History of artificial neural networks

{{main|Perceptron}}

The simplest feedforward network consists of a single weight layer without activation functions. It would be just a linear map, and training it would be linear regression. Linear regression by least squares method was used by Adrien-Marie Legendre (1805) and Carl Friedrich Gauss (1795) for the prediction of planetary movement.Merriman, Mansfield. A List of Writings Relating to the Method of Least Squares: With Historical and Critical Notes. Vol. 4. Academy, 1877.{{cite journal |last=Stigler |first=Stephen M. |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}}{{cite book |last=Bretscher |first=Otto |title=Linear Algebra With Applications |publisher=Prentice Hall |year=1995 |edition=3rd |location=Upper Saddle River, NJ}}{{cite book |last=Stigler |first=Stephen M. |author-link=Stephen Stigler |url=https://archive.org/details/historyofstatist00stig |title=The History of Statistics: The Measurement of Uncertainty before 1900 |publisher=Harvard |year=1986 |isbn=0-674-40340-1 |location=Cambridge |url-access=registration}}

A Logical Calculus of the Ideas Immanent in Nervous Activity (Warren McCulloch and Walter Pitts, 1943) studied several abstract models for neural networks using symbolic logic of Rudolf Carnap and Principia Mathematica. The paper argued that several abstract models of neural networks (some learning, some not learning) have the same computational power as Turing machines.{{cite journal |last1=McCulloch |first1=Warren |author-link=Warren Sturgis McCulloch |last2=Pitts |first2=Walter |author-link2=Walter Pitts |year=1943 |title=A Logical Calculus of Ideas Immanent in Nervous Activity |url=https://link.springer.com/article/10.1007/BF02478259 |journal=Bulletin of Mathematical Biophysics |volume=5 |issue=4 |pages=115–133 |doi=10.1007/BF02478259 |pmid=|url-access=subscription }} 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. This work led to work on nerve networks and their link to finite automata.{{Citation |last=Kleene |first=S. C. |title=Representation of Events in Nerve Nets and Finite Automata |date=1956-12-31 |work=Automata Studies. (AM-34) |pages=3–42 |editor-last=Shannon |editor-first=C. E. |url=https://www.degruyter.com/document/doi/10.1515/9781400882618-002/html |access-date=2024-10-14 |publisher=Princeton University Press |doi=10.1515/9781400882618-002 |isbn=978-1-4008-8261-8 |editor2-last=McCarthy |editor2-first=J.|url-access=subscription }}

In the early 1940s, D. O. Hebb{{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}} created a learning hypothesis based on the mechanism of neural plasticity that became known as Hebbian learning. Hebbian learning is unsupervised learning. This evolved into models for long-term potentiation. Researchers started applying these ideas to computational models in 1948 with Turing's B-type machines. B. Farley and Wesley A. Clark{{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}} (1954) first used computational machines, then called "calculators", to simulate a Hebbian network. Other neural network computational machines were created by Rochester, Holland, Habit and Duda (1956).{{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}}

Frank Rosenblatt (1958) created the perceptron, an algorithm for pattern recognition. A multilayer perceptron (MLP) comprised 3 layers: an input layer, a hidden layer with randomized weights that did not learn, and an output layer. With mathematical notation, Rosenblatt described circuitry not in the basic perceptron, such as the exclusive-or circuit that could not be processed by neural networks at the time. In 1959, a biological model proposed by Nobel laureates Hubel and Wiesel was based on their discovery of two types of cells in the primary visual cortex: simple cells and complex cells.{{cite book|url={{google books |plainurl=y |id=8YrxWojxUA4C|page=106}}|title=Brain and visual perception: the story of a 25-year collaboration|author=David H. Hubel and Torsten N. Wiesel|publisher=Oxford University Press US|year=2005|isbn=978-0-19-517618-6|page=106}} He later published a 1962 book also introduced variants and computer experiments, including a version with four-layer perceptrons where the last two layers have learned weights (and thus a proper multilayer perceptron).{{cite book |last=Rosenblatt |first=Frank |author-link=Frank Rosenblatt |title=Principles of Neurodynamics |publisher=Spartan, New York |year=1962}}{{rp|section 16}} Some consider that the 1962 book developed and explored all of the basic ingredients of the deep learning systems of today.{{cite book |last1=Tappert |first1=Charles C. |title=2019 International Conference on Computational Science and Computational Intelligence (CSCI) |publisher=IEEE |year=2019 |isbn=978-1-7281-5584-5 |pages=343–348 |chapter=Who Is the Father of Deep Learning? |doi=10.1109/CSCI49370.2019.00067 |access-date=31 May 2021 |chapter-url=https://ieeexplore.ieee.org/document/9070967 |s2cid=216043128}}

Some say that research stagnated following Marvin Minsky and Papert Perceptrons (1969).{{cite book|url={{google books |plainurl=y |id=Ow1OAQAAIAAJ}}|title=Perceptrons: An Introduction to Computational Geometry|last1=Minsky|first1=Marvin|last2=Papert|first2=Seymour|publisher=MIT Press|year=1969|isbn=978-0-262-63022-1}}

Group method of data handling, a method to train arbitrarily deep neural networks was published by Alexey Ivakhnenko and Lapa in 1967, which they regarded as a form of polynomial regression,{{cite book |last1=Ivakhnenko |first1=A. G. |url={{google books |plainurl=y |id=rGFgAAAAMAAJ}} |title=Cybernetics and Forecasting Techniques |last2=Lapa |first2=V. G. |publisher=American Elsevier Publishing Co. |year=1967 |isbn=978-0-444-00020-0}} or a generalization of Rosenblatt's perceptron.{{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|url-access=subscription }} A 1971 paper described a deep network with eight layers trained by this method.{{Cite journal |last=Ivakhnenko |first=Alexey |date=1971 |title=Polynomial theory of complex systems |url=http://gmdh.net/articles/history/polynomial.pdf |url-status=live |journal=IEEE Transactions on Systems, Man, and Cybernetics |volume=SMC-1 |issue=4 |pages=364–378 |doi=10.1109/TSMC.1971.4308320 |archive-url=https://web.archive.org/web/20170829230621/http://www.gmdh.net/articles/history/polynomial.pdf |archive-date=2017-08-29 |access-date=2019-11-05}}

The first deep learning multilayer perceptron trained by stochastic gradient descent{{Cite journal |last1=Robbins |first1=H. |author-link=Herbert Robbins |last2=Monro |first2=S. |year=1951 |title=A Stochastic Approximation Method |journal=The Annals of Mathematical Statistics |volume=22 |issue=3 |pages=400 |doi=10.1214/aoms/1177729586 |doi-access=free}} was published in 1967 by Shun'ichi Amari.{{cite journal |last1=Amari |first1=Shun'ichi |author-link=Shun'ichi Amari |date=1967 |title=A theory of adaptive pattern classifier |journal=IEEE Transactions |volume=EC |issue=16 |pages=279–307}} In computer experiments conducted by Amari's student Saito, a five layer MLP with two modifiable layers learned internal representations to classify non-linearily separable pattern classes.{{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}} Subsequent developments in hardware and hyperparameter tunings have made end-to-end stochastic gradient descent the currently dominant training technique.

