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data-mw-deduplicate="TemplateStyles:r1236090951">.mw-parser-output .hatnote{font-style:italic}.mw-parser-output div.hatnote{padding-left:1.6em;margin-bottom:0.5em}.mw-parser-output .hatnote i{font-style:normal}.mw-parser-output .hatnote+link+.hatnote{margin-top:-0.5em}@media print{body.ns-0 .mw-parser-output .hatnote{display:none!important}}</style><div role="note" class="hatnote navigation-not-searchable">This article is about the computational models used for artificial intelligence. For other uses, see <a href="/wiki/Neural_network_(disambiguation)" class="mw-disambig" title="Neural network (disambiguation)">Neural network (disambiguation)</a>.</div> In <a href="/wiki/Machine_learning" title="Machine learning">machine learning</a>, a neural network (also artificial neural network or neural net, abbreviated ANN or NN) is a <a href="/wiki/Machine_learning#Models" title="Machine learning">model</a> inspired by the structure and function of <a href="/wiki/Biological_neural_network" class="mw-redirect" title="Biological neural network">biological neural networks</a> in animal <a href="/wiki/Brain" title="Brain">brains</a>.<a href="#cite_note-1">[1]</a><a href="#cite_note-2">[2]</a> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Colored_neural_network.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/4/46/Colored_neural_network.svg/250px-Colored_neural_network.svg.png" decoding="async" width="250" height="301" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/46/Colored_neural_network.svg/375px-Colored_neural_network.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/46/Colored_neural_network.svg/500px-Colored_neural_network.svg.png 2x" data-file-width="296" data-file-height="356"></a><figcaption>An artificial neural network is an interconnected group of nodes, inspired by a simplification of <a href="/wiki/Neuron" title="Neuron">neurons</a> in a <a href="/wiki/Brain" title="Brain">brain</a>. Here, each circular node represents an <a href="/wiki/Artificial_neuron" title="Artificial neuron">artificial neuron</a> and an arrow represents a connection from the output of one artificial neuron to the input of another.</figcaption></figure> <style data-mw-deduplicate="TemplateStyles:r1244144826">.mw-parser-output .machine-learning-list-title{background-color:#ddddff}html.skin-theme-clientpref-night .mw-parser-output .machine-learning-list-title{background-color:#222}@media(prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .machine-learning-list-title{background-color:#222}}</style> <style data-mw-deduplicate="TemplateStyles:r1129693374">.mw-parser-output .hlist dl,.mw-parser-output .hlist ol,.mw-parser-output .hlist ul{margin:0;padding:0}.mw-parser-output .hlist dd,.mw-parser-output .hlist dt,.mw-parser-output .hlist li{margin:0;display:inline}.mw-parser-output .hlist.inline,.mw-parser-output .hlist.inline dl,.mw-parser-output .hlist.inline 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ol>li:first-child::before{content:" ("counter(listitem)"\a0 "}</style><style data-mw-deduplicate="TemplateStyles:r1246091330">.mw-parser-output .sidebar{width:22em;float:right;clear:right;margin:0.5em 0 1em 1em;background:var(--background-color-neutral-subtle,#f8f9fa);border:1px solid var(--border-color-base,#a2a9b1);padding:0.2em;text-align:center;line-height:1.4em;font-size:88%;border-collapse:collapse;display:table}body.skin-minerva .mw-parser-output .sidebar{display:table!important;float:right!important;margin:0.5em 0 1em 1em!important}.mw-parser-output .sidebar-subgroup{width:100%;margin:0;border-spacing:0}.mw-parser-output .sidebar-left{float:left;clear:left;margin:0.5em 1em 1em 0}.mw-parser-output .sidebar-none{float:none;clear:both;margin:0.5em 1em 1em 0}.mw-parser-output .sidebar-outer-title{padding:0 0.4em 0.2em;font-size:125%;line-height:1.2em;font-weight:bold}.mw-parser-output .sidebar-top-image{padding:0.4em}.mw-parser-output .sidebar-top-caption,.mw-parser-output .sidebar-pretitle-with-top-image,.mw-parser-output .sidebar-caption{padding:0.2em 0.4em 0;line-height:1.2em}.mw-parser-output .sidebar-pretitle{padding:0.4em 0.4em 0;line-height:1.2em}.mw-parser-output .sidebar-title,.mw-parser-output .sidebar-title-with-pretitle{padding:0.2em 0.8em;font-size:145%;line-height:1.2em}.mw-parser-output .sidebar-title-with-pretitle{padding:0.1em 0.4em}.mw-parser-output .sidebar-image{padding:0.2em 0.4em 0.4em}.mw-parser-output .sidebar-heading{padding:0.1em 0.4em}.mw-parser-output .sidebar-content{padding:0 0.5em 0.4em}.mw-parser-output .sidebar-content-with-subgroup{padding:0.1em 0.4em 0.2em}.mw-parser-output .sidebar-above,.mw-parser-output .sidebar-below{padding:0.3em 0.8em;font-weight:bold}.mw-parser-output .sidebar-collapse .sidebar-above,.mw-parser-output .sidebar-collapse .sidebar-below{border-top:1px solid #aaa;border-bottom:1px solid #aaa}.mw-parser-output .sidebar-navbar{text-align:right;font-size:115%;padding:0 0.4em 0.4em}.mw-parser-output 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.mw-parser-output .sidebar:not(.notheme) .sidebar-title-with-pretitle{background:transparent!important}html.skin-theme-clientpref-os .mw-parser-output .sidebar:not(.notheme) .sidebar-title-with-pretitle a{color:var(--color-progressive)!important}}@media print{body.ns-0 .mw-parser-output .sidebar{display:none!important}}</style><style data-mw-deduplicate="TemplateStyles:r886047488">.mw-parser-output .nobold{font-weight:normal}</style><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r886047488"> An ANN consists of connected units or nodes called <a href="/wiki/Artificial_neuron" title="Artificial neuron">artificial neurons</a>, which loosely model the <a href="/wiki/Neuron" title="Neuron">neurons</a> in the brain. These are connected by edges, which model the <a href="/wiki/Synapse" title="Synapse">synapses</a> in the brain. Each artificial neuron receives signals from connected neurons, then processes them and sends a signal to other connected neurons. The "signal" is a <a href="/wiki/Real_number" title="Real number">real number</a>, and the output of each neuron is computed by some non-linear function of the sum of its inputs, called the <a href="/wiki/Activation_function" title="Activation function">activation function</a>. The strength of the signal at each connection is determined by a <a href="/wiki/Weighting" title="Weighting">weight</a>, which adjusts during the learning process. Typically, neurons are aggregated into layers. Different layers may perform different transformations on their inputs. Signals travel from the first layer (the input layer) to the last layer (the output layer), possibly passing through multiple intermediate layers (<a href="/wiki/Hidden_layer" title="Hidden layer">hidden layers</a>). A network is typically called a deep neural network if it has at least two hidden layers.