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History of artificial neural networks

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Artificial neural networks (ANNs) are models created using machine learning to perform a number of tasks. Their creation was inspired by neural circuitry.[1][lower-alpha 1] While some of the computational implementations ANNs relate to earlier discoveries in mathematics, the first implementation of ANNs was by psychologist Frank Rosenblatt, who developed the perceptron.[1] Little research was conducted on ANNs in the 1970s and 1980s, with the AAAI calling that period an "AI winter".[2]

Later, advances in hardware and the development of the backpropagation algorithm as well as recurrent neural networks and convolutional neural networks, renewed interest in ANNs. The 2010s, saw the development of a deep neural network (a neural network with many layers) called AlexNet.[3] It greatly outperformed other image recognition models, and is thought to have launched the ongoing AI spring, and further increasing interest in ANNs.[4] The transformer architecture was first described in 2017 as a method to teach ANNs grammatical dependencies in language,[5] and is the predominant architecture used by large language models, such as GPT-4. Diffusion models were first described in 2015, and began to be used by image generation models such as DALL-E in the 2020s.[citation needed]

Linear neural network

The simplest kind of feedforward neural network is a linear network, which consists of a single layer of output nodes; 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 in each node. The mean squared errors between these calculated outputs and a 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 Legendre (1805) and Gauss (1795) for the prediction of planetary movement.[6][7][8][9][10]

Perceptrons and other early neural networks

Warren McCulloch and Walter Pitts[11] (1943) also considered a non-learning computational model for neural networks.[12] 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.[13]

In the early 1940s, D. O. Hebb[14] 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. Farley and Clark[15] (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).[16]

Rosenblatt[1] (1958) created the perceptron, an algorithm for pattern recognition. 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.[17]

Some say that research stagnated following Minsky and Papert (1969),[18] who discovered that basic perceptrons were incapable of processing the exclusive-or circuit and that computers lacked sufficient power to process useful neural networks. However, by the time this book came out, methods for training multilayer perceptrons (MLPs) by deep learning were already known.[9]

First deep learning

The first deep learning MLP was published by Alexey Grigorevich Ivakhnenko and Valentin Lapa in 1965, as the Group Method of Data Handling.[19][20][21] This method employs incremental layer by layer training based on regression analysis, where useless units in hidden layers are pruned with the help of a validation set.

The first deep learning MLP trained by stochastic gradient descent[22] was published in 1967 by Shun'ichi Amari.[23][9] In computer experiments conducted by Amari's student Saito, a five layer MLP with two modifiable layers learned useful internal representations to classify non-linearily separable pattern classes.[9]

Backpropagation

Main page: Backpropagation

The backpropagation algorithm is an efficient application of the Leibniz chain rule (1673)[24] to networks of differentiable nodes.[9] It is also known as the reverse mode of automatic differentiation or reverse accumulation, due to Seppo Linnainmaa (1970).[25][26][27][28][9] The term "back-propagating errors" was introduced in 1962 by Frank Rosenblatt,[29][9] but he did not have an implementation of this procedure, although Henry J. Kelley had a continuous precursor of backpropagation[30] already in 1960 in the context of control theory.[9] In 1982, Paul Werbos applied backpropagation to MLPs in the way that has become standard.[31] In 1986, David E. Rumelhart et al. published an experimental analysis of the technique.[32]

Recurrent network architectures

Main page: Recurrent neural network

Wilhelm Lenz and Ernst Ising created and analyzed the Ising model (1925)[33] which is essentially a non-learning artificial recurrent neural network (RNN) consisting of neuron-like threshold elements.[9] In 1972, Shun'ichi Amari made this architecture adaptive.[34][9] His learning RNN was popularised by John Hopfield in 1982.[35]

Self-organizing maps

Main page: Self-organizing map

Self-organizing maps (SOMs) were described by Teuvo Kohonen in 1982.[36][37] SOMs are neurophysiologically inspired[38] 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,[39] 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.