{{main|Backpropagation}}

Backpropagation is an efficient application of the chain rule derived by Gottfried Wilhelm Leibniz in 1673{{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}} to networks of differentiable nodes. The terminology "back-propagating errors" was actually introduced in 1962 by Rosenblatt, 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.{{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}} The modern form of backpropagation was developed multiple times in early 1970s. The earliest published instance was Seppo Linnainmaa's master thesis (1970).{{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}}{{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}} Paul Werbos developed it independently in 1971,{{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}} but had difficulty publishing it until 1982.{{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}} In 1986, David E. Rumelhart et al. popularized backpropagation.{{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|url-access=subscription }}

{{main|Recurrent neural network}}

One origin of the recurrent neural network (RNN) was statistical mechanics. The Ising model was developed by Wilhelm Lenz{{Citation |last=Lenz |first=W. |title=Beiträge zum Verständnis der magnetischen Eigenschaften in festen Körpern |journal=Physikalische Zeitschrift |volume=21 |pages=613–615 |year=1920 |postscript=. |author-link=Wilhelm Lenz}} and Ernst Ising{{citation |last=Ising |first=E. |title=Beitrag zur Theorie des Ferromagnetismus |journal=Z. Phys. |volume=31 |issue=1 |pages=253–258 |year=1925 |bibcode=1925ZPhy...31..253I |doi=10.1007/BF02980577 |s2cid=122157319}} in the 1920s{{cite journal |last1=Brush |first1=Stephen G. |year=1967 |title=History of the Lenz-Ising Model |journal=Reviews of Modern Physics |volume=39 |issue=4 |pages=883–893 |bibcode=1967RvMP...39..883B |doi=10.1103/RevModPhys.39.883}} as a simple statistical mechanical model of magnets at equilibrium. Glauber in 1963 studied the Ising model evolving in time, as a process towards equilibrium (Glauber dynamics), adding in the component of time.{{cite journal |last1=Glauber |first1=Roy J. |date=February 1963 |title=Roy J. Glauber "Time-Dependent Statistics of the Ising Model" |url=https://aip.scitation.org/doi/abs/10.1063/1.1703954 |journal=Journal of Mathematical Physics |volume=4 |issue=2 |pages=294–307 |doi=10.1063/1.1703954 |access-date=2021-03-21|url-access=subscription }} Shun'ichi Amari in 1972 proposed to modify the weights of an Ising model by Hebbian learning rule as a model of associative memory, adding in the component of learning.{{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|url-access=subscription }} This was popularized as the Hopfield network (1982).{{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}}

Another origin of RNN was neuroscience. The word "recurrent" is used to describe loop-like structures in anatomy. In 1901, Cajal observed "recurrent semicircles" in the cerebellar cortex.{{Cite journal |last1=Espinosa-Sanchez |first1=Juan Manuel |last2=Gomez-Marin |first2=Alex |last3=de Castro |first3=Fernando |date=2023-07-05 |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 }} In 1933, Lorente de Nó discovered "recurrent, reciprocal connections" by Golgi's method, and proposed that excitatory loops explain certain aspects of the vestibulo-ocular reflex.{{Cite journal |last=de NÓ |first=R. Lorente |date=1933-08-01 |title=Vestibulo-Ocular Reflex Arc |url=http://archneurpsyc.jamanetwork.com/article.aspx?doi=10.1001/archneurpsyc.1933.02240140009001 |journal=Archives of Neurology and Psychiatry |volume=30 |issue=2 |pages=245 |doi=10.1001/archneurpsyc.1933.02240140009001 |issn=0096-6754|url-access=subscription }}{{Cite journal |last=Larriva-Sahd |first=Jorge A. |date=2014-12-03 |title=Some predictions of Rafael Lorente de Nó 80 years later |journal=Frontiers in Neuroanatomy |volume=8 |pages=147 |doi=10.3389/fnana.2014.00147 |issn=1662-5129 |pmc=4253658 |pmid=25520630 |doi-access=free}} Hebb considered "reverberating circuit" as an explanation for short-term memory.{{Cite web |title=reverberating circuit |url=https://www.oxfordreference.com/display/10.1093/oi/authority.20110803100417461 |access-date=2024-07-27 |website=Oxford Reference}} {{Harvard citation|McCulloch|Pitts|1943}} considered neural networks that contains cycles, and noted that the current activity of such networks can be affected by activity indefinitely far in the past.

Two early influential works were the Jordan network (1986) and the Elman network (1990), which applied RNN to study cognitive psychology. In 1993, a neural history compressor system solved a "Very Deep Learning" task that required more than 1000 subsequent layers in an RNN unfolded in time.{{Cite book |last=Schmidhuber |first=Jürgen |url=ftp://ftp.idsia.ch/pub/juergen/habilitation.pdf |title=Habilitation thesis: System modeling and optimization |year=1993}}{{Dead link|date=June 2024|bot=InternetArchiveBot|fix-attempted=yes}} Page 150 ff demonstrates credit assignment across the equivalent of 1,200 layers in an unfolded RNN.

Sepp Hochreiter's diploma thesis (1991)S. Hochreiter., "[http://people.idsia.ch/~juergen/SeppHochreiter1991ThesisAdvisorSchmidhuber.pdf Untersuchungen zu dynamischen neuronalen Netzen]". {{Webarchive|url=https://web.archive.org/web/20150306075401/http://people.idsia.ch/~juergen/SeppHochreiter1991ThesisAdvisorSchmidhuber.pdf|date=2015-03-06}}. Diploma thesis. Institut f. Informatik, Technische Univ. Munich. Advisor: J. Schmidhuber, 1991. proposed the neural history compressor, and identified and analyzed the vanishing gradient problem.{{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={{google books |plainurl=y |id=NWOcMVA64aAC}}}} In 1993, a neural history compressor system solved a "Very Deep Learning" task that required more than 1000 subsequent layers in an RNN unfolded in time.{{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=ftp://ftp.idsia.ch/pub/juergen/chunker.pdf |journal=Neural Computation |volume=4 |issue=2 |pages=234–242 |doi=10.1162/neco.1992.4.2.234 |archive-url=https://web.archive.org/web/20170706014739/ftp://ftp.idsia.ch/pub/juergen/chunker.pdf |archive-date=2017-07-06 |url-status=dead |s2cid=18271205}} Hochreiter proposed recurrent residual connections to solve the vanishing gradient problem. This led to the long short-term memory (LSTM), published in 1995.{{Cite Q|Q98967430}} LSTM can learn "very deep learning" tasks{{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}} with long credit assignment paths that require memories of events that happened thousands of discrete time steps before. That LSTM was not yet the modern architecture, which required a "forget gate", introduced in 1999,{{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}} which became the standard RNN architecture.

Long short-term memory (LSTM) networks were invented by Hochreiter and Schmidhuber in 1995 and set accuracy records in multiple applications domains.{{Cite journal |last1=Hochreiter |first1=Sepp |author-link=Sepp Hochreiter |last2=Schmidhuber |first2=Jürgen |date=1997-11-01 |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}} It became the default choice for RNN architecture.

Around 2006, LSTM started to revolutionize speech recognition, outperforming traditional models in certain speech applications.{{Cite journal |last1=Graves |first1=Alex |last2=Schmidhuber |first2=Jürgen |date=2005-07-01 |title=Framewise phoneme classification with bidirectional LSTM and other neural network architectures |journal=Neural Networks |series=IJCNN 2005 |volume=18 |issue=5 |pages=602–610 |citeseerx=10.1.1.331.5800 |doi=10.1016/j.neunet.2005.06.042 |pmid=16112549 |s2cid=1856462}}{{Cite conference |last1=Fernández |first1=Santiago |last2=Graves |first2=Alex |last3=Schmidhuber |first3=Jürgen |year=2007 |title=An Application of Recurrent Neural Networks to Discriminative Keyword Spotting |url=http://dl.acm.org/citation.cfm?id=1778066.1778092 |series=ICANN'07 |location=Berlin, Heidelberg |publisher=Springer-Verlag |pages=220–229 |isbn=978-3-540-74693-5 |book-title=Proceedings of the 17th International Conference on Artificial Neural Networks}} LSTM also improved large-vocabulary speech recognition{{Cite web |last1=Sak |first1=Haşim |last2=Senior |first2=Andrew |last3=Beaufays |first3=Françoise |year=2014 |title=Long Short-Term Memory recurrent neural network architectures for large scale acoustic modeling |url=https://research.google.com/pubs/archive/43905.pdf |publisher=Google Research}}{{cite arXiv |eprint=1410.4281 |class=cs.CL |first1=Xiangang |last1=Li |first2=Xihong |last2=Wu |title=Constructing Long Short-Term Memory based Deep Recurrent Neural Networks for Large Vocabulary Speech Recognition |date=2014-10-15}} and text-to-speech synthesis{{cite conference |last1=Fan |first1=Bo |last2=Wang |first2=Lijuan |last3=Soong |first3=Frank K. |last4=Xie |first4=Lei |date=2015 |title=Photo-Real Talking Head with Deep Bidirectional LSTM |pages=4884–8 |doi=10.1109/ICASSP.2015.7178899 |isbn=978-1-4673-6997-8 |chapter-url= |editor= |book-title=Proceedings of ICASSP 2015 IEEE International Conference on Acoustics, Speech and Signal Processing}} and was used in Google voice search, and dictation on Android devices.{{Cite web |last1=Sak |first1=Haşim |last2=Senior |first2=Andrew |last3=Rao |first3=Kanishka |last4=Beaufays |first4=Françoise |last5=Schalkwyk |first5=Johan |date=September 2015 |title=Google voice search: faster and more accurate |url=http://googleresearch.blogspot.ch/2015/09/google-voice-search-faster-and-more.html}}