<a href="#cite_note-3">[3]</a> Artificial neural networks are used for various tasks, including <a href="/wiki/Predictive_modeling" class="mw-redirect" title="Predictive modeling">predictive modeling</a>, <a href="/wiki/Adaptive_control" title="Adaptive control">adaptive control</a>, and solving problems in <a href="/wiki/Artificial_intelligence" title="Artificial intelligence">artificial intelligence</a>. They can learn from experience, and can derive conclusions from a complex and seemingly unrelated set of information. <style data-mw-deduplicate="TemplateStyles:r886046785">.mw-parser-output .toclimit-2 .toclevel-1 ul,.mw-parser-output .toclimit-3 .toclevel-2 ul,.mw-parser-output .toclimit-4 .toclevel-3 ul,.mw-parser-output .toclimit-5 .toclevel-4 ul,.mw-parser-output .toclimit-6 .toclevel-5 ul,.mw-parser-output .toclimit-7 .toclevel-6 ul{display:none}</style><div class="toclimit-3"><div id="toc" class="toc" role="navigation" aria-labelledby="mw-toc-heading"><input type="checkbox" role="button" id="toctogglecheckbox" class="toctogglecheckbox" style="display:none"><div class="toctitle" lang="en" dir="ltr"><h2 id="mw-toc-heading">Contents</h2><label class="toctogglelabel" for="toctogglecheckbox"></label></div> <ul> <li class="toclevel-1 tocsection-1"><a href="#Training">1 Training</a></li> <li class="toclevel-1 tocsection-2"><a href="#History">2 History</a> <ul> <li class="toclevel-2 tocsection-3"><a href="#Early_work">2.1 Early work</a></li> <li class="toclevel-2 tocsection-4"><a href="#Deep_learning_breakthroughs_in_the_1960s_and_1970s">2.2 Deep learning breakthroughs in the 1960s and 1970s</a></li> <li class="toclevel-2 tocsection-5"><a href="#Backpropagation">2.3 Backpropagation</a></li> <li class="toclevel-2 tocsection-6"><a href="#Convolutional_neural_networks">2.4 Convolutional neural networks</a></li> <li class="toclevel-2 tocsection-7"><a href="#Recurrent_neural_networks">2.5 Recurrent neural networks</a></li> <li class="toclevel-2 tocsection-8"><a href="#Deep_learning">2.6 Deep learning</a></li> </ul> </li> <li class="toclevel-1 tocsection-9"><a href="#Models">3 Models</a> <ul> <li class="toclevel-2 tocsection-10"><a href="#Artificial_neurons">3.1 Artificial neurons</a></li> <li class="toclevel-2 tocsection-11"><a href="#Organization">3.2 Organization</a></li> <li class="toclevel-2 tocsection-12"><a href="#Hyperparameter">3.3 Hyperparameter</a></li> <li class="toclevel-2 tocsection-13"><a href="#Learning">3.4 Learning</a> <ul> <li class="toclevel-3 tocsection-14"><a href="#Learning_rate">3.4.1 Learning rate</a></li> <li class="toclevel-3 tocsection-15"><a href="#Cost_function">3.4.2 Cost function</a></li> <li class="toclevel-3 tocsection-16"><a href="#Backpropagation_2">3.4.3 Backpropagation</a></li> </ul> </li> <li class="toclevel-2 tocsection-17"><a href="#Learning_paradigms">3.5 Learning paradigms</a> <ul> <li class="toclevel-3 tocsection-18"><a href="#Supervised_learning">3.5.1 Supervised learning</a></li> <li class="toclevel-3 tocsection-19"><a href="#Unsupervised_learning">3.5.2 Unsupervised learning</a></li> <li class="toclevel-3 tocsection-20"><a href="#Reinforcement_learning">3.5.3 Reinforcement learning</a></li> <li class="toclevel-3 tocsection-21"><a href="#Self-learning">3.5.4 Self-learning</a></li> <li class="toclevel-3 tocsection-22"><a href="#Neuroevolution">3.5.5 Neuroevolution</a></li> </ul> </li> <li class="toclevel-2 tocsection-23"><a href="#Stochastic_neural_network">3.6 Stochastic neural network</a></li> <li class="toclevel-2 tocsection-24"><a href="#Other">3.7 Other</a> <ul> <li class="toclevel-3 tocsection-25"><a href="#Modes">3.7.1 Modes</a></li> </ul> </li> </ul> </li> <li class="toclevel-1 tocsection-26"><a href="#Types">4 Types</a></li> <li class="toclevel-1 tocsection-27"><a href="#Network_design">5 Network design</a></li> <li class="toclevel-1 tocsection-28"><a href="#Applications">6 Applications</a></li> <li class="toclevel-1 tocsection-29"><a href="#Theoretical_properties">7 Theoretical properties</a> <ul> <li class="toclevel-2 tocsection-30"><a href="#Computational_power">7.1 Computational power</a></li> <li class="toclevel-2 tocsection-31"><a href="#Capacity">7.2 Capacity</a></li> <li class="toclevel-2 tocsection-32"><a href="#Convergence">7.3 Convergence</a></li> <li class="toclevel-2 tocsection-33"><a href="#Generalization_and_statistics">7.4 Generalization and statistics</a></li> </ul> </li> <li class="toclevel-1 tocsection-34"><a href="#Criticism">8 Criticism</a> <ul> <li class="toclevel-2 tocsection-35"><a href="#Training_2">8.1 Training</a></li> <li class="toclevel-2 tocsection-36"><a href="#Theory">8.2 Theory</a></li> <li class="toclevel-2 tocsection-37"><a href="#Hardware">8.3 Hardware</a></li> <li class="toclevel-2 tocsection-38"><a href="#Practical_counterexamples">8.4 Practical counterexamples</a></li> <li class="toclevel-2 tocsection-39"><a href="#Hybrid_approaches">8.5 Hybrid approaches</a></li> <li class="toclevel-2 tocsection-40"><a href="#Dataset_bias">8.6 Dataset bias</a></li> </ul> </li> <li class="toclevel-1 tocsection-41"><a href="#Gallery">9 Gallery</a></li> <li class="toclevel-1 tocsection-42"><a href="#Recent_advancements_and_future_directions">10 Recent advancements and future directions</a> <ul> <li class="toclevel-2 tocsection-43"><a href="#Image_processing">10.1 Image processing</a></li> <li class="toclevel-2 tocsection-44"><a href="#Speech_recognition">10.2 Speech recognition</a></li> <li class="toclevel-2 tocsection-45"><a href="#Natural_language_processing">10.3 Natural language processing</a></li> <li class="toclevel-2 tocsection-46"><a href="#Control_systems">10.4 Control systems</a></li> <li class="toclevel-2 tocsection-47"><a href="#Finance">10.5 Finance</a></li> <li class="toclevel-2 tocsection-48"><a href="#Medicine">10.6 Medicine</a></li> <li class="toclevel-2 tocsection-49"><a href="#Content_creation">10.7 Content creation</a></li> </ul> </li> <li class="toclevel-1 tocsection-50"><a href="#See_also">11 See also</a></li> <li class="toclevel-1 tocsection-51"><a href="#References">12 References</a></li> <li class="toclevel-1 tocsection-52"><a href="#Bibliography">13 Bibliography</a></li> <li class="toclevel-1 tocsection-53"><a href="#External_links">14 External links</a></li> </ul> </div> </div> </section><div class="mw-heading mw-heading2 section-heading" onclick="mfTempOpenSection(1)"><h2 id="Training">Training</h2> <a role="button" href="/w/index.php?title=Neural_network_(machine_learning)&action=edit&section=1" title="Edit section: Training" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> edit </a> </div><section class="mf-section-1 collapsible-block" id="mf-section-1"> Neural networks are typically trained through <a href="/wiki/Empirical_risk_minimization" title="Empirical risk minimization">empirical risk minimization</a>. This method is based on the idea of optimizing the network's parameters to minimize the difference, or empirical risk, between the predicted output and the actual target values in a given dataset.<a href="#cite_note-:2-4">[4]</a> Gradient-based methods such as <a href="/wiki/Backpropagation" title="Backpropagation">backpropagation</a> are usually used to estimate the parameters of the network.<a href="#cite_note-:2-4">[4]</a> During the training phase, ANNs learn from <a href="/wiki/Labeled_data" title="Labeled data">labeled</a> training data by iteratively updating their parameters to minimize a defined <a href="/wiki/Loss_functions_for_classification" title="Loss functions for classification">loss function</a>.