-status=live }}</ref> which introduced the important concepts of self-supervised pre-training (the "P" in [[ChatGPT]]) and neural [[knowledge distillation]].<ref name=DLhistory/> In 1993, a neural history compressor system solved a "Very Deep Learning" task that required more than 1000 subsequent [[Layer (deep learning)|layers]] in an RNN unfolded in time.<ref name="schmidhuber19932">{{Cite book |last=Schmidhuber |first=Jürgen |url=https://sferics.idsia.ch/pub/juergen/habilitation.pdf |title=Habilitation thesis: System modeling and optimization |year=1993 |archive-date=7 August 2024 |access-date=21 September 2024 |archive-url=https://web.archive.org/web/20240807084323/https://sferics.idsia.ch/pub/juergen/habilitation.pdf |url-status=live }} Page 150 ff demonstrates credit assignment across the equivalent of 1,200 layers in an unfolded RNN.</ref>

In 1991, [[Sepp Hochreiter]]'s diploma thesis<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=6 March 2015}}, ''Diploma thesis. Institut f. Informatik, Technische Univ. Munich. Advisor: J. Schmidhuber'', 1991.</ref> identified and analyzed the [[vanishing gradient problem]]<ref name="HOCH1991" /><ref name="HOCH2001">{{cite book |last=Hochreiter |first=S. |title=A Field Guide to Dynamical Recurrent Networks |date=15 January 2001 |publisher=John Wiley & Sons |isbn=978-0-7803-5369-5 |editor-last1=Kolen |editor-first1=John F. |chapter=Gradient flow in recurrent nets: the difficulty of learning long-term dependencies |display-authors=etal |editor-last2=Kremer |editor-first2=Stefan C. |chapter-url=https://books.google.com/books?id=NWOcMVA64aAC |access-date=26 June 2017 |archive-date=19 May 2024 |archive-url=https://web.archive.org/web/20240519081124/https://books.google.com/books?id=NWOcMVA64aAC |url-status=live }}</ref> and proposed recurrent [[Residual neural network|residual]] connections to solve it. He and Schmidhuber introduced [[long short-term memory]] (LSTM), which set accuracy records in multiple applications domains.<ref>{{Cite Q|Q98967430}}</ref><ref name="lstm2">{{Cite journal |last1=Hochreiter |first1=Sepp |author-link=Sepp Hochreiter |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 |pmid=9377276 |s2cid=1915014}}</ref> This was not yet the modern version of LSTM, which required the forget gate, which was introduced in 1999.<ref name="lstm1999">{{Cite book |last1=Gers |first1=Felix |title=9th International Conference on Artificial Neural Networks: ICANN '99 |last2=Schmidhuber |first2=Jürgen |last3=Cummins |first3=Fred |year=1999 |isbn=0-85296-721-7 |volume=1999 |pages=850–855 |chapter=Learning to forget: Continual prediction with LSTM |doi=10.1049/cp:19991218}}</ref> It became the default choice for RNN architecture.

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=1 January 1985 |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 |archive-date=17 September 2024 |access-date=7 August 2024 |archive-url=https://web.archive.org/web/20240917124802/https://www.sciencedirect.com/science/article/pii/S0364021385800124 |url-status=live }}</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 |archive-date=14 July 2023 |access-date=7 August 2024 |archive-url=https://web.archive.org/web/20230714174222/https://stanford.edu/~jlmcc/papers/PDP/Volume%201/Chap6_PDP86.pdf |url-status=live }}</ref> [[Helmholtz machine]],<ref name="“nc95“">{{Cite journal |last1=Peter |first1=Dayan |author-link1=Peter Dayan |last2=Hinton |first2=Geoffrey E. |author-link2=Geoffrey Hinton |last3=Neal |first3=Radford M. |author-link3=Radford M. Neal |last4=Zemel |first4=Richard S. |author-link4=Richard Zemel |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 |hdl=21.11116/0000-0002-D6D3-E}} {{closed access}}</ref> and the [[wake-sleep algorithm]].<ref name=":13">{{Cite journal |last1=Hinton |first1=Geoffrey E. |author-link=Geoffrey Hinton |last2=Dayan |first2=Peter |author-link2=Peter Dayan |last3=Frey |first3=Brendan J. |author-link3=Brendan Frey |last4=Neal |first4=Radford |date=26 May 1995 |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}}</ref> These were designed for unsupervised learning of deep generative models.