LSTM broke records for improved machine translation,{{Cite journal |last1=Sutskever |first1=Ilya |last2=Vinyals |first2=Oriol |last3=Le |first3=Quoc V. |year=2014 |title=Sequence to Sequence Learning with Neural Networks |url=https://papers.nips.cc/paper/5346-sequence-to-sequence-learning-with-neural-networks.pdf |journal=Electronic Proceedings of the Neural Information Processing Systems Conference |volume=27 |page=5346 |arxiv=1409.3215 |bibcode=2014arXiv1409.3215S}} language modeling{{cite arXiv |eprint=1602.02410 |class=cs.CL |first1=Rafal |last1=Jozefowicz |first2=Oriol |last2=Vinyals |title=Exploring the Limits of Language Modeling |date=2016-02-07 |last3=Schuster |first3=Mike |last4=Shazeer |first4=Noam |last5=Wu |first5=Yonghui}} and Multilingual Language Processing.{{cite arXiv |eprint=1512.00103 |class=cs.CL |first1=Dan |last1=Gillick |first2=Cliff |last2=Brunk |title=Multilingual Language Processing From Bytes |date=2015-11-30 |last3=Vinyals |first3=Oriol |last4=Subramanya |first4=Amarnag}} LSTM combined with convolutional neural networks (CNNs) improved automatic image captioning.{{cite arXiv |eprint=1411.4555 |class=cs.CV |first1=Oriol |last1=Vinyals |first2=Alexander |last2=Toshev |title=Show and Tell: A Neural Image Caption Generator |date=2014-11-17 |last3=Bengio |first3=Samy |last4=Erhan |first4=Dumitru}}

{{main|Convolutional neural network}}

The origin of the CNN architecture is the "neocognitron"{{cite journal |last1=Fukushima |first1=K. |year=2007 |title=Neocognitron |journal=Scholarpedia |volume=2 |issue=1 |page=1717 |doi=10.4249/scholarpedia.1717 |bibcode=2007SchpJ...2.1717F |doi-access=free}} introduced by Kunihiko Fukushima in 1980.{{cite journal |last=Fukushima |first=Kunihiko |title=Neocognitron: A Self-organizing Neural Network Model for a Mechanism of Pattern Recognition Unaffected by Shift in Position |journal=Biological Cybernetics |year=1980 |volume=36 |issue=4 |pages=193–202 |url=https://www.cs.princeton.edu/courses/archive/spr08/cos598B/Readings/Fukushima1980.pdf |access-date=16 November 2013 |doi=10.1007/BF00344251 |pmid=7370364 |s2cid=206775608}}{{cite journal |first1=Yann |last1=LeCun |first2=Yoshua |last2=Bengio |first3=Geoffrey |last3=Hinton |title=Deep learning |journal=Nature |volume=521 |issue=7553 |year=2015 |pages=436–444 |doi=10.1038/nature14539 |pmid=26017442 |bibcode=2015Natur.521..436L |s2cid=3074096|url=https://hal.science/hal-04206682/file/Lecun2015.pdf }}

It was inspired by work of Hubel and Wiesel in the 1950s and 1960s which showed that cat visual cortices contain neurons that individually respond to small regions of the visual field.

The neocognitron introduced the two basic types of layers in CNNs: convolutional layers, and downsampling layers. A convolutional layer contains units whose receptive fields cover a patch of the previous layer. The weight vector (the set of adaptive parameters) of such a unit is often called a filter. Units can share filters. Downsampling layers contain units whose receptive fields cover patches of previous convolutional layers. Such a unit typically computes the average of the activations of the units in its patch. This downsampling helps to correctly classify objects in visual scenes even when the objects are shifted.

In 1969, Kunihiko Fukushima also introduced the ReLU (rectified linear unit) activation function.{{cite journal |first1=K. |last1=Fukushima |title=Visual feature extraction by a multilayered network of analog threshold elements |journal=IEEE Transactions on Systems Science and Cybernetics |volume=5 |issue=4 |date=1969 |pages=322–333 |doi=10.1109/TSSC.1969.300225}}{{cite arXiv |eprint=2212.11279 |class=cs.NE |first=Juergen |last=Schmidhuber |author-link=Juergen Schmidhuber |title=Annotated History of Modern AI and Deep Learning |date=2022}} The rectifier has become the most popular activation function for CNNs and deep neural networks in general.{{cite arXiv |last1=Ramachandran |first1=Prajit |last2=Barret |first2=Zoph |last3=Quoc |first3=V. Le |date=October 16, 2017 |title=Searching for Activation Functions |eprint=1710.05941 |class=cs.NE}}

The time delay neural network (TDNN) was introduced in 1987 by Alex Waibel and was one of the first CNNs, as it achieved shift invariance.{{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)}} It did so by utilizing weight sharing in combination with backpropagation training.Alexander Waibel et al., [http://www.inf.ufrgs.br/~engel/data/media/file/cmp121/waibel89_TDNN.pdf Phoneme Recognition Using Time-Delay Neural Networks] IEEE Transactions on Acoustics, Speech, and Signal Processing, Volume 37, No. 3, pp. 328. – 339 March 1989. Thus, while also using a pyramidal structure as in the neocognitron, it performed a global optimization of the weights instead of a local one.

In 1988, Wei Zhang et al. applied backpropagation to a CNN (a simplified Neocognitron with convolutional interconnections between the image feature layers and the last fully connected layer) for alphabet recognition. They also proposed an implementation of the CNN with an optical computing system.{{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}}{{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 |doi=10.1364/AO.29.004790 |pmid=20577468 |bibcode=1990ApOpt..29.4790Z|url-access=subscription }}

Kunihiko Fukushima published the neocognitron in 1980.{{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}} Max pooling appears in a 1982 publication on the neocognitron.{{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 }} In 1989, Yann LeCun et al. trained a CNN with the purpose of recognizing handwritten ZIP codes on mail. While the algorithm worked, training required 3 days.LeCun et al., "Backpropagation Applied to Handwritten Zip Code Recognition," Neural Computation, 1, pp. 541–551, 1989.{{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}} It used max pooling. Learning was fully automatic, performed better than manual coefficient design, and was suited to a broader range of image recognition problems and image types.