<a href="#cite_note-:4-5">[5]</a> This method allows the network to generalize to unseen data.<style data-mw-deduplicate="TemplateStyles:r1237032888/mw-parser-output/.tmulti">.mw-parser-output .tmulti .multiimageinner{display:flex;flex-direction:column}.mw-parser-output .tmulti .trow{display:flex;flex-direction:row;clear:left;flex-wrap:wrap;width:100%;box-sizing:border-box}.mw-parser-output .tmulti .tsingle{margin:1px;float:left}.mw-parser-output .tmulti .theader{clear:both;font-weight:bold;text-align:center;align-self:center;background-color:transparent;width:100%}.mw-parser-output .tmulti .thumbcaption{background-color:transparent}.mw-parser-output .tmulti .text-align-left{text-align:left}.mw-parser-output .tmulti .text-align-right{text-align:right}.mw-parser-output .tmulti .text-align-center{text-align:center}@media all and (max-width:720px){.mw-parser-output .tmulti .thumbinner{width:100%!important;box-sizing:border-box;max-width:none!important;align-items:center}.mw-parser-output .tmulti .trow{justify-content:center}.mw-parser-output .tmulti .tsingle{float:none!important;max-width:100%!important;box-sizing:border-box;text-align:center}.mw-parser-output .tmulti .tsingle .thumbcaption{text-align:left}.mw-parser-output .tmulti .trow>.thumbcaption{text-align:center}}@media screen{html.skin-theme-clientpref-night .mw-parser-output .tmulti .multiimageinner img{background-color:white}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .tmulti .multiimageinner img{background-color:white}}</style><div class="thumb tmulti tright"><div class="thumbinner multiimageinner" style="width:392px;max-width:392px"><div class="trow"><div class="tsingle" style="width:167px;max-width:167px"><div class="thumbimage" style="height:188px;overflow:hidden"><a href="/wiki/File:Simplified_neural_network_training_example.svg" class="mw-file-description"><noscript><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/0/0c/Simplified_neural_network_training_example.svg/165px-Simplified_neural_network_training_example.svg.png" decoding="async" width="165" height="189" class="mw-file-element" data-file-width="773" data-file-height="884"></noscript><span class="lazy-image-placeholder" style="width: 165px;height: 189px;" data-src="//upload.wikimedia.org/wikipedia/commons/thumb/0/0c/Simplified_neural_network_training_example.svg/165px-Simplified_neural_network_training_example.svg.png" data-alt="" data-width="165" data-height="189" data-srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/0c/Simplified_neural_network_training_example.svg/248px-Simplified_neural_network_training_example.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/0c/Simplified_neural_network_training_example.svg/330px-Simplified_neural_network_training_example.svg.png 2x" data-class="mw-file-element"> </a></div><div class="thumbcaption">Simplified example of training a neural network in object detection: The network is trained by multiple images that are known to depict <a href="/wiki/Starfish" title="Starfish">starfish</a> and <a href="/wiki/Sea_urchin" title="Sea urchin">sea urchins</a>, which are correlated with "nodes" that represent visual <a href="/wiki/Feature_(computer_vision)" title="Feature (computer vision)">features</a>. The starfish match with a ringed texture and a star outline, whereas most sea urchins match with a striped texture and oval shape. However, the instance of a ring textured sea urchin creates a weakly weighted association between them.</div></div><div class="tsingle" style="width:221px;max-width:221px"><div class="thumbimage" style="height:188px;overflow:hidden"><a href="/wiki/File:Simplified_neural_network_example.svg" class="mw-file-description"><noscript><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/b/b7/Simplified_neural_network_example.svg/219px-Simplified_neural_network_example.svg.png" decoding="async" width="219" height="188" class="mw-file-element" data-file-width="1028" data-file-height="882"></noscript><span class="lazy-image-placeholder" style="width: 219px;height: 188px;" data-src="//upload.wikimedia.org/wikipedia/commons/thumb/b/b7/Simplified_neural_network_example.svg/219px-Simplified_neural_network_example.svg.png" data-alt="" data-width="219" data-height="188" data-srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/b7/Simplified_neural_network_example.svg/329px-Simplified_neural_network_example.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/b7/Simplified_neural_network_example.svg/438px-Simplified_neural_network_example.svg.png 2x" data-class="mw-file-element"> </a></div><div class="thumbcaption">Subsequent run of the network on an input image (left):<a href="#cite_note-6">[6]</a> The network correctly detects the starfish. However, the weakly weighted association between ringed texture and sea urchin also confers a weak signal to the latter from one of two intermediate nodes. In addition, a shell that was not included in the training gives a weak signal for the oval shape, also resulting in a weak signal for the sea urchin output. These weak signals may result in a <a href="/wiki/False_positive" class="mw-redirect" title="False positive">false positive</a> result for sea urchin. In reality, textures and outlines would not be represented by single nodes, but rather by associated weight patterns of multiple nodes.</div></div></div></div></div> </section><div class="mw-heading mw-heading2 section-heading" onclick="mfTempOpenSection(2)"><h2 id="History">History</h2> <a role="button" href="/w/index.php?title=Neural_network_(machine_learning)&action=edit&section=2" title="Edit section: History" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> edit </a> </div><section class="mf-section-2 collapsible-block" id="mf-section-2"> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/History_of_artificial_neural_networks" title="History of artificial neural networks">History of artificial neural networks</a></div> <div class="mw-heading mw-heading3"><h3 id="Early_work">Early work</h3> <a role="button" href="/w/index.php?title=Neural_network_(machine_learning)&action=edit&section=3" title="Edit section: Early work" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> edit </a> </div> Today's deep neural networks are based on early work in <a href="/wiki/Statistics" title="Statistics">statistics</a> over 200 years ago. The simplest kind of <a href="/wiki/Feedforward_neural_network" title="Feedforward neural network">feedforward neural network</a> (FNN) is a linear network, which consists of a single layer of output nodes with linear activation functions; the inputs are fed directly to the outputs via a series of weights. The sum of the products of the weights and the inputs is calculated at each node. The <a href="/wiki/Mean_squared_error" title="Mean squared error">mean squared errors</a> between these calculated outputs and the given target values are minimized by creating an adjustment to the weights. This technique has been known for over two centuries as the <a href="/wiki/Method_of_least_squares" class="mw-redirect" title="Method of least squares">method of least squares</a> or <a href="/wiki/Linear_regression" title="Linear regression">linear regression</a>. It was used as a means of finding a good rough linear fit to a set of points by <a href="/wiki/Adrien-Marie_Legendre" title="Adrien-Marie Legendre">Legendre</a> (1805) and <a href="/wiki/Gauss" class="mw-redirect" title="Gauss">Gauss</a> (1795) for the prediction of planetary movement.