=== Deep learning ===
Between 2009 and 2012, ANNs began winning prizes in image recognition contests, approaching human level performance on various tasks, initially in [[pattern recognition]] and [[handwriting recognition]].<ref>[http://www.kurzweilai.net/how-bio-inspired-deep-learning-keeps-winning-competitions 2012 Kurzweil AI Interview] {{Webarchive|url=https://web.archive.org/web/20180831075249/http://www.kurzweilai.net/how-bio-inspired-deep-learning-keeps-winning-competitions |date=31 August 2018 }} with Juergen Schmidhuber on the eight competitions won by his Deep Learning team 2009–2012</ref><ref>{{Cite web|url=http://www.kurzweilai.net/how-bio-inspired-deep-learning-keeps-winning-competitions|title=How bio-inspired deep learning keeps winning competitions {{!}} KurzweilAI|website=kurzweilai.net|access-date=16 June 2017|archive-url=https://web.archive.org/web/20180831075249/http://www.kurzweilai.net/how-bio-inspired-deep-learning-keeps-winning-competitions|archive-date=31 August 2018}}</ref> In 2011, a CNN named ''DanNet<ref name=":32">{{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=":62">{{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 |url-status=live |journal=International Joint Conference on Artificial Intelligence |doi=10.5591/978-1-57735-516-8/ijcai11-210 |archive-url=https://web.archive.org/web/20140929094040/http://ijcai.org/papers11/Papers/IJCAI11-210.pdf |archive-date=29 September 2014 |access-date=13 June 2017}}</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="SCHIDHUB4">{{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 |pmid=25462637 |s2cid=11715509}}</ref> It then won more contests.<ref name=":82">{{Cite book |last1=Ciresan |first1=Dan |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 |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 |access-date=13 June 2017 |editor-last2=Burges |editor-first2=C. J. C. |editor-last3=Bottou |editor-first3=L. |editor-last4=Weinberger |editor-first4=K. Q. |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 |archive-date=9 August 2017 |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">{{Cite book |last1=Ciresan |first1=D. |title=2012 IEEE Conference on Computer Vision and Pattern Recognition |last2=Meier |first2=U. |last3=Schmidhuber |first3=J. |year=2012 |isbn=978-1-4673-1228-8 |pages=3642–3649 |chapter=Multi-column deep neural networks for image classification |doi=10.1109/cvpr.2012.6248110 |arxiv=1202.2745 |s2cid=2161592}}</ref>

In October 2012, [[AlexNet]] by [[Alex Krizhevsky]], [[Ilya Sutskever]], and Geoffrey Hinton<ref name="krizhevsky20122">{{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 |url-status=live |journal=NIPS 2012: Neural Information Processing Systems, Lake Tahoe, Nevada |archive-url=https://web.archive.org/web/20170110123024/http://www.cs.toronto.edu/~kriz/imagenet_classification_with_deep_convolutional.pdf |archive-date=10 January 2017 |access-date=24 May 2017}}</ref> won the large-scale [[ImageNet competition]] by a significant margin over shallow machine learning methods. Further incremental improvements included the VGG-16 network by [[Karen Simonyan (scientist)|Karen Simonyan]] and [[Andrew Zisserman]]<ref name="VGG">{{cite arXiv |eprint=1409.1556 |class=cs.CV |first1=Karen |last1=Simonyan |first2=Zisserman |last2=Andrew |title=Very Deep Convolution Networks for Large Scale Image Recognition |year=2014}}</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 |archive-date=30 September 2024 |access-date=7 August 2024 |archive-url=https://web.archive.org/web/20240930225513/https://static.googleusercontent.com/media/research.google.com/en//pubs/archive/43022.pdf |url-status=live }}</ref>