Subsequently, Wei Zhang, et al. modified their model by removing the last fully connected layer and applied it for medical image object segmentation in 1991{{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 |doi=10.1364/AO.30.004211 |pmid=20706526 |bibcode=1991ApOpt..30.4211Z|url-access=subscription }} and breast cancer detection in mammograms in 1994.{{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 |doi=10.1118/1.597177 |pmid=8058017 |bibcode=1994MedPh..21..517Z|url-access=subscription }}

In a variant of the neocognitron called the cresceptron, instead of using Fukushima's spatial averaging, J. Weng et al. also used max-pooling where a downsampling unit computes the maximum of the activations of the units in its patch.J. Weng, N. Ahuja and T. S. Huang, "[http://www.cse.msu.edu/~weng/research/CresceptronIJCNN1992.pdf Cresceptron: a self-organizing neural network which grows adaptively]," Proc. International Joint Conference on Neural Networks, Baltimore, Maryland, vol I, pp. 576–581, June, 1992.J. Weng, N. Ahuja and T. S. Huang, "[http://www.cse.msu.edu/~weng/research/CresceptronICCV1993.pdf Learning recognition and segmentation of 3-D objects from 2-D images]," Proc. 4th International Conf. Computer Vision, Berlin, Germany, pp. 121–128, May, 1993.J. Weng, N. Ahuja and T. S. Huang, "[http://www.cse.msu.edu/~weng/research/CresceptronIJCV.pdf Learning recognition and segmentation using the Cresceptron]," International Journal of Computer Vision, vol. 25, no. 2, pp. 105–139, Nov. 1997.{{cite book |first1=J |last1=Weng |first2=N |last2=Ahuja |first3=TS |last3=Huang |title=1993 (4th) International Conference on Computer Vision |chapter=Learning recognition and segmentation of 3-D objects from 2-D images |s2cid=8619176 |year=1993 |pages=121–128 |doi=10.1109/ICCV.1993.378228 |isbn=0-8186-3870-2}}

LeNet-5, a 7-level CNN by Yann LeCun et al. in 1998,{{cite journal |last=LeCun |first=Yann |author2=Léon Bottou |author3=Yoshua Bengio |author4=Patrick Haffner |title=Gradient-based learning applied to document recognition |journal=Proceedings of the IEEE |year=1998 |volume=86 |issue=11 |pages=2278–2324 |url=http://yann.lecun.com/exdb/publis/pdf/lecun-01a.pdf |access-date=October 7, 2016 |doi=10.1109/5.726791 |citeseerx=10.1.1.32.9552|s2cid=14542261 }} that classifies digits, was applied by several banks to recognize hand-written numbers on checks ({{Langx|en-GB|cheques}}) digitized in 32x32 pixel images. The ability to process higher-resolution images requires larger and more layers of CNNs, so this technique is constrained by the availability of computing resources.

In 2010, Backpropagation training through max-pooling was accelerated by GPUs and shown to perform better than other pooling variants.Dominik Scherer, Andreas C. Müller, and Sven Behnke: "[https://www.ais.uni-bonn.de/papers/icann2010_maxpool.pdf Evaluation of Pooling Operations in Convolutional Architectures for Object Recognition]," In 20th International Conference Artificial Neural Networks (ICANN), pp. 92–101, 2010. {{doi|10.1007/978-3-642-15825-4_10}}.

Behnke (2003) relied only on the sign of the gradient (Rprop){{cite book|url=http://www.ais.uni-bonn.de/books/LNCS2766.pdf|title=Hierarchical Neural Networks for Image Interpretation.|author=Sven Behnke|publisher=Springer|year=2003|series=Lecture Notes in Computer Science|volume=2766}} on problems such as image reconstruction and face localization. Rprop is a first-order optimization algorithm created by Martin Riedmiller and Heinrich Braun in 1992.Martin Riedmiller und Heinrich Braun: Rprop – A Fast Adaptive Learning Algorithm. Proceedings of the International Symposium on Computer and Information Science VII, 1992

The deep learning revolution started around CNN- and GPU-based computer vision.

Although CNNs trained by backpropagation had been around for decades and GPU implementations of NNs for years,{{cite journal |last1=Oh |first1=K.-S. |last2=Jung |first2=K. |year=2004 |title=GPU implementation of neural networks |journal=Pattern Recognition |volume=37 |issue=6 |pages=1311–1314 |bibcode=2004PatRe..37.1311O |doi=10.1016/j.patcog.2004.01.013}} including CNNs,{{Citation |last1=Chellapilla |first1=Kumar |title=High performance convolutional neural networks for document processing |date=2006 |url=https://hal.inria.fr/inria-00112631/document |access-date=2021-02-14 |archive-url=https://web.archive.org/web/20200518193413/https://hal.inria.fr/inria-00112631/document |archive-date=2020-05-18 |url-status=live |last2=Puri |first2=Sidd |last3=Simard |first3=Patrice}} faster implementations of CNNs on GPUs were needed to progress on computer vision. Later, as deep learning becomes widespread, specialized hardware and algorithm optimizations were developed specifically for deep learning.{{cite arXiv |eprint=1703.09039 |class=cs.CV |first1=Vivienne |last1=Sze |first2=Yu-Hsin |last2=Chen |author1-link=Vivienne Sze |title=Efficient Processing of Deep Neural Networks: A Tutorial and Survey |last3=Yang |first3=Tien-Ju |last4=Emer |first4=Joel |year=2017}}

A key advance for the deep learning revolution was hardware advances, especially GPU. Some early work dated back to 2004. In 2009, Raina, Madhavan, and Andrew Ng reported a 100M deep belief network trained on 30 Nvidia GeForce GTX 280 GPUs, an early demonstration of GPU-based deep learning. They reported up to 70 times faster training.{{Cite book |last1=Raina |first1=Rajat |last2=Madhavan |first2=Anand |last3=Ng |first3=Andrew Y. |chapter=Large-scale deep unsupervised learning using graphics processors |date=2009-06-14 |title=Proceedings of the 26th Annual International Conference on Machine Learning |chapter-url=https://doi.org/10.1145/1553374.1553486 |series=ICML '09 |location=New York, NY, USA |publisher=Association for Computing Machinery |pages=873–880 |doi=10.1145/1553374.1553486 |isbn=978-1-60558-516-1}}

In 2011, a CNN named DanNet{{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}}{{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=2014-09-29 |access-date=2017-06-13}} 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. It then won more contests.{{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=2017-06-13 |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=2017-08-09 |url-status=live}}{{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}} They also showed how max-pooling CNNs on GPU improved performance significantly.{{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}}

Many discoveries were empirical and focused on engineering. For example, in 2011, Xavier Glorot, Antoine Bordes and Yoshua Bengio found that the ReLU worked better than widely used activation functions prior to 2011.

In October 2012, AlexNet by Alex Krizhevsky, Ilya Sutskever, and Geoffrey Hinton{{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=2017-01-10 |access-date=2017-05-24}} 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 and Andrew Zisserman{{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}} and Google's Inceptionv3.{{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 }}

The success in image classification was then extended to the more challenging task of generating descriptions (captions) for images, often as a combination of CNNs and LSTMs.{{cite arXiv |eprint=1411.4555 |class=cs.CV |first1=Oriol |last1=Vinyals |first2=Alexander |last2=Toshev |title=Show and Tell: A Neural Image Caption Generator |last3=Bengio |first3=Samy |last4=Erhan |first4=Dumitru |year=2014}}.{{cite arXiv |eprint=1411.4952 |class=cs.CV |first1=Hao |last1=Fang |first2=Saurabh |last2=Gupta |title=From Captions to Visual Concepts and Back |last3=Iandola |first3=Forrest |last4=Srivastava |first4=Rupesh |last5=Deng |first5=Li |last6=Dollár |first6=Piotr |last7=Gao |first7=Jianfeng |last8=He |first8=Xiaodong |last9=Mitchell |first9=Margaret |last10=Platt |first10=John C |last11=Lawrence Zitnick |first11=C |last12=Zweig |first12=Geoffrey |year=2014}}.{{cite arXiv |eprint=1411.2539 |class=cs.LG |first1=Ryan |last1=Kiros |first2=Ruslan |last2=Salakhutdinov |title=Unifying Visual-Semantic Embeddings with Multimodal Neural Language Models |last3=Zemel |first3=Richard S |year=2014}}.