<a href="#cite_note-legendre1805-7">[7]</a><a href="#cite_note-gauss1795-8">[8]</a><a href="#cite_note-brertscher-9">[9]</a><a href="#cite_note-DLhistory-10">[10]</a><a href="#cite_note-stigler-11">[11]</a> Historically, digital computers such as the <a href="/wiki/Von_Neumann_model" class="mw-redirect" title="Von Neumann model">von Neumann model</a> operate via the execution of explicit instructions with access to memory by a number of processors. Some neural networks, on the other hand, originated from efforts to model information processing in biological systems through the framework of <a href="/wiki/Connectionism" title="Connectionism">connectionism</a>. Unlike the von Neumann model, connectionist computing does not separate memory and processing. <a href="/wiki/Warren_McCulloch" class="mw-redirect" title="Warren McCulloch">Warren McCulloch</a> and <a href="/wiki/Walter_Pitts" title="Walter Pitts">Walter Pitts</a><a href="#cite_note-WM-12">[12]</a> (1943) considered a non-learning computational model for neural networks.<a href="#cite_note-13">[13]</a> 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 <a href="/wiki/Artificial_intelligence" title="Artificial intelligence">artificial intelligence</a>. In the late 1940s, <a href="/wiki/Donald_O._Hebb" title="Donald O. Hebb">D. O. Hebb</a><a href="#cite_note-14">[14]</a> proposed a learning <a href="/wiki/Hypothesis" title="Hypothesis">hypothesis</a> based on the mechanism of <a href="/wiki/Neuroplasticity" title="Neuroplasticity">neural plasticity</a> that became known as <a href="/wiki/Hebbian_learning" class="mw-redirect" title="Hebbian learning">Hebbian learning</a>. It was used in many early neural networks, such as Rosenblatt's <a href="/wiki/Perceptron" title="Perceptron">perceptron</a> and the <a href="/wiki/Hopfield_network" title="Hopfield network">Hopfield network</a>. Farley and <a href="/wiki/Wesley_A._Clark" title="Wesley A. Clark">Clark</a><a href="#cite_note-15">[15]</a> (1954) used computational machines to simulate a Hebbian network. Other neural network computational machines were created by <a href="/wiki/Nathaniel_Rochester_(computer_scientist)" title="Nathaniel Rochester (computer scientist)">Rochester</a>, Holland, Habit and Duda (1956).<a href="#cite_note-16">[16]</a> In 1958, psychologist <a href="/wiki/Frank_Rosenblatt" title="Frank Rosenblatt">Frank Rosenblatt</a> described the perceptron, one of the first implemented artificial neural networks,<a href="#cite_note-17">[17]</a><a href="#cite_note-18">[18]</a><a href="#cite_note-Werbos_1975-19">[19]</a><a href="#cite_note-20">[20]</a> funded by the United States <a href="/wiki/Office_of_Naval_Research" title="Office of Naval Research">Office of Naval Research</a>.<a href="#cite_note-Olazaran-21">[21]</a> R. D. Joseph (1960)<a href="#cite_note-joseph1960-22">[22]</a> mentions an even earlier perceptron-like device by Farley and Clark:<a href="#cite_note-DLhistory-10">[10]</a> "Farley and Clark of MIT Lincoln Laboratory actually preceded Rosenblatt in the development of a perceptron-like device." However, "they dropped the subject." The perceptron raised public excitement for research in Artificial Neural Networks, causing the US government to drastically increase funding. This contributed to "the Golden Age of AI" fueled by the optimistic claims made by computer scientists regarding the ability of perceptrons to emulate human intelligence.<a href="#cite_note-:08-23">[23]</a> The first perceptrons did not have adaptive hidden units. However, Joseph (1960)<a href="#cite_note-joseph1960-22">[22]</a> also discussed <a href="/wiki/Multilayer_perceptrons" class="mw-redirect" title="Multilayer perceptrons">multilayer perceptrons</a> with an adaptive hidden layer. Rosenblatt (1962)<a href="#cite_note-rosenblatt1962-24">[24]</a>: section 16 cited and adopted these ideas, also crediting work by H. D. Block and B. W. Knight. Unfortunately, these early efforts did not lead to a working learning algorithm for hidden units, i.e., <a href="/wiki/Deep_learning" title="Deep learning">deep learning</a>. <div class="mw-heading mw-heading3"><h3 id="Deep_learning_breakthroughs_in_the_1960s_and_1970s">Deep learning breakthroughs in the 1960s and 1970s</h3> <a role="button" href="/w/index.php?title=Neural_network_(machine_learning)&action=edit&section=4" title="Edit section: Deep learning breakthroughs in the 1960s and 1970s" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> edit </a> </div> Fundamental research was conducted on ANNs in the 1960s and 1970s. The first working <a href="/wiki/Deep_learning" title="Deep learning">deep learning</a> algorithm was the <a href="/wiki/Group_method_of_data_handling" title="Group method of data handling">Group method of data handling</a>, a method to train arbitrarily deep neural networks, published by <a href="/wiki/Alexey_Ivakhnenko" title="Alexey Ivakhnenko">Alexey Ivakhnenko</a> and Lapa in <a href="/wiki/Ukraine" title="Ukraine">Ukraine</a> (1965). They regarded it as a form of polynomial regression,<a href="#cite_note-ivak1965-25">[25]</a> or a generalization of Rosenblatt's perceptron.<a href="#cite_note-26">[26]</a> A 1971 paper described a deep network with eight layers trained by this method,<a href="#cite_note-ivak1971-27">[27]</a> which is based on layer by layer training through regression analysis. Superfluous hidden units are pruned using a separate validation set. Since the activation functions of the nodes are Kolmogorov-Gabor polynomials, these were also the first deep networks with multiplicative units or "gates."<a href="#cite_note-DLhistory-10">[10]</a> The first deep learning <a href="/wiki/Multilayer_perceptron" title="Multilayer perceptron">multilayer perceptron</a> trained by <a href="/wiki/Stochastic_gradient_descent" title="Stochastic gradient descent">stochastic gradient descent</a><a href="#cite_note-robbins1951-28">[28]</a> was published in 1967 by <a href="/wiki/Shun%27ichi_Amari" title="Shun'ichi Amari">Shun'ichi Amari</a>.<a href="#cite_note-Amari1967-29">[29]</a> In computer experiments conducted by Amari's student Saito, a five layer MLP with two modifiable layers learned <a href="/wiki/Knowledge_representation" class="mw-redirect" title="Knowledge representation">internal representations</a> to classify non-linearily separable pattern classes.<a href="#cite_note-DLhistory-10">[10]</a> Subsequent developments in hardware and hyperparameter tunings have made end-to-end <a href="/wiki/Stochastic_gradient_descent" title="Stochastic gradient descent">stochastic gradient descent</a> the currently dominant training technique. In 1969, <a href="/wiki/Kunihiko_Fukushima" title="Kunihiko Fukushima">Kunihiko Fukushima</a> introduced the <a href="/wiki/Rectifier_(neural_networks)" title="Rectifier (neural networks)">ReLU</a> (rectified linear unit) <a href="/wiki/Activation_function" title="Activation function">activation function</a>.