In 2012, [[Andrew Ng|Ng]] and [[Jeff Dean (computer scientist)|Dean]] created a network that learned to recognize higher-level concepts, such as cats, only from watching unlabeled images.<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> Unsupervised pre-training and increased computing power from [[GPU]]s and [[distributed computing]] allowed the use of larger networks, particularly in image and visual recognition problems, which became known as "deep learning".<ref name=":4" />

[[Radial basis function network|Radial basis function]] and wavelet networks were introduced in 2013. These can be shown to offer best approximation properties and have been applied in [[nonlinear system identification]] and classification applications.<ref name="SAB1" />

[[Generative adversarial network]] (GAN) ([[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> became state of the art in generative modeling during 2014–2018 period. The GAN principle was originally published in 1991 by Jürgen Schmidhuber who called it "artificial curiosity": two neural networks 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="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> 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. Excellent image quality is achieved by [[Nvidia]]'s [[StyleGAN]] (2018)<ref name="SyncedReview201822">{{Cite web |date=14 December 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=3 October 2019 |website=SyncedReview.com |archive-date=12 September 2024 |archive-url=https://web.archive.org/web/20240912080503/https://syncedreview.com/2018/12/14/gan-2-0-nvidias-hyperrealistic-face-generator/ |url-status=live }}</ref> based on the Progressive GAN by Tero Karras et al.<ref name="progressiveGAN201722">{{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|deepfakes]].<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|Diffusion models]] (2015)<ref>{{Cite journal |last1=Sohl-Dickstein |first1=Jascha |last2=Weiss |first2=Eric |last3=Maheswaranathan |first3=Niru |last4=Ganguli |first4=Surya |date=1 June 2015 |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 |archive-date=21 September 2024 |access-date=7 August 2024 |archive-url=https://web.archive.org/web/20240921065319/http://proceedings.mlr.press/v37/sohl-dickstein15.pdf |url-status=live }}</ref> eclipsed GANs in generative modeling since then, with systems such as [[DALL·E 2]] (2022) and [[Stable Diffusion]] (2022).

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=10 April 2015 |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="prelu2">{{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="resnet2">{{Cite conference |last1=He |first1=Kaiming |last2=Zhang |first2=Xiangyu |last3=Ren |first3=Shaoqing |last4=Sun |first4=Jian |date=10 December 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,<ref name="highway20153">{{cite arXiv |eprint=1505.00387 |class=cs.LG |first1=Rupesh Kumar |last1=Srivastava |first2=Klaus |last2=Greff |title=Highway Networks |date=2 May 2015 |last3=Schmidhuber |first3=Jürgen}}</ref> and the residual neural network (ResNet) in December 2015.<ref name="resnet20153">{{Cite conference |last1=He |first1=Kaiming |last2=Zhang |first2=Xiangyu |last3=Ren |first3=Shaoqing |last4=Sun |first4=Jian |date=2016 |title=Deep Residual Learning for Image Recognition |url=https://ieeexplore.ieee.org/document/7780459 |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 |journal=2016 IEEE Conference on Computer Vision and Pattern Recognition (CVPR) |access-date=15 April 2023 |archive-date=7 October 2024 |archive-url=https://web.archive.org/web/20241007202422/https://ieeexplore.ieee.org/document/7780459 |url-status=live }}</ref><ref>{{Cite web |last=Linn |first=Allison |date=10 December 2015 |title=Microsoft researchers win ImageNet computer vision challenge |url=https://blogs.microsoft.com/ai/microsoft-researchers-win-imagenet-computer-vision-challenge/ |access-date=29 June 2024 |website=The AI Blog |language=en-US |archive-date=21 May 2023 |archive-url=https://archive.today/20230521191955/https://blogs.microsoft.com/ai/microsoft-researchers-win-imagenet-computer-vision-challenge/ |url-status=live }}</ref> ResNet behaves like an open-gated Highway Net. 