In 2014, the state of the art was training “very deep neural network” with 20 to 30 layers.{{Citation |last1=Simonyan |first1=Karen |title=Very Deep Convolutional Networks for Large-Scale Image Recognition |date=2015-04-10 |arxiv=1409.1556 |last2=Zisserman |first2=Andrew}} Stacking too many layers led to a steep reduction in training accuracy,{{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}} known as the "degradation" problem.{{Cite conference |last1=He |first1=Kaiming |last2=Zhang |first2=Xiangyu |last3=Ren |first3=Shaoqing |last4=Sun |first4=Jian |date=10 Dec 2015 |title=Deep Residual Learning for Image Recognition |arxiv=1512.03385}} In 2015, two techniques were developed concurrently to train very deep networks: highway network{{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}} and residual neural network (ResNet).{{Cite book |last1=He |first1=Kaiming |last2=Zhang |first2=Xiangyu |last3=Ren |first3=Shaoqing |last4=Sun |first4=Jian |title=2016 IEEE Conference on Computer Vision and Pattern Recognition (CVPR) |chapter=Deep Residual Learning for Image Recognition |date=2016 |chapter-url=https://ieeexplore.ieee.org/document/7780459 |publisher=IEEE |pages=770–778 |arxiv=1512.03385 |doi=10.1109/CVPR.2016.90 |isbn=978-1-4673-8851-1 }} The ResNet research team attempted to train deeper ones by empirically testing various tricks for training deeper networks until they discovered the deep residual network architecture.{{Cite web |last=Linn |first=Allison |date=2015-12-10 |title=Microsoft researchers win ImageNet computer vision challenge |url=https://blogs.microsoft.com/ai/microsoft-researchers-win-imagenet-computer-vision-challenge/ |access-date=2024-06-29 |website=The AI Blog |language=en-US}}

{{main|Generative adversarial network}}

In 1991, Juergen Schmidhuber published "artificial curiosity", neural networks in a zero-sum game.{{cite conference |last1=Schmidhuber |first1=Jürgen |author-link=Juergen Schmidhuber |date=1991 |title=A possibility for implementing curiosity and boredom in model-building neural controllers |publisher=MIT Press/Bradford Books |pages=222–227 |book-title=Proc. SAB'1991}} 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. GANs can be regarded as a case where the environmental reaction is 1 or 0 depending on whether the first network's output is in a given set.{{Cite journal |last=Schmidhuber |first=Jürgen |author-link=Juergen 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 |arxiv=1906.04493 |doi=10.1016/j.neunet.2020.04.008 |pmid=32334341 |s2cid=216056336}} It was extended to "predictability minimization" to create disentangled representations of input patterns.{{Cite journal |last=Schmidhuber |first=Jürgen |author-link=Juergen Schmidhuber |date=November 1992 |title=Learning Factorial Codes by Predictability Minimization |journal=Neural Computation |language=en |volume=4 |issue=6 |pages=863–879 |doi=10.1162/neco.1992.4.6.863 |s2cid=42023620}}{{Cite journal |last1=Schmidhuber |first1=Jürgen |last2=Eldracher |first2=Martin |last3=Foltin |first3=Bernhard |date=1996 |title=Semilinear predictability minimzation produces well-known feature detectors |journal=Neural Computation |language=en |volume=8 |issue=4 |pages=773–786 |doi=10.1162/neco.1996.8.4.773 |s2cid=16154391}}

Other people had similar ideas but did not develop them similarly. An idea involving adversarial networks was published in a 2010 blog post by Olli Niemitalo.{{cite web |last1=Niemitalo |first1=Olli |date=February 24, 2010 |title=A method for training artificial neural networks to generate missing data within a variable context |url=http://yehar.com:80/blog/?p=167 |url-status=live |archive-url=https://web.archive.org/web/20120312111546/http://yehar.com/blog/?p=167 |archive-date=March 12, 2012 |access-date=February 22, 2019 |newspaper=Internet Archive (Wayback Machine)}} This idea was never implemented and did not involve stochasticity in the generator and thus was not a generative model. It is now known as a conditional GAN or cGAN.{{citation needed|date=May 2025}} An idea similar to GANs was used to model animal behavior by Li, Gauci and Gross in 2013.{{cite conference |last1=Li |first1=Wei |last2=Gauci |first2=Melvin |last3=Gross |first3=Roderich |date=July 6, 2013 |title=Proceeding of the fifteenth annual conference on Genetic and evolutionary computation conference - GECCO '13 |location=Amsterdam, the Netherlands |publisher=ACM |pages=223–230 |doi=10.1145/2463372.2465801 |isbn=9781450319638 |chapter=A Coevolutionary Approach to Learn Animal Behavior Through Controlled Interaction |book-title=Proceedings of the 15th Annual Conference on Genetic and Evolutionary Computation (GECCO 2013)}}

Another inspiration for GANs was noise-contrastive estimation,{{cite journal |last1=Gutmann |first1=Michael |last2=Hyvärinen |first2=Aapo |title=Noise-Contrastive Estimation |url=http://proceedings.mlr.press/v9/gutmann10a/gutmann10a.pdf |journal=International Conference on AI and Statistics}} which uses the same loss function as GANs and which Goodfellow studied during his PhD in 2010–2014.

Generative adversarial network (GAN) by (Ian Goodfellow et al., 2014){{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}} became state of the art in generative modeling during 2014-2018 period. Excellent image quality is achieved by Nvidia's StyleGAN (2018){{Cite web |date=December 14, 2018 |title=GAN 2.0: NVIDIA's Hyperrealistic Face Generator |url=https://syncedreview.com/2018/12/14/gan-2-0-nvidias-hyperrealistic-face-generator/ |access-date=October 3, 2019 |website=SyncedReview.com}} based on the Progressive GAN by Tero Karras et al.{{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.}} 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 deepfakes.{{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}} Diffusion models (2015){{Cite journal |last1=Sohl-Dickstein |first1=Jascha |last2=Weiss |first2=Eric |last3=Maheswaranathan |first3=Niru |last4=Ganguli |first4=Surya |date=2015-06-01 |title=Deep Unsupervised Learning using Nonequilibrium Thermodynamics |url=http://proceedings.mlr.press/v37/sohl-dickstein15.pdf |journal=Proceedings of the 32nd International Conference on Machine Learning |language=en |publisher=PMLR |volume=37 |pages=2256–2265|arxiv=1503.03585 }} eclipsed GANs in generative modeling since then, with systems such as DALL·E 2 (2022) and Stable Diffusion (2022).

{{Main|Attention (machine learning)|Transformer (deep learning architecture)}}

The human selective attention had been studied in neuroscience and cognitive psychology.{{Cite book |last1=Kramer |first1=Arthur F. |url=http://www.oxfordscholarship.com/view/10.1093/acprof:oso/9780195305722.001.0001/acprof-9780195305722 |title=Attention: From Theory to Practice |last2=Wiegmann |first2=Douglas A. |last3=Kirlik |first3=Alex |date=2006-12-28 |publisher=Oxford University Press |isbn=978-0-19-530572-2 |chapter=1 Attention: From History to Application |doi=10.1093/acprof:oso/9780195305722.003.0001}} Selective attention of audition was studied in the cocktail party effect (Colin Cherry, 1953).{{cite journal |vauthors=Cherry EC |year=1953 |title=Some Experiments on the Recognition of Speech, with One and with Two Ears |url=http://www.ee.columbia.edu/~dpwe/papers/Cherry53-cpe.pdf |journal=The Journal of the Acoustical Society of America |volume=25 |issue=5 |pages=975–79 |bibcode=1953ASAJ...25..975C |doi=10.1121/1.1907229 |issn=0001-4966 |hdl-access=free |hdl=11858/00-001M-0000-002A-F750-3}} (Donald Broadbent, 1958) proposed the filter model of attention.{{cite book |last=Broadbent |first=D |author-link=Donald Broadbent |title=Perception and Communication |publisher=Pergamon Press |year=1958 |location=London}} Selective attention of vision was studied in the 1960s by George Sperling's partial report paradigm. It was also noticed that saccade control is modulated by cognitive processes, in that the eye moves preferentially towards areas of high salience. As the fovea of the eye is small, the eye cannot sharply resolve all of the visual field at once. The use of saccade control allows the eye to quickly scan important features of a scene.{{Cite journal |last1=Kowler |first1=Eileen |last2=Anderson |first2=Eric |last3=Dosher |first3=Barbara |last4=Blaser |first4=Erik |date=1995-07-01 |title=The role of attention in the programming of saccades |url=https://dx.doi.org/10.1016/0042-6989%2894%2900279-U |journal=Vision Research |volume=35 |issue=13 |pages=1897–1916 |doi=10.1016/0042-6989(94)00279-U |pmid=7660596 |issn=0042-6989|url-access=subscription }}