<a href="#cite_note-DLhistory-10">[10]</a><a href="#cite_note-Fukushima1969-30">[30]</a><a href="#cite_note-sonoda17-31">[31]</a> The rectifier has become the most popular activation function for deep learning.<a href="#cite_note-32">[32]</a> Nevertheless, research stagnated in the United States following the work of <a href="/wiki/Marvin_Minsky" title="Marvin Minsky">Minsky</a> and <a href="/wiki/Seymour_Papert" title="Seymour Papert">Papert</a> (1969),<a href="#cite_note-:132-33">[33]</a> who emphasized that basic perceptrons were incapable of processing the exclusive-or circuit. This insight was irrelevant for the deep networks of Ivakhnenko (1965) and Amari (1967). In 1976 transfer learning was introduced in neural networks learning. <a href="#cite_note-34">[34]</a> <a href="#cite_note-35">[35]</a> Deep learning architectures for <a href="/wiki/Convolutional_neural_network" title="Convolutional neural network">convolutional neural networks</a> (CNNs) with convolutional layers and downsampling layers and weight replication began with the <a href="/wiki/Neocognitron" title="Neocognitron">Neocognitron</a> introduced by <a href="/wiki/Kunihiko_Fukushima" title="Kunihiko Fukushima">Kunihiko Fukushima</a> in 1979, though not trained by backpropagation.<a href="#cite_note-FUKU1979-36">[36]</a><a href="#cite_note-FUKU1980-37">[37]</a><a href="#cite_note-SCHIDHUB4-38">[38]</a> <div class="mw-heading mw-heading3"><h3 id="Backpropagation">Backpropagation</h3> <a role="button" href="/w/index.php?title=Neural_network_(machine_learning)&action=edit&section=5" title="Edit section: Backpropagation" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> edit </a> </div> <a href="/wiki/Backpropagation" title="Backpropagation">Backpropagation</a> is an efficient application of the <a href="/wiki/Chain_rule" title="Chain rule">chain rule</a> derived by <a href="/wiki/Gottfried_Wilhelm_Leibniz" title="Gottfried Wilhelm Leibniz">Gottfried Wilhelm Leibniz</a> in 1673<a href="#cite_note-leibniz16762-39">[39]</a> to networks of differentiable nodes. The terminology "back-propagating errors" was actually introduced in 1962 by Rosenblatt,<a href="#cite_note-rosenblatt1962-24">[24]</a> but he did not know how to implement this, although <a href="/wiki/Henry_J._Kelley" title="Henry J. Kelley">Henry J. Kelley</a> had a continuous precursor of backpropagation in 1960 in the context of <a href="/wiki/Control_theory" title="Control theory">control theory</a>.<a href="#cite_note-kelley19602-40">[40]</a> In 1970, <a href="/wiki/Seppo_Linnainmaa" title="Seppo Linnainmaa">Seppo Linnainmaa</a> published the modern form of <a href="/wiki/Backpropagation" title="Backpropagation">backpropagation</a> in his master thesis (1970).<a href="#cite_note-lin19703-41">[41]</a><a href="#cite_note-lin19763-42">[42]</a><a href="#cite_note-DLhistory-10">[10]</a> G.M. Ostrovski et al. republished it in 1971.<a href="#cite_note-ostrowski1971-43">[43]</a><a href="#cite_note-backprop-44">[44]</a> <a href="/wiki/Paul_Werbos" title="Paul Werbos">Paul Werbos</a> applied backpropagation to neural networks in 1982<a href="#cite_note-werbos1982-45">[45]</a><a href="#cite_note-:1-46">[46]</a> (his 1974 PhD thesis, reprinted in a 1994 book,<a href="#cite_note-werbos1974-47">[47]</a> did not yet describe the algorithm<a href="#cite_note-backprop-44">[44]</a>). In 1986, <a href="/wiki/David_E._Rumelhart" class="mw-redirect" title="David E. Rumelhart">David E. Rumelhart</a> et al. popularised backpropagation but did not cite the original work.<a href="#cite_note-48">[48]</a> <div class="mw-heading mw-heading3"><h3 id="Convolutional_neural_networks">Convolutional neural networks</h3> <a role="button" href="/w/index.php?title=Neural_network_(machine_learning)&action=edit&section=6" title="Edit section: Convolutional neural networks" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> edit </a> </div> <a href="/wiki/Kunihiko_Fukushima" title="Kunihiko Fukushima">Kunihiko Fukushima</a>'s <a href="/wiki/Convolutional_neural_network" title="Convolutional neural network">convolutional neural network</a> (CNN) architecture of 1979<a href="#cite_note-FUKU1979-36">[36]</a> also introduced <a href="/wiki/Max_pooling" class="mw-redirect" title="Max pooling">max pooling</a>,<a href="#cite_note-49">[49]</a> a popular downsampling procedure for CNNs. CNNs have become an essential tool for <a href="/wiki/Computer_vision" title="Computer vision">computer vision</a>. The <a href="/wiki/Time_delay_neural_network" title="Time delay neural network">time delay neural network</a> (TDNN) was introduced in 1987 by <a href="/wiki/Alex_Waibel" title="Alex Waibel">Alex Waibel</a> to apply CNN to phoneme recognition. It used convolutions, weight sharing, and backpropagation.<a href="#cite_note-Waibel1987-50">[50]</a><a href="#cite_note-speechsignal-51">[51]</a> In 1988, Wei Zhang applied a backpropagation-trained CNN to alphabet recognition.<a href="#cite_note-wz1988-52">[52]</a> In 1989, <a href="/wiki/Yann_LeCun" title="Yann LeCun">Yann LeCun</a> et al. created a CNN called <a href="/wiki/LeNet" title="LeNet">LeNet</a> for <a href="/wiki/Handwriting_recognition" title="Handwriting recognition">recognizing handwritten ZIP codes</a> on mail. Training required 3 days.<a href="#cite_note-LECUN1989-53">[53]</a> In 1990, Wei Zhang implemented a CNN on <a href="/wiki/Optical_computing" title="Optical computing">optical computing</a> hardware.<a href="#cite_note-wz1990-54">[54]</a> In 1991, a CNN was applied to medical image object segmentation<a href="#cite_note-55">[55]</a> and breast cancer detection in mammograms.<a href="#cite_note-56">[56]</a> <a href="/wiki/LeNet" title="LeNet">LeNet</a>-5 (1998), a 7-level CNN by <a href="/wiki/Yann_LeCun" title="Yann LeCun">Yann LeCun</a> et al., that classifies digits, was applied by several banks to recognize hand-written numbers on checks digitized in 32×32 pixel images.<a href="#cite_note-lecun98-57">[57]</a> From 1988 onward,<a href="#cite_note-Qian1988-58">[58]</a><a href="#cite_note-Bohr1988-59">[59]</a> the use of neural networks transformed the field of <a href="/wiki/Protein_structure_prediction" title="Protein structure prediction">protein structure prediction</a>, in particular when the first cascading networks were trained on profiles (matrices) produced by multiple <a href="/wiki/Sequence_alignment" title="Sequence alignment">sequence alignments</a>.<a href="#cite_note-Rost1993-60">[60]</a> <div class="mw-heading mw-heading3"><h3 id="Recurrent_neural_networks">Recurrent neural networks</h3> <a role="button" href="/w/index.php?title=Neural_network_(machine_learning)&action=edit&section=7" title="Edit section: Recurrent neural networks" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> edit </a> </div> One origin of RNN was <a href="/wiki/Statistical_mechanics" title="Statistical mechanics">statistical mechanics</a>. In 1972, <a href="/wiki/Shun%27ichi_Amari" title="Shun'ichi Amari">Shun'ichi Amari</a> proposed to modify the weights of an <a href="/wiki/Ising_model" title="Ising model">Ising model</a> by <a href="/wiki/Hebbian_theory" title="Hebbian theory">Hebbian learning</a> rule as a model of associative memory, adding in the component of learning.