Convolutional neural networks (CNNs)

Main page: Convolutional neural network

The origin of the CNN architecture is the "neocognitron"[40] introduced by Kunihiko Fukushima in 1980.[41][42] 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.[43][9] The rectifier has become the most popular activation function for CNNs and deep neural networks in general.[44]

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.[45] It did so by utilizing weight sharing in combination with backpropagation training.[46] Thus, while also using a pyramidal structure as in the neocognitron, it performed a global optimization of the weights instead of a local one.[45]

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.[47][48]

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.[49] 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[50] and breast cancer detection in mammograms in 1994.[51]

In 1990 Yamaguchi et al. introduced max-pooling, a fixed filtering operation that calculates and propagates the maximum value of a given region. They combined TDNNs with max-pooling in order to realize a speaker independent isolated word recognition system.[52] 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.[53][54][55][56] Max-pooling is often used in modern CNNs.[57]

LeNet-5, a 7-level CNN by Yann LeCun et al. in 1998,[58] that classifies digits, was applied by several banks to recognize hand-written numbers on checks (British English: 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.[59] Behnke (2003) relied only on the sign of the gradient (Rprop)[60] 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.[61]

In 2011, a deep GPU-based CNN called "DanNet" by Dan Ciresan, Ueli Meier, and Juergen Schmidhuber achieved human-competitive performance for the first time in computer vision contests.[62] Subsequently, a similar GPU-based CNN by Alex Krizhevsky, Ilya Sutskever, and Geoffrey Hinton won the ImageNet Large Scale Visual Recognition Challenge 2012.[63] A very deep CNN with over 100 layers by Kaiming He, Xiangyu Zhang, Shaoqing Ren, and Jian Sun of Microsoft won the ImageNet 2015 contest.[64]

ANNs were able to guarantee shift invariance to deal with small and large natural objects in large cluttered scenes, only when invariance extended beyond shift, to all ANN-learned concepts, such as location, type (object class label), scale, lighting and others. This was realized in Developmental Networks (DNs)[65] whose embodiments are Where-What Networks, WWN-1 (2008)[66] through WWN-7 (2013).[67]

Artificial curiosity and generative adversarial networks

Main page: Generative adversarial network

In 1991, Juergen Schmidhuber published adversarial neural networks that contest with each other in the form of a zero-sum game, where one network's gain is the other network's loss.[68][69][70] The first network is a generative model that models a probability distribution over output patterns. The second network learns by gradient descent to predict the reactions of the environment to these patterns. This was called "artificial curiosity." Earlier adversarial machine learning systems "neither involved unsupervised neural networks nor were about modeling data nor used gradient descent."[70]

In 2014, this adversarial principle was used in a generative adversarial network (GAN) by Ian Goodfellow et al.[71] Here the environmental reaction is 1 or 0 depending on whether the first network's output is in a given set. This can be used to create realistic deepfakes.[72]

In 1992, Schmidhuber also published another type of gradient-based adversarial neural networks where the goal of the zero-sum game is to create disentangled representations of input patterns. This was called predictability minimization.[73][74]

Nvidia's StyleGAN (2018)[75] is based on the Progressive GAN by Tero Karras, Timo Aila, Samuli Laine, and Jaakko Lehtinen.[76] Here the GAN generator is grown from small to large scale in a pyramidal fashion. StyleGANs improve consistency between fine and coarse details in the generator network.

Transformers and their variants

Main page: Transformer (machine learning model)

Many modern large language models such as ChatGPT, GPT-4, and BERT use a feedforward neural network called Transformer by Ashish Vaswani et. al. in their 2017 paper "Attention Is All You Need."[77] Transformers have increasingly become the model of choice for natural language processing problems,[78] replacing recurrent neural networks (RNNs) such as long short-term memory (LSTM).[79]

Basic ideas for this go back a long way: in 1992, Juergen Schmidhuber published the Transformer with "linearized self-attention" (save for a normalization operator),[80] which is also called the "linear Transformer."[81][82][9] He advertised it as an "alternative to RNNs"[80] that can learn "internal spotlights of attention,"[83] and experimentally applied it to problems of variable binding.[80] Here a slow feedforward neural network learns by gradient descent to control the fast weights of another neural network through outer products of self-generated activation patterns called "FROM" and "TO" which in Transformer terminology are called "key" and "value" for "self-attention."[82] This fast weight "attention mapping" is applied to queries. The 2017 Transformer[77] combines this with a softmax operator and a projection matrix.[9]

Transformers are also increasingly being used in computer vision.[84]

Deep learning with unsupervised or self-supervised pre-training

In the 1980s, backpropagation did not work well for deep FNNs and RNNs. Here the word "deep" refers to the number of layers through which the data is transformed. More precisely, deep learning systems have a substantial credit assignment path (CAP) depth.[85] The CAP is the chain of transformations from input to output. CAPs describe potentially causal connections between input and output. For an FNN, the depth of the CAPs is that of the network and is the number of hidden layers plus one (as the output layer is also parameterized). For RNNs, in which a signal may propagate through a layer more than once, the CAP depth is potentially unlimited.