These researches inspired algorithms, such as a variant of the Neocognitron.{{Cite journal |last=Fukushima |first=Kunihiko |date=1987-12-01 |title=Neural network model for selective attention in visual pattern recognition and associative recall |url=https://opg.optica.org/abstract.cfm?URI=ao-26-23-4985 |journal=Applied Optics |language=en |volume=26 |issue=23 |pages=4985–4992 |doi=10.1364/AO.26.004985 |pmid=20523477 |bibcode=1987ApOpt..26.4985F |issn=0003-6935|url-access=subscription }}{{cite arXiv|last1=Ba |first1=Jimmy |title=Multiple Object Recognition with Visual Attention |date=2015-04-23 |last2=Mnih |first2=Volodymyr |last3=Kavukcuoglu |first3=Koray|class=cs.LG |eprint=1412.7755 }} Conversely, developments in neural networks had inspired circuit models of biological visual attention.{{Citation |last1=Koch |first1=Christof |title=Shifts in Selective Visual Attention: Towards the Underlying Neural Circuitry |date=1987 |work=Matters of Intelligence: Conceptual Structures in Cognitive Neuroscience |pages=115–141 |editor-last=Vaina |editor-first=Lucia M. |url=https://doi.org/10.1007/978-94-009-3833-5_5 |access-date=2024-08-06 |place=Dordrecht |publisher=Springer Netherlands |language=en |doi=10.1007/978-94-009-3833-5_5 |isbn=978-94-009-3833-5 |last2=Ullman |first2=Shimon|url-access=subscription }}{{Cite journal |last=Soydaner |first=Derya |date=August 2022 |title=Attention mechanism in neural networks: where it comes and where it goes |url=https://link.springer.com/10.1007/s00521-022-07366-3 |journal=Neural Computing and Applications |language=en |volume=34 |issue=16 |pages=13371–13385 |doi=10.1007/s00521-022-07366-3 |issn=0941-0643|arxiv=2204.13154 }}

A key aspect of attention mechanism is the use of multiplicative operations, which had been studied under the names of higher-order neural networks,{{Cite journal |last1=Giles |first1=C. Lee |last2=Maxwell |first2=Tom |date=1987-12-01 |title=Learning, invariance, and generalization in high-order neural networks |url=https://opg.optica.org/abstract.cfm?URI=ao-26-23-4972 |journal=Applied Optics |language=en |volume=26 |issue=23 |pages=4972–4978 |doi=10.1364/AO.26.004972 |pmid=20523475 |issn=0003-6935|url-access=subscription }} multiplication units,{{Cite journal |last1=Feldman |first1=J. A. |last2=Ballard |first2=D. H. |date=1982-07-01 |title=Connectionist models and their properties |url=https://www.sciencedirect.com/science/article/pii/S0364021382800013 |journal=Cognitive Science |volume=6 |issue=3 |pages=205–254 |doi=10.1016/S0364-0213(82)80001-3 |issn=0364-0213|url-access=subscription }} sigma-pi units,{{Cite book |last1=Rumelhart |first1=David E. |url=https://stanford.edu/~jlmcc/papers/PDP/Chapter2.pdf |title=Parallel Distributed Processing, Volume 1: Explorations in the Microstructure of Cognition: Foundations, Chapter 2 |last2=Mcclelland |first2=James L. |last3=Group |first3=PDP Research |date=1987-07-29 |publisher=Bradford Books |isbn=978-0-262-68053-0 |location=Cambridge, Mass |language=en}} fast weight controllers,{{Cite journal |last=Schmidhuber |first=Jürgen |date=January 1992 |title=Learning to Control Fast-Weight Memories: An Alternative to Dynamic Recurrent Networks |url=https://direct.mit.edu/neco/article/4/1/131-139/5620 |journal=Neural Computation |language=en |volume=4 |issue=1 |pages=131–139 |doi=10.1162/neco.1992.4.1.131 |issn=0899-7667|url-access=subscription }} and hyper-networks.{{cite arXiv|last1=Ha |first1=David |title=HyperNetworks |date=2016-12-01 |eprint=1609.09106 |last2=Dai |first2=Andrew |last3=Le |first3=Quoc V.|class=cs.LG }}

During the deep learning era, attention mechanism was developed solve similar problems in encoding-decoding.{{Cite journal |last1=Niu |first1=Zhaoyang |last2=Zhong |first2=Guoqiang |last3=Yu |first3=Hui |date=2021-09-10 |title=A review on the attention mechanism of deep learning |url=https://www.sciencedirect.com/science/article/pii/S092523122100477X |journal=Neurocomputing |volume=452 |pages=48–62 |doi=10.1016/j.neucom.2021.03.091 |issn=0925-2312|url-access=subscription }}

The idea of encoder-decoder sequence transduction had been developed in the early 2010s. The papers most commonly cited as the originators that produced seq2seq are two papers from 2014.{{Cite journal |last1=Cho |first1=Kyunghyun |last2=van Merrienboer |first2=Bart |last3=Gulcehre |first3=Caglar |last4=Bahdanau |first4=Dzmitry |last5=Bougares |first5=Fethi |last6=Schwenk |first6=Holger |last7=Bengio |first7=Yoshua |date=2014-06-03 |title=Learning Phrase Representations using RNN Encoder-Decoder for Statistical Machine Translation |arxiv=1406.1078 }}{{cite arXiv |eprint=1409.3215 |class=cs.CL |first1=Ilya |last1=Sutskever |first2=Oriol |last2=Vinyals |title=Sequence to sequence learning with neural networks |date=14 Dec 2014 |last3=Le |first3=Quoc Viet}} A seq2seq architecture employs two RNN, typically LSTM, an "encoder" and a "decoder", for sequence transduction, such as machine translation. They became state of the art in machine translation, and was instrumental in the development of attention mechanism and Transformer.

An image captioning model was proposed in 2015, citing inspiration from the seq2seq model.{{Cite journal |last1=Vinyals |first1=Oriol |last2=Toshev |first2=Alexander |last3=Bengio |first3=Samy |last4=Erhan |first4=Dumitru |date=2015 |title=Show and Tell: A Neural Image Caption Generator |url=https://www.cv-foundation.org/openaccess/content_cvpr_2015/html/Vinyals_Show_and_Tell_2015_CVPR_paper.html |pages=3156–3164|arxiv=1411.4555 }} that would encode an input image into a fixed-length vector. (Xu et al. 2015),{{Cite journal |last1=Xu |first1=Kelvin |last2=Ba |first2=Jimmy |last3=Kiros |first3=Ryan |last4=Cho |first4=Kyunghyun |last5=Courville |first5=Aaron |last6=Salakhudinov |first6=Ruslan |last7=Zemel |first7=Rich |last8=Bengio |first8=Yoshua |date=2015-06-01 |title=Show, Attend and Tell: Neural Image Caption Generation with Visual Attention |url=https://proceedings.mlr.press/v37/xuc15.html |journal=Proceedings of the 32nd International Conference on Machine Learning |language=en |publisher=PMLR |pages=2048–2057|arxiv=1502.03044 }} citing (Bahdanau et al. 2014),{{cite arXiv |last1=Bahdanau |first1=Dzmitry |title=Neural Machine Translation by Jointly Learning to Align and Translate |date=2016-05-19 |last2=Cho |first2=Kyunghyun |last3=Bengio |first3=Yoshua|class=cs.CL |eprint=1409.0473 }} applied the attention mechanism as used in the seq2seq model to image captioning.