{{Main|Transformer (deep learning architecture)#History}}

During the 2010s, the [[seq2seq]] model was developed, and attention mechanisms were added. It led to the modern Transformer architecture in 2017 in ''[[Attention Is All You Need]]''.<ref name="vaswani2017">{{cite arXiv |eprint=1706.03762 |class=cs.CL |first1=Ashish |last1=Vaswani |first2=Noam |last2=Shazeer |title=Attention Is All You Need |date=12 June 2017 |last8=Polosukhin |first8=Illia |last7=Kaiser |first7=Lukasz |last6=Gomez |first6=Aidan N. |last5=Jones |first5=Llion |last4=Uszkoreit |first4=Jakob |last3=Parmar |first3=Niki}}</ref>
It requires computation time that is quadratic in the size of the context window. Jürgen Schmidhuber's fast weight controller (1992)<ref name="transform19922">{{cite journal |last1=Schmidhuber |first1=Jürgen |author-link1=Jürgen Schmidhuber |date=1992 |title=Learning to control fast-weight memories: an alternative to recurrent nets. |url=https://archive.org/download/wikipedia-scholarly-sources-corpus/10.1162.zip/10.1162%252Fneco.1992.4.1.131.pdf |journal=Neural Computation |volume=4 |issue=1 |pages=131–139 |doi=10.1162/neco.1992.4.1.131 |s2cid=16683347}}</ref> scales linearly and was later shown to be equivalent to the unnormalized linear Transformer.<ref name="fastlinear20202">{{cite conference |last1=Katharopoulos |first1=Angelos |last2=Vyas |first2=Apoorv |last3=Pappas |first3=Nikolaos |last4=Fleuret |first4=François |date=2020 |title=Transformers are RNNs: Fast autoregressive Transformers with linear attention |url=https://paperswithcode.com/paper/a-decomposable-attention-model-for-natural |publisher=PMLR |pages=5156–5165 |book-title=ICML 2020 |access-date=21 September 2024 |archive-date=11 July 2023 |archive-url=https://web.archive.org/web/20230711021546/https://paperswithcode.com/paper/a-decomposable-attention-model-for-natural |url-status=live }}</ref><ref name="schlag20212">{{cite conference |last1=Schlag |first1=Imanol |last2=Irie |first2=Kazuki |last3=Schmidhuber |first3=Jürgen |author-link3=Juergen Schmidhuber |date=2021 |title=Linear Transformers Are Secretly Fast Weight Programmers |publisher=Springer |pages=9355–9366 |book-title=ICML 2021}}</ref><ref name="DLhistory" />
Transformers have increasingly become the model of choice for [[natural language processing]].<ref name="wolf2020">{{cite book |last1=Wolf |first1=Thomas |title=Proceedings of the 2020 Conference on Empirical Methods in Natural Language Processing: System Demonstrations |last2=Debut |first2=Lysandre |last3=Sanh |first3=Victor |last4=Chaumond |first4=Julien |last5=Delangue |first5=Clement |last6=Moi |first6=Anthony |last7=Cistac |first7=Pierric |last8=Rault |first8=Tim |last9=Louf |first9=Remi |year=2020 |pages=38–45 |chapter=Transformers: State-of-the-Art Natural Language Processing |doi=10.18653/v1/2020.emnlp-demos.6 |last10=Funtowicz |first10=Morgan |last11=Davison |first11=Joe |last12=Shleifer |first12=Sam |last13=von Platen |first13=Patrick |last14=Ma |first14=Clara |last15=Jernite |first15=Yacine |last16=Plu |first16=Julien |last17=Xu |first17=Canwen |last18=Le Scao |first18=Teven |last19=Gugger |first19=Sylvain |last20=Drame |first20=Mariama |last21=Lhoest |first21=Quentin |last22=Rush |first22=Alexander |s2cid=208117506}}</ref> Many modern [[large language model]]s such as [[ChatGPT]], [[GPT-4]], and [[BERT (language model)|BERT]] use this architecture.