To overcome this problem, Juergen Schmidhuber (1992) proposed a self-supervised hierarchy of RNNs pre-trained one level at a time by self-supervised learning.[86] This "neural history compressor" uses predictive coding to learn internal representations at multiple self-organizing time scales.[9] The deep architecture may be used to reproduce the original data from the top level feature activations.[86] The RNN hierarchy can be "collapsed" into a single RNN, by "distilling" a higher level "chunker" network into a lower level "automatizer" network.[86][9] In 1993, a chunker solved a deep learning task whose CAP depth exceeded 1000.[87] Such history compressors can substantially facilitate downstream supervised deep learning.[9]

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[88] 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.[89][90] 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.[91]

The vanishing gradient problem and its solutions

Main page: Long short-term memory

Sepp Hochreiter's diploma thesis (1991)[92] was called "one of the most important documents in the history of machine learning" by his supervisor Juergen Schmidhuber.[9] Hochreiter not only tested the neural history compressor,[86] but also identified and analyzed the vanishing gradient problem.[92][93] He proposed recurrent residual connections to solve this problem. This led to the deep learning method called long short-term memory (LSTM), published in 1997.[94] LSTM recurrent neural networks can learn "very deep learning" tasks[85] with long credit assignment paths that require memories of events that happened thousands of discrete time steps before. The "vanilla LSTM" with forget gate was introduced in 1999 by Felix Gers, Schmidhuber and Fred Cummins.[95] LSTM has become the most cited neural network of the 20th century.[9]

In 2015, Rupesh Kumar Srivastava, Klaus Greff, and Schmidhuber used LSTM principles to create the Highway network, a feedforward neural network with hundreds of layers, much deeper than previous networks.[96][97] 7 months later, Kaiming He, Xiangyu Zhang; Shaoqing Ren, and Jian Sun won the ImageNet 2015 competition with an open-gated or gateless Highway network variant called Residual neural network.[98] This has become the most cited neural network of the 21st century.[9]

In 2011, Xavier Glorot, Antoine Bordes and Yoshua Bengio found that the ReLU[43] of Kunihiko Fukushima also helps to overcome the vanishing gradient problem,[99] compared to widely used activation functions prior to 2011.

Hardware-based designs

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.[100]

Computational devices were created in CMOS, for both biophysical simulation and neuromorphic computing inspired by the structure and function of the human brain. Nanodevices[101] 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).[102] Ciresan and colleagues (2010)[103] in Schmidhuber's group showed that despite the vanishing gradient problem, GPUs make backpropagation feasible for many-layered feedforward neural networks.

Contests

Between 2009 and 2012, recurrent neural networks and deep feedforward neural networks developed in Schmidhuber's research group won eight international competitions in pattern recognition and machine learning.[104][105] For example, the bi-directional and multi-dimensional long short-term memory (LSTM)[106][107][108][109] of Graves et al. won three competitions in connected handwriting recognition at the 2009 International Conference on Document Analysis and Recognition (ICDAR), without any prior knowledge about the three languages to be learned.[108][107]

Ciresan and colleagues won pattern recognition contests, including the IJCNN 2011 Traffic Sign Recognition Competition,[110] the ISBI 2012 Segmentation of Neuronal Structures in Electron Microscopy Stacks challenge[111] and others. Their neural networks were the first pattern recognizers to achieve human-competitive/superhuman performance[62] on benchmarks such as traffic sign recognition (IJCNN 2012), or the MNIST handwritten digits problem.