<a href="#cite_note-61">[61]</a> This was popularized as the <a href="/wiki/Hopfield_network" title="Hopfield network">Hopfield network</a> by <a href="/wiki/John_Hopfield" title="John Hopfield">John Hopfield</a>(1982).<a href="#cite_note-Hopfield19822-62">[62]</a> Another origin of RNN was neuroscience. The word "recurrent" is used to describe loop-like structures in anatomy. In 1901, <a href="/wiki/Santiago_Ram%C3%B3n_y_Cajal" title="Santiago Ramón y Cajal">Cajal</a> observed "recurrent semicircles" in the <a href="/wiki/Cerebellum" title="Cerebellum">cerebellar cortex</a>.<a href="#cite_note-63">[63]</a> <a href="/wiki/Donald_O._Hebb" title="Donald O. Hebb">Hebb</a> considered "reverberating circuit" as an explanation for short-term memory.<a href="#cite_note-64">[64]</a> The McCulloch and Pitts paper (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.<a href="#cite_note-WM-12">[12]</a> In 1982 a recurrent neural network, with an array architecture (rather than a multilayer perceptron architecture), named Crossbar Adaptive Array <a href="#cite_note-CAA1982-65">[65]</a><a href="#cite_note-">[66]</a> used direct recurrent connections from the output to the supervisor (teaching ) inputs. In addition of computing actions (decisions), it computed internal state evaluations (emotions) of the consequence situations. Eliminating the external supervisor, it introduced the self-learning method in neural networks. In cognitive psychology, the journal American Psychologist in early 1980's carried out a debate on relation between cognition and emotion. Zajonc in 1980 stated that emotion is computed first and is independent from cognition, while Lazarus in 1982 stated that cognition is computed first and is inseparable from emotion. <a href="#cite_note-67">[67]</a><a href="#cite_note-68">[68]</a> In 1982 the Crossbar Adaptive Array gave a neural network model of cognition-emotion relation. <a href="#cite_note-CAA1982-65">[65]</a><a href="#cite_note-69">[69]</a> It was an example of a debate where an AI system, a recurrent neural network, contributed to an issue in the same time addressed by cognitive psychology. Two early influential works were the <a href="/wiki/Recurrent_neural_network#Jordan_network" title="Recurrent neural network">Jordan network</a> (1986) and the <a href="/wiki/Recurrent_neural_network#Elman_network" title="Recurrent neural network">Elman network</a> (1990), which applied RNN to study <a href="/wiki/Cognitive_psychology" title="Cognitive psychology">cognitive psychology</a>. In the 1980s, backpropagation did not work well for deep RNNs. To overcome this problem, in 1991, <a href="/wiki/J%C3%BCrgen_Schmidhuber" title="Jürgen Schmidhuber">Jürgen Schmidhuber</a> proposed the "neural sequence chunker" or "neural history compressor"<a href="#cite_note-chunker1991-70">[70]</a><a href="#cite_note-schmidhuber1992-71">[71]</a> which introduced the important concepts of self-supervised pre-training (the "P" in <a href="/wiki/ChatGPT" title="ChatGPT">ChatGPT</a>) and neural <a href="/wiki/Knowledge_distillation" title="Knowledge distillation">knowledge distillation</a>.<a href="#cite_note-DLhistory-10">[10]</a> In 1993, a neural history compressor system solved a "Very Deep Learning" task that required more than 1000 subsequent <a href="/wiki/Layer_(deep_learning)" title="Layer (deep learning)">layers</a> in an RNN unfolded in time.<a href="#cite_note-schmidhuber19932-72">[72]</a> In 1991, <a href="/wiki/Sepp_Hochreiter" title="Sepp Hochreiter">Sepp Hochreiter</a>'s diploma thesis <a href="#cite_note-HOCH1991-73">[73]</a> identified and analyzed the <a href="/wiki/Vanishing_gradient_problem" title="Vanishing gradient problem">vanishing gradient problem</a><a href="#cite_note-HOCH1991-73">[73]</a><a href="#cite_note-HOCH2001-74">[74]</a> and proposed recurrent <a href="/wiki/Residual_neural_network" title="Residual neural network">residual</a> connections to solve it. He and Schmidhuber introduced <a href="/wiki/Long_short-term_memory" title="Long short-term memory">long short-term memory</a> (LSTM), which set accuracy records in multiple applications domains.<a href="#cite_note-75">[75]</a><a href="#cite_note-lstm2-76">[76]</a> This was not yet the modern version of LSTM, which required the forget gate, which was introduced in 1999.<a href="#cite_note-lstm1999-77">[77]</a> It became the default choice for RNN architecture. During 1985–1995, inspired by statistical mechanics, several architectures and methods were developed by <a href="/wiki/Terry_Sejnowski" title="Terry Sejnowski">Terry Sejnowski</a>, <a href="/wiki/Peter_Dayan" title="Peter Dayan">Peter Dayan</a>, <a href="/wiki/Geoffrey_Hinton" title="Geoffrey Hinton">Geoffrey Hinton</a>, etc., including the <a href="/wiki/Boltzmann_machine" title="Boltzmann machine">Boltzmann machine</a>,<a href="#cite_note-78">[78]</a> <a href="/wiki/Restricted_Boltzmann_machine" title="Restricted Boltzmann machine">restricted Boltzmann machine</a>,<a href="#cite_note-79">[79]</a> <a href="/wiki/Helmholtz_machine" title="Helmholtz machine">Helmholtz machine</a>,<a href="#cite_note-%E2%80%9Cnc95%E2%80%9C-80">[80]</a> and the <a href="/wiki/Wake-sleep_algorithm" title="Wake-sleep algorithm">wake-sleep algorithm</a>.<a href="#cite_note-:13-81">[81]</a> These were designed for unsupervised learning of deep generative models. <div class="mw-heading mw-heading3"><h3 id="Deep_learning">Deep learning</h3> <a role="button" href="/w/index.php?title=Neural_network_(machine_learning)&action=edit&section=8" title="Edit section: Deep learning" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> edit </a> </div> Between 2009 and 2012, ANNs began winning prizes in image recognition contests, approaching human level performance on various tasks, initially in <a href="/wiki/Pattern_recognition" title="Pattern recognition">pattern recognition</a> and <a href="/wiki/Handwriting_recognition" title="Handwriting recognition">handwriting recognition</a>.<a href="#cite_note-82">[82]</a><a href="#cite_note-83">[83]</a> In 2011, a CNN named DanNet<a href="#cite_note-:32-84">[84]</a><a href="#cite_note-:62-85">[85]</a> by Dan Ciresan, Ueli Meier, Jonathan Masci, <a href="/wiki/Luca_Maria_Gambardella" title="Luca Maria Gambardella">Luca Maria Gambardella</a>, and <a href="/wiki/J%C3%BCrgen_Schmidhuber" title="Jürgen Schmidhuber">Jürgen Schmidhuber</a> achieved for the first time superhuman performance in a visual pattern recognition contest, outperforming traditional methods by a factor of 3.<a href="#cite_note-SCHIDHUB4-38">[38]</a> It then won more contests.<a href="#cite_note-:82-86">[86]</a><a href="#cite_note-ciresan2013miccai-87">[87]</a> They also showed how <a href="/wiki/Max_pooling" class="mw-redirect" title="Max pooling">max-pooling</a> CNNs on GPU improved performance significantly.