One problem with seq2seq models was their use of recurrent neural networks, which are not parallelizable as both the encoder and the decoder processes the sequence token-by-token. The decomposable attention attempted to solve this problem by processing the input sequence in parallel, before computing a "soft alignment matrix" ("alignment" is the terminology used by (Bahdanau et al. 2014)). This allowed parallel processing.

The idea of using attention mechanism for self-attention, instead of in an encoder-decoder (cross-attention), was also proposed during this period, such as in differentiable neural computers and neural Turing machines.{{cite arXiv |last1=Graves |first1=Alex |title=Neural Turing Machines |date=2014-12-10 |last2=Wayne |first2=Greg |last3=Danihelka |first3=Ivo|class=cs.NE |eprint=1410.5401 }} It was termed intra-attention{{cite arXiv |last1=Cheng |first1=Jianpeng |title=Long Short-Term Memory-Networks for Machine Reading |date=2016-09-20 |eprint=1601.06733 |last2=Dong |first2=Li |last3=Lapata |first3=Mirella|class=cs.CL }} where an LSTM is augmented with a memory network as it encodes an input sequence.

These strands of development were combined in the Transformer architecture, published in Attention Is All You Need (2017). Subsequently, attention mechanisms were extended within the framework of Transformer architecture.

Seq2seq models with attention still suffered from the same issue with recurrent networks, which is that they are hard to parallelize, which prevented them to be accelerated on GPUs. In 2016, decomposable attention applied attention mechanism to the feedforward network, which are easy to parallelize.{{cite arXiv |eprint=1606.01933 |class=cs.CL |first1=Ankur P. |last1=Parikh |first2=Oscar |last2=Täckström |title=A Decomposable Attention Model for Natural Language Inference |date=2016-09-25 |last3=Das |first3=Dipanjan |last4=Uszkoreit |first4=Jakob}} One of its authors, Jakob Uszkoreit, suspected that attention without recurrence is sufficient for language translation, thus the title "attention is all you need".{{Cite magazine |last=Levy |first=Steven |title=8 Google Employees Invented Modern AI. Here's the Inside Story |url=https://www.wired.com/story/eight-google-employees-invented-modern-ai-transformers-paper/ |url-status=live |archive-url=https://web.archive.org/web/20240320101528/https://www.wired.com/story/eight-google-employees-invented-modern-ai-transformers-paper/ |archive-date=20 March 2024 |access-date=2024-08-06 |magazine=Wired |language=en-US |issn=1059-1028}}

In 2017, the original (100M-sized) encoder-decoder transformer model was proposed in the "Attention is all you need" paper. At the time, the focus of the research was on improving seq2seq for machine translation, by removing its recurrence to processes all tokens in parallel, but preserving its dot-product attention mechanism to keep its text processing performance.{{cite journal |last1=Vaswani |first1=Ashish |author1-link=Ashish Vaswani |last2=Shazeer |first2=Noam |last3=Parmar |first3=Niki |last4=Uszkoreit |first4=Jakob |last5=Jones |first5=Llion |last6=Gomez |first6=Aidan N |author6-link=Aidan Gomez |last7=Kaiser |first7=Łukasz |last8=Polosukhin |first8=Illia |date=2017 |title=Attention is All you Need |url=https://proceedings.neurips.cc/paper/2017/file/3f5ee243547dee91fbd053c1c4a845aa-Paper.pdf |journal=Advances in Neural Information Processing Systems |publisher=Curran Associates, Inc. |volume=30}} Its parallelizability was an important factor to its widespread use in large neural networks.{{cite arXiv |last1=Peng |first1=Bo |title=RWKV: Reinventing RNNs for the Transformer Era |date=2023-12-10 |eprint=2305.13048 |last2=Alcaide |first2=Eric |last3=Anthony |first3=Quentin |last4=Albalak |first4=Alon |last5=Arcadinho |first5=Samuel |last6=Biderman |first6=Stella |last7=Cao |first7=Huanqi |last8=Cheng |first8=Xin |last9=Chung |first9=Michael|class=cs.CL }}

{{main|Self-organizing map}}

Self-organizing maps (SOMs) were described by Teuvo Kohonen in 1982.{{cite journal |last1=Kohonen |first1=Teuvo |last2=Honkela |first2=Timo |year=2007 |title=Kohonen Network |journal=Scholarpedia |volume=2 |issue=1 |pages=1568 |bibcode=2007SchpJ...2.1568K |doi=10.4249/scholarpedia.1568 |doi-access=free}}{{cite journal |last=Kohonen |first=Teuvo |year=1982 |title=Self-Organized Formation of Topologically Correct Feature Maps |journal=Biological Cybernetics |volume=43 |pages=59–69 |doi=10.1007/bf00337288 |s2cid=206775459 |number=1}} SOMs are neurophysiologically inspired{{cite journal |last1=Von der Malsburg |first1=C |year=1973 |title=Self-organization of orientation sensitive cells in the striate cortex |journal=Kybernetik |volume=14 |issue=2 |pages=85–100 |doi=10.1007/bf00288907 |pmid=4786750 |s2cid=3351573}} artificial neural networks that learn low-dimensional representations of high-dimensional data while preserving the topological structure of the data. They are trained using competitive learning.

SOMs create internal representations reminiscent of the cortical homunculus, a distorted representation of the human body, based on a neurological "map" of the areas and proportions of the human brain dedicated to processing sensory functions, for different parts of the body.

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,{{Cite journal |last1=Ackley |first1=David H. |last2=Hinton |first2=Geoffrey E. |last3=Sejnowski |first3=Terrence J. |date=1985-01-01 |title=A learning algorithm for boltzmann machines |url=https://www.sciencedirect.com/science/article/pii/S0364021385800124 |journal=Cognitive Science |volume=9 |issue=1 |pages=147–169 |doi=10.1016/S0364-0213(85)80012-4 |issn=0364-0213}} restricted Boltzmann machine,{{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}} Helmholtz machine,{{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}} and the wake-sleep algorithm.{{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=1995-05-26 |title=The wake-sleep algorithm for unsupervised neural networks |journal=Science |volume=268 |issue=5214 |pages=1158–1161 |bibcode=1995Sci...268.1158H |doi=10.1126/science.7761831 |pmid=7761831 |s2cid=871473}} These were designed for unsupervised learning of deep generative models. However, those were more computationally expensive compared to backpropagation. Boltzmann machine learning algorithm, published in 1985, was briefly popular before being eclipsed by the backpropagation algorithm in 1986. (p. 112 {{Cite book |last=Sejnowski |first=Terrence J. |title=The deep learning revolution |date=2018 |publisher=The MIT Press |isbn=978-0-262-03803-4 |location=Cambridge, Massachusetts}}).