Researchers demonstrated (2010) that deep neural networks interfaced to a hidden Markov model with context-dependent states that define the neural network output layer can drastically reduce errors in large-vocabulary speech recognition tasks such as voice search.[citation needed]

GPU-based implementations[112] of this approach won many pattern recognition contests, including the IJCNN 2011 Traffic Sign Recognition Competition,[110] the ISBI 2012 Segmentation of neuronal structures in EM stacks challenge,[111] the ImageNet Competition[63] and others.

Deep, highly nonlinear neural architectures similar to the neocognitron[113] and the "standard architecture of vision",[114] inspired by simple and complex cells, were pre-trained with unsupervised methods by Hinton.[90][89] A team from his lab won a 2012 contest sponsored by Merck to design software to help find molecules that might identify new drugs.[115]

Notes

  1. ↑ Neurons generate an action potential—the release of neurotransmitters that are chemical inputs to other neurons—based on the sum of its incoming chemical inputs.

References

  1. ↑ 1.0 1.1 1.2 Rosenblatt, F. (1958). "The Perceptron: A Probabilistic Model For Information Storage And Organization In The Brain". Psychological Review 65 (6): 386–408. doi:10.1037/h0042519. PMID 13602029. 
  2. ↑ Crevier, Daniel (1993), AI: The Tumultuous Search for Artificial Intelligence, New York, NY: BasicBooks, ISBN:0-465-02997-3 
  3. ↑ Krizhevsky, Alex; Sutskever, Ilya; Hinton, Geoffrey E. (2017-05-24). "ImageNet classification with deep convolutional neural networks". Communications of the ACM 60 (6): 84–90. doi:10.1145/3065386. ISSN 0001-0782. https://papers.nips.cc/paper/4824-imagenet-classification-with-deep-convolutional-neural-networks.pdf. 
  4. ↑ Gershgorn, Dave (26 July 2017). "The data that transformed AI research—and possibly the world". https://qz.com/1034972/the-data-that-changed-the-direction-of-ai-research-and-possibly-the-world/. 
  5. ↑ Vaswani, Ashish; Shazeer, Noam; Parmar, Niki; Uszkoreit, Jakob; Jones, Llion; Gomez, Aidan N; Kaiser, Łukasz; Polosukhin, Illia (2017). "Attention is All you Need". Advances in Neural Information Processing Systems (Curran Associates, Inc.) 30. https://proceedings.neurips.cc/paper/2017/file/3f5ee243547dee91fbd053c1c4a845aa-Paper.pdf. 
  6. ↑ Mansfield Merriman, "A List of Writings Relating to the Method of Least Squares"
  7. ↑ Stigler, Stephen M. (1981). "Gauss and the Invention of Least Squares". Ann. Stat. 9 (3): 465–474. doi:10.1214/aos/1176345451. 
  8. ↑ Bretscher, Otto (1995). Linear Algebra With Applications (3rd ed.). Upper Saddle River, NJ: Prentice Hall. 
  9. ↑ 9.00 9.01 9.02 9.03 9.04 9.05 9.06 9.07 9.08 9.09 9.10 9.11 9.12 9.13 9.14 9.15 9.16 9.17 9.18 Schmidhuber, Juergen (2022). "Annotated History of Modern AI and Deep Learning". arXiv:2212.11279 [cs.NE].
  10. ↑ Stigler, Stephen M. (1986). The History of Statistics: The Measurement of Uncertainty before 1900. Cambridge: Harvard. ISBN 0-674-40340-1. https://archive.org/details/historyofstatist00stig. 
  11. ↑ McCulloch, Warren; Walter Pitts (1943). "A Logical Calculus of Ideas Immanent in Nervous Activity". Bulletin of Mathematical Biophysics 5 (4): 115–133. doi:10.1007/BF02478259. 
  12. ↑ Kleene, S.C. (1956). "Representation of Events in Nerve Nets and Finite Automata". Annals of Mathematics Studies (Princeton University Press) (34): pp. 3–41. https://www.degruyter.com/view/books/9781400882618/9781400882618-002/9781400882618-002.xml. 