<a href="#cite_note-:9-88">[88]</a> In October 2012, <a href="/wiki/AlexNet" title="AlexNet">AlexNet</a> by <a href="/wiki/Alex_Krizhevsky" title="Alex Krizhevsky">Alex Krizhevsky</a>, <a href="/wiki/Ilya_Sutskever" title="Ilya Sutskever">Ilya Sutskever</a>, and <a href="/wiki/Geoffrey_Hinton" title="Geoffrey Hinton">Geoffrey Hinton</a><a href="#cite_note-krizhevsky20122-89">[89]</a> won the large-scale <a href="/wiki/ImageNet_competition" class="mw-redirect" title="ImageNet competition">ImageNet competition</a> by a significant margin over shallow machine learning methods. Further incremental improvements included the VGG-16 network by <a href="/wiki/Karen_Simonyan" title="Karen Simonyan">Karen Simonyan</a> and <a href="/wiki/Andrew_Zisserman" title="Andrew Zisserman">Andrew Zisserman</a><a href="#cite_note-VGG-90">[90]</a> and Google's <a href="/wiki/Inceptionv3" class="mw-redirect" title="Inceptionv3">Inceptionv3</a>.<a href="#cite_note-szegedy-91">[91]</a> In 2012, <a href="/wiki/Andrew_Ng" title="Andrew Ng">Ng</a> and <a href="/wiki/Jeff_Dean_(computer_scientist)" class="mw-redirect" title="Jeff Dean (computer scientist)">Dean</a> created a network that learned to recognize higher-level concepts, such as cats, only from watching unlabeled images.<a href="#cite_note-ng2012-92">[92]</a> Unsupervised pre-training and increased computing power from <a href="/wiki/GPU" class="mw-redirect" title="GPU">GPUs</a> and <a href="/wiki/Distributed_computing" title="Distributed computing">distributed computing</a> allowed the use of larger networks, particularly in image and visual recognition problems, which became known as "deep learning".<a href="#cite_note-:4-5">[5]</a> <a href="/wiki/Radial_basis_function_network" title="Radial basis function network">Radial basis function</a> and wavelet networks were introduced in 2013. These can be shown to offer best approximation properties and have been applied in <a href="/wiki/Nonlinear_system_identification" title="Nonlinear system identification">nonlinear system identification</a> and classification applications.<a href="#cite_note-SAB1-93">[93]</a> <a href="/wiki/Generative_adversarial_network" title="Generative adversarial network">Generative adversarial network</a> (GAN) (<a href="/wiki/Ian_Goodfellow" title="Ian Goodfellow">Ian Goodfellow</a> et al., 2014)<a href="#cite_note-GANnips-94">[94]</a> became state of the art in generative modeling during 2014–2018 period. The GAN principle was originally published in 1991 by <a href="/wiki/J%C3%BCrgen_Schmidhuber" title="Jürgen Schmidhuber">Jürgen Schmidhuber</a> who called it "artificial curiosity": two neural networks contest with each other in the form of a <a href="/wiki/Zero-sum_game" title="Zero-sum game">zero-sum game</a>, where one network's gain is the other network's loss.<a href="#cite_note-curiosity1991-95">[95]</a><a href="#cite_note-gancurpm2020-96">[96]</a> The first network is a <a href="/wiki/Generative_model" title="Generative model">generative model</a> that models a <a href="/wiki/Probability_distribution" title="Probability distribution">probability distribution</a> over output patterns. The second network learns by <a href="/wiki/Gradient_descent" title="Gradient descent">gradient descent</a> to predict the reactions of the environment to these patterns. Excellent image quality is achieved by <a href="/wiki/Nvidia" title="Nvidia">Nvidia</a>'s <a href="/wiki/StyleGAN" title="StyleGAN">StyleGAN</a> (2018)<a href="#cite_note-SyncedReview201822-97">[97]</a> based on the Progressive GAN by Tero Karras et al.<a href="#cite_note-progressiveGAN201722-98">[98]</a> 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 <a href="/wiki/Deepfake" title="Deepfake">deepfakes</a>.<a href="#cite_note-99">[99]</a> <a href="/wiki/Diffusion_model" title="Diffusion model">Diffusion models</a> (2015)<a href="#cite_note-100">[100]</a> eclipsed GANs in generative modeling since then, with systems such as <a href="/wiki/DALL%C2%B7E_2" class="mw-redirect" title="DALL·E 2">DALL·E 2</a> (2022) and <a href="/wiki/Stable_Diffusion" title="Stable Diffusion">Stable Diffusion</a> (2022). In 2014, the state of the art was training "very deep neural network" with 20 to 30 layers.<a href="#cite_note-101">[101]</a> Stacking too many layers led to a steep reduction in <a href="/wiki/Training,_validation,_and_test_data_sets" title="Training, validation, and test data sets">training</a> accuracy,<a href="#cite_note-prelu2-102">[102]</a> known as the "degradation" problem.<a href="#cite_note-resnet2-103">[103]</a> In 2015, two techniques were developed to train very deep networks: the <a href="/wiki/Highway_network" title="Highway network">highway network</a> was published in May 2015,<a href="#cite_note-highway20153-104">[104]</a> and the <a href="/wiki/Residual_neural_network" title="Residual neural network">residual neural network</a> (ResNet) in December 2015.<a href="#cite_note-resnet20153-105">[105]</a><a href="#cite_note-106">[106]</a> ResNet behaves like an open-gated Highway Net. <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Transformer_(deep_learning_architecture)#History" title="Transformer (deep learning architecture)">Transformer (deep learning architecture) § History</a></div> During the 2010s, the <a href="/wiki/Seq2seq" title="Seq2seq">seq2seq</a> model was developed, and attention mechanisms were added. It led to the modern Transformer architecture in 2017 in <a href="/wiki/Attention_Is_All_You_Need" title="Attention Is All You Need">Attention Is All You Need</a>.<a href="#cite_note-vaswani2017-107">[107]</a> It requires computation time that is quadratic in the size of the context window. <a href="/wiki/J%C3%BCrgen_Schmidhuber" title="Jürgen Schmidhuber">Jürgen Schmidhuber</a>'s fast weight controller (1992)<a href="#cite_note-transform19922-108">[108]</a> scales linearly and was later shown to be equivalent to the unnormalized linear Transformer.<a href="#cite_note-fastlinear20202-109">[109]</a><a href="#cite_note-schlag20212-110">[110]</a><a href="#cite_note-DLhistory-10">[10]</a> Transformers have increasingly become the model of choice for <a href="/wiki/Natural_language_processing" title="Natural language processing">natural language processing</a>.