Geoffrey Hinton et al. (2006) proposed learning a high-level internal representation using successive layers of binary or real-valued latent variables with a restricted Boltzmann machine{{cite book |last1=Smolensky |first1=P. |author-link1=Paul Smolensky |url=https://archive.org/details/paralleldistribu00rume/page/194 |title=Parallel Distributed Processing: Explorations in the Microstructure of Cognition |year=1986 |isbn=9780262680530 |editor=D. E. Rumelhart |volume=1 |pages=[https://archive.org/details/paralleldistribu00rume/page/194 194–281] |chapter=Information processing in dynamical systems: Foundations of harmony theory. |publisher=MIT Press |editor2=J. L. McClelland |editor3=PDP Research Group |chapter-url=http://portal.acm.org/citation.cfm?id=104290}} to model each layer. This RBM is a generative stochastic feedforward neural network that can learn a probability distribution over its set of inputs. Once sufficiently many layers have been learned, the deep architecture may be used as a generative model by reproducing the data when sampling down the model (an "ancestral pass") from the top level feature activations.{{cite journal |last1=Hinton |first1=G. E. |author-link1=Geoffrey Hinton |last2=Osindero |first2=S. |last3=Teh |first3=Y. |year=2006 |title=A fast learning algorithm for deep belief nets |url=http://www.cs.toronto.edu/~hinton/absps/fastnc.pdf |journal=Neural Computation |volume=18 |issue=7 |pages=1527–1554 |citeseerx=10.1.1.76.1541 |doi=10.1162/neco.2006.18.7.1527 |pmid=16764513 |s2cid=2309950}}{{Cite journal |last=Hinton |first=Geoffrey |date=2009-05-31 |title=Deep belief networks |journal=Scholarpedia |volume=4 |issue=5 |pages=5947 |bibcode=2009SchpJ...4.5947H |doi=10.4249/scholarpedia.5947 |issn=1941-6016 |doi-access=free}}

In 2012, Andrew Ng and Jeff Dean created an FNN that learned to recognize higher-level concepts, such as cats, only from watching unlabeled images taken from YouTube videos.{{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}}

Knowledge distillation or model distillation is the process of transferring knowledge from a large model to a smaller one. The idea of using the output of one neural network to train another neural network was studied as the teacher-student network configuration.{{Cite journal |last1=Watkin |first1=Timothy L. H. |last2=Rau |first2=Albrecht |last3=Biehl |first3=Michael |date=1993-04-01 |title=The statistical mechanics of learning a rule |url=https://link.aps.org/doi/10.1103/RevModPhys.65.499 |journal=Reviews of Modern Physics |volume=65 |issue=2 |pages=499–556 |doi=10.1103/RevModPhys.65.499|bibcode=1993RvMP...65..499W }} In 1992, several papers studied the statistical mechanics of teacher-student network configuration, where both networks are committee machines{{Cite journal |last1=Schwarze |first1=H |last2=Hertz |first2=J |date=1992-10-15 |title=Generalization in a Large Committee Machine |url=https://iopscience.iop.org/article/10.1209/0295-5075/20/4/015 |journal=Europhysics Letters |volume=20 |issue=4 |pages=375–380 |doi=10.1209/0295-5075/20/4/015 |bibcode=1992EL.....20..375S |issn=0295-5075|url-access=subscription }}{{Cite journal |last1=Mato |first1=G |last2=Parga |first2=N |date=1992-10-07 |title=Generalization properties of multilayered neural networks |url=https://iopscience.iop.org/article/10.1088/0305-4470/25/19/017 |journal=Journal of Physics A: Mathematical and General |volume=25 |issue=19 |pages=5047–5054 |doi=10.1088/0305-4470/25/19/017 |bibcode=1992JPhA...25.5047M |issn=0305-4470|url-access=subscription }} or both are parity machines.{{Cite journal |last1=Hansel |first1=D |last2=Mato |first2=G |last3=Meunier |first3=C |date=1992-11-01 |title=Memorization Without Generalization in a Multilayered Neural Network |url=https://iopscience.iop.org/article/10.1209/0295-5075/20/5/015 |journal=Europhysics Letters |volume=20 |issue=5 |pages=471–476 |doi=10.1209/0295-5075/20/5/015 |bibcode=1992EL.....20..471H |issn=0295-5075|url-access=subscription }}

Another early example of network distillation was also published in 1992, in the field of recurrent neural networks (RNNs). The problem was sequence prediction. It was solved by two RNNs. One of them ("atomizer") predicted the sequence, and another ("chunker") predicted the errors of the atomizer. Simultaneously, the atomizer predicted the internal states of the chunker. After the atomizer manages to predict the chunker's internal states well, it would start fixing the errors, and soon the chunker is obsoleted, leaving just one RNN in the end.{{cite journal |last1=Schmidhuber |first1=Jürgen |year=1992 |title=Learning complex, extended sequences using the principle of history compression |url=ftp://ftp.idsia.ch/pub/juergen/chunker.pdf |journal=Neural Computation |volume=4 |issue=2 |pages=234–242 |doi=10.1162/neco.1992.4.2.234 |archive-url=https://web.archive.org/web/20170706014739/ftp://ftp.idsia.ch/pub/juergen/chunker.pdf |archive-date=2017-07-06 |url-status=dead |s2cid=18271205 }}

A related methodology was model compression or pruning, where a trained network is reduced in size. It was inspired by neurobiological studies showing that the human brain is resistant to damage, and was studied in the 1980s, via methods such as Biased Weight Decay{{Cite journal |last1=Hanson |first1=Stephen |last2=Pratt |first2=Lorien |date=1988 |title=Comparing Biases for Minimal Network Construction with Back-Propagation |url=https://proceedings.neurips.cc/paper/1988/hash/1c9ac0159c94d8d0cbedc973445af2da-Abstract.html |journal=Advances in Neural Information Processing Systems |publisher=Morgan-Kaufmann |volume=1}} and Optimal Brain Damage.{{Cite journal |last1=LeCun |first1=Yann |last2=Denker |first2=John |last3=Solla |first3=Sara |date=1989 |title=Optimal Brain Damage |url=https://proceedings.neurips.cc/paper/1989/hash/6c9882bbac1c7093bd25041881277658-Abstract.html |journal=Advances in Neural Information Processing Systems |publisher=Morgan-Kaufmann |volume=2}}

The development of metal–oxide–semiconductor (MOS) very-large-scale integration (VLSI), combining millions or billions of MOS transistors onto a single chip in the form of complementary MOS (CMOS) technology, enabled the development of practical artificial neural networks in the 1980s.{{cite book|url=http://fennetic.net/irc/Christopher%20R.%20Carroll%20Carver%20Mead%20Mohammed%20Ismail%20Analog%20VLSI%20Implementation%20of%20Neural%20Systems.pdf|title=Analog VLSI Implementation of Neural Systems|date=8 May 1989|publisher=Kluwer Academic Publishers|isbn=978-1-4613-1639-8|last1=Mead|first1=Carver A.|author1-link=Carver Mead|last2=Ismail|first2=Mohammed|series=The Kluwer International Series in Engineering and Computer Science|volume=80|location=Norwell, MA|doi=10.1007/978-1-4613-1639-8}}

Computational devices were created in CMOS, for both biophysical simulation and neuromorphic computing inspired by the structure and function of the human brain. Nanodevices{{cite journal|last1=Yang|first1=J. J.|last2=Pickett|first2=M. D.|last3=Li|first3=X. M.|last4=Ohlberg|first4=D. A. A.|last5=Stewart|first5=D. R.|last6=Williams|first6=R. S.|year=2008|title=Memristive switching mechanism for metal/oxide/metal nanodevices|journal=Nat. Nanotechnol.|volume=3|issue=7|pages=429–433|doi=10.1038/nnano.2008.160|pmid=18654568|bibcode=2008NatNa...3..429Y }} for very large scale principal components analyses and convolution may create a new class of neural computing because they are fundamentally analog rather than digital (even though the first implementations may use digital devices).{{cite journal|last1=Strukov|first1=D. B.|last2=Snider|first2=G. S.|last3=Stewart|first3=D. R.|last4=Williams|first4=R. S.|year=2008|title=The missing memristor found|journal=Nature|volume=453|issue=7191|pages=80–83|bibcode=2008Natur.453...80S|doi=10.1038/nature06932|pmid=18451858|s2cid=4367148}}

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• {{Cite web|url=https://drive.google.com/file/d/1f0sPHv7ozHafASPwIOfuvF_RvP3FDPY0|title=Lecun 2019-7-11 ACM Tech Talk|website=Google Docs|access-date=2020-02-13}}

Category:Computational statistics

Category:Computational neuroscience