  13. ↑ Kleene, S.C. (1956). "Representation of Events in Nerve Nets and Finite Automata". Annals of Mathematics Studies (Princeton University Press) (34): pp. 3–41. https://www.degruyter.com/view/books/9781400882618/9781400882618-002/9781400882618-002.xml. 
  14. ↑ Hebb, Donald (1949). The Organization of Behavior. New York: Wiley. ISBN 978-1-135-63190-1. https://books.google.com/books?id=ddB4AgAAQBAJ. 
  15. ↑ Farley, B.G.; W.A. Clark (1954). "Simulation of Self-Organizing Systems by Digital Computer". IRE Transactions on Information Theory 4 (4): 76–84. doi:10.1109/TIT.1954.1057468. 
  16. ↑ Rochester, N.; J.H. Holland; L.H. Habit; W.L. Duda (1956). "Tests on a cell assembly theory of the action of the brain, using a large digital computer". IRE Transactions on Information Theory 2 (3): 80–93. doi:10.1109/TIT.1956.1056810. 
  17. ↑ David H. Hubel and Torsten N. Wiesel (2005). Brain and visual perception: the story of a 25-year collaboration. Oxford University Press US. p. 106. ISBN 978-0-19-517618-6. https://books.google.com/books?id=8YrxWojxUA4C&pg=PA106. 
  18. ↑ Minsky, Marvin; Papert, Seymour (1969). Perceptrons: An Introduction to Computational Geometry. MIT Press. ISBN 978-0-262-63022-1. https://books.google.com/books?id=Ow1OAQAAIAAJ. 
  19. ↑ Schmidhuber, J. (2015). "Deep Learning in Neural Networks: An Overview". Neural Networks 61: 85–117. doi:10.1016/j.neunet.2014.09.003. PMID 25462637. 
  20. ↑ Ivakhnenko, A. G. (1973). Cybernetic Predicting Devices. CCM Information Corporation. https://books.google.com/books?id=FhwVNQAACAAJ. 
  21. ↑ Ivakhnenko, A. G.; Grigorʹevich Lapa, Valentin (1967). Cybernetics and forecasting techniques. American Elsevier Pub. Co.. https://books.google.com/books?id=rGFgAAAAMAAJ. 
  22. ↑ Robbins, H.; Monro, S. (1951). "A Stochastic Approximation Method". The Annals of Mathematical Statistics 22 (3): 400. doi:10.1214/aoms/1177729586. 
  23. ↑ Amari, Shun'ichi (1967). "A theory of adaptive pattern classifier". IEEE Transactions EC (16): 279–307. 
  24. ↑ Leibniz, Gottfried Wilhelm Freiherr von (1920) (in en). 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). Open court publishing Company. ISBN 9780598818461. https://books.google.com/books?id=bOIGAAAAYAAJ&q=leibniz+altered+manuscripts&pg=PA90. 
  25. ↑ Linnainmaa, Seppo (1970). The representation of the cumulative rounding error of an algorithm as a Taylor expansion of the local rounding errors (Masters) (in suomi). University of Helsinki. pp. 6–7.
  26. ↑ Linnainmaa, Seppo (1976). "Taylor expansion of the accumulated rounding error". BIT Numerical Mathematics 16 (2): 146–160. doi:10.1007/bf01931367. 
  27. ↑ Griewank, Andreas (2012). "Who Invented the Reverse Mode of Differentiation?". Optimization Stories. Documenta Matematica, Extra Volume ISMP. pp. 389–400. 
  28. ↑ Griewank, Andreas; Walther, Andrea (2008). Evaluating Derivatives: Principles and Techniques of Algorithmic Differentiation, Second Edition. SIAM. ISBN 978-0-89871-776-1. https://books.google.com/books?id=xoiiLaRxcbEC. 
  29. ↑ Rosenblatt, Frank (1962). Principles of Neurodynamics. Spartan, New York. 
  30. ↑ Kelley, Henry J. (1960). "Gradient theory of optimal flight paths". ARS Journal 30 (10): 947–954. doi:10.2514/8.5282. 
  31. ↑ Werbos, Paul (1982). "Applications of advances in nonlinear sensitivity analysis". System modeling and optimization. Springer. pp. 762–770. http://werbos.com/Neural/SensitivityIFIPSeptember1981.pdf. Retrieved 2 July 2017. 
  32. ↑ Rumelhart, David E., Geoffrey E. Hinton, and R. J. Williams. "Learning Internal Representations by Error Propagation". David E. Rumelhart, James L. McClelland, and the PDP research group. (editors), Parallel distributed processing: Explorations in the microstructure of cognition, Volume 1: Foundation. MIT Press, 1986.
  33. ↑ Brush, Stephen G. (1967). "History of the Lenz-Ising Model". Reviews of Modern Physics 39 (4): 883–893. doi:10.1103/RevModPhys.39.883. Bibcode: 1967RvMP...39..883B. 
  34. ↑ Amari, Shun-Ichi (1972). "Learning patterns and pattern sequences by self-organizing nets of threshold elements". IEEE Transactions C (21): 1197–1206. 
  35. ↑ Hopfield, J. J. (1982). "Neural networks and physical systems with emergent collective computational abilities". Proceedings of the National Academy of Sciences 79 (8): 2554–2558. doi:10.1073/pnas.79.8.2554. PMID 6953413. Bibcode: 1982PNAS...79.2554H. 
  36. ↑ Kohonen, Teuvo; Honkela, Timo (2007). "Kohonen Network". Scholarpedia 2 (1): 1568. doi:10.4249/scholarpedia.1568. Bibcode: 2007SchpJ...2.1568K. 
  37. ↑ Kohonen, Teuvo (1982). "Self-Organized Formation of Topologically Correct Feature Maps". Biological Cybernetics 43 (1): 59–69. doi:10.1007/bf00337288. 
  38. ↑ Von der Malsburg, C (1973). "Self-organization of orientation sensitive cells in the striate cortex". Kybernetik 14 (2): 85–100. doi:10.1007/bf00288907. PMID 4786750. 
  39. ↑ "Homunculus | Meaning & Definition in UK English | Lexico.com" (in en). https://www.lexico.com/definition/homunculus. 
  40. ↑ Fukushima, K. (2007). "Neocognitron". Scholarpedia 2 (1): 1717. doi:10.4249/scholarpedia.1717. Bibcode: 2007SchpJ...2.1717F. 
  41. ↑ Fukushima, Kunihiko (1980). "Neocognitron: A Self-organizing Neural Network Model for a Mechanism of Pattern Recognition Unaffected by Shift in Position". Biological Cybernetics 36 (4): 193–202. doi:10.1007/BF00344251. PMID 7370364. https://www.cs.princeton.edu/courses/archive/spr08/cos598B/Readings/Fukushima1980.pdf. Retrieved 16 November 2013. 
  42. ↑ LeCun, Yann; Bengio, Yoshua; Hinton, Geoffrey (2015). "Deep learning". Nature 521 (7553): 436–444. doi:10.1038/nature14539. PMID 26017442. Bibcode: 2015Natur.521..436L. 
  43. ↑ 43.0 43.1 Fukushima, K. (1969). "Visual feature extraction by a multilayered network of analog threshold elements". IEEE Transactions on Systems Science and Cybernetics 5 (4): 322–333. doi:10.1109/TSSC.1969.300225. 
  44. ↑ Ramachandran, Prajit; Barret, Zoph; Quoc, V. Le (October 16, 2017). "Searching for Activation Functions". arXiv:1710.05941 [cs.NE].
  45. ↑ 45.0 45.1 Waibel, Alex (December 1987). "Phoneme Recognition Using Time-Delay Neural Networks". Meeting of the Institute of Electrical, Information and Communication Engineers (IEICE). Tokyo, Japan. 
  46. ↑ Alexander Waibel et al., Phoneme Recognition Using Time-Delay Neural Networks IEEE Transactions on Acoustics, Speech, and Signal Processing, Volume 37, No. 3, pp. 328. – 339 March 1989.
  47. ↑ Zhang, Wei (1988). "Shift-invariant pattern recognition neural network and its optical architecture". Proceedings of Annual Conference of the Japan Society of Applied Physics. https://drive.google.com/file/d/1nN_5odSG_QVae54EsQN_qSz-0ZsX6wA0/view?usp=sharing. 
  48. ↑ Zhang, Wei (1990). "Parallel distributed processing model with local space-invariant interconnections and its optical architecture". Applied Optics 29 (32): 4790–7. doi:10.1364/AO.29.004790. PMID 20577468. Bibcode: 1990ApOpt..29.4790Z. https://drive.google.com/file/d/0B65v6Wo67Tk5ODRzZmhSR29VeDg/view?usp=sharing. 
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