<a href="#cite_note-wolf2020-111">[111]</a> Many modern <a href="/wiki/Large_language_model" title="Large language model">large language models</a> such as <a href="/wiki/ChatGPT" title="ChatGPT">ChatGPT</a>, <a href="/wiki/GPT-4" title="GPT-4">GPT-4</a>, and <a href="/wiki/BERT_(language_model)" title="BERT (language model)">BERT</a> use this architecture. </section><div class="mw-heading mw-heading2 section-heading" onclick="mfTempOpenSection(3)"><h2 id="Models">Models</h2> <a role="button" href="/w/index.php?title=Neural_network_(machine_learning)&action=edit&section=9" title="Edit section: Models" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> edit </a> </div><section class="mf-section-3 collapsible-block" id="mf-section-3"> <style data-mw-deduplicate="TemplateStyles:r1251242444">.mw-parser-output .ambox{border:1px solid #a2a9b1;border-left:10px solid #36c;background-color:#fbfbfb;box-sizing:border-box}.mw-parser-output .ambox+link+.ambox,.mw-parser-output .ambox+link+style+.ambox,.mw-parser-output .ambox+link+link+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+style+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+link+.ambox{margin-top:-1px}html body.mediawiki .mw-parser-output .ambox.mbox-small-left{margin:4px 1em 4px 0;overflow:hidden;width:238px;border-collapse:collapse;font-size:88%;line-height:1.25em}.mw-parser-output .ambox-speedy{border-left:10px solid #b32424;background-color:#fee7e6}.mw-parser-output .ambox-delete{border-left:10px solid #b32424}.mw-parser-output .ambox-content{border-left:10px solid #f28500}.mw-parser-output .ambox-style{border-left:10px solid #fc3}.mw-parser-output .ambox-move{border-left:10px solid #9932cc}.mw-parser-output .ambox-protection{border-left:10px solid #a2a9b1}.mw-parser-output .ambox .mbox-text{border:none;padding:0.25em 0.5em;width:100%}.mw-parser-output .ambox .mbox-image{border:none;padding:2px 0 2px 0.5em;text-align:center}.mw-parser-output .ambox .mbox-imageright{border:none;padding:2px 0.5em 2px 0;text-align:center}.mw-parser-output .ambox .mbox-empty-cell{border:none;padding:0;width:1px}.mw-parser-output .ambox .mbox-image-div{width:52px}@media(min-width:720px){.mw-parser-output .ambox{margin:0 10%}}@media print{body.ns-0 .mw-parser-output .ambox{display:none!important}}</style><table class="box-Confusing plainlinks metadata ambox ambox-style ambox-confusing" role="presentation"><tbody><tr><td class="mbox-text"><div class="mbox-text-span">This section may be <a href="/wiki/Wikipedia:Vagueness" title="Wikipedia:Vagueness">confusing or unclear</a> to readers. Please help <a href="/wiki/Wikipedia:Please_clarify" title="Wikipedia:Please clarify">clarify the section</a>. There might be a discussion about this on <a href="/wiki/Talk:Neural_network_(machine_learning)" title="Talk:Neural network (machine learning)">the talk page</a>. (April 2017) (<a href="/wiki/Help:Maintenance_template_removal" title="Help:Maintenance template removal">Learn how and when to remove this message</a>)</div></td></tr></tbody></table><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Further information: <a href="/wiki/Mathematics_of_artificial_neural_networks" title="Mathematics of artificial neural networks">Mathematics of artificial neural networks</a></div><figure class="mw-default-size mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Neuron3.png" class="mw-file-description"><noscript><img src="//upload.wikimedia.org/wikipedia/commons/thumb/4/44/Neuron3.png/300px-Neuron3.png" decoding="async" width="300" height="159" class="mw-file-element" data-file-width="415" data-file-height="220"></noscript><span class="lazy-image-placeholder" style="width: 300px;height: 159px;" data-src="//upload.wikimedia.org/wikipedia/commons/thumb/4/44/Neuron3.png/300px-Neuron3.png" data-width="300" data-height="159" data-srcset="//upload.wikimedia.org/wikipedia/commons/4/44/Neuron3.png 1.5x" data-class="mw-file-element"> </a><figcaption>Neuron and myelinated axon, with signal flow from inputs at dendrites to outputs at axon terminals</figcaption></figure> ANNs began as an attempt to exploit the architecture of the human brain to perform tasks that conventional algorithms had little success with. They soon reoriented towards improving empirical results, abandoning attempts to remain true to their biological precursors. ANNs have the ability to learn and model non-linearities and complex relationships. This is achieved by neurons being connected in various patterns, allowing the output of some neurons to become the input of others. The network forms a <a href="/wiki/Directed_graph" title="Directed graph">directed</a>, <a href="/wiki/Weighted_graph" class="mw-redirect" title="Weighted graph">weighted graph</a>.<a href="#cite_note-Zell1994ch5.2-112">[112]</a> An artificial neural network consists of simulated neurons. Each neuron is connected to other <a href="/wiki/Vertex_(graph_theory)" title="Vertex (graph theory)">nodes</a> via <a href="/wiki/Glossary_of_graph_theory_terms#edge" class="mw-redirect" title="Glossary of graph theory terms">links</a> like a biological axon-synapse-dendrite connection. All the nodes connected by links take in some data and use it to perform specific operations and tasks on the data. Each link has a weight, determining the strength of one node's influence on another,<a href="#cite_note-Winston-113">[113]</a> allowing weights to choose the signal between neurons. <div class="mw-heading mw-heading3"><h3 id="Artificial_neurons">Artificial neurons</h3> <a role="button" href="/w/index.php?title=Neural_network_(machine_learning)&action=edit&section=10" title="Edit section: Artificial neurons" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> edit </a> </div> ANNs are composed of <a href="/wiki/Artificial_neurons" class="mw-redirect" title="Artificial neurons">artificial neurons</a> which are conceptually derived from biological <a href="/wiki/Neuron" title="Neuron">neurons</a>. Each artificial neuron has inputs and produces a single output which can be sent to multiple other neurons.<a href="#cite_note-Abbod2007-114">[114]</a> The inputs can be the feature values of a sample of external data, such as images or documents, or they can be the outputs of other neurons. The outputs of the final output neurons of the neural net accomplish the task, such as recognizing an object in an image.[<a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed">citation needed</a>] To find the output of the neuron we take the weighted sum of all the inputs, weighted by the weights of the connections from the inputs to the neuron. We add a bias term to this sum.<a href="#cite_note-DAWSON1998-115">[115]</a> This weighted sum is sometimes called the activation. This weighted sum is then passed through a (usually nonlinear) <a href="/wiki/Activation_function" title="Activation function">activation function</a> to produce the output. The initial inputs are external data, such as images and documents. The ultimate outputs accomplish the task, such as recognizing an object in an image.<a href="#cite_note-116">[116]</a> <div class="mw-heading mw-heading3"><h3 id="Organization">Organization</h3> <a role="button" href="/w/index.php?title=Neural_network_(machine_learning)&action=edit&section=11" title="Edit section: Organization" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> edit </a> </div> The neurons are typically organized into multiple layers, especially in <a href="/wiki/Deep_learning" title="Deep learning">deep learning</a>. Neurons of one layer connect only to neurons of the immediately preceding and immediately following layers. The layer that receives external data is the input layer. The layer that produces the ultimate result is the output layer. In between them are zero or more hidden layers. Single layer and unlayered networks are also used. Between two layers, multiple connection patterns are possible. They can be 'fully connected', with every neuron in one layer connecting to every neuron in the next layer. They can be pooling, where a group of neurons in one layer connects to a single neuron in the next layer, thereby reducing the number of neurons in that layer.<a href="#cite_note-flexible-117">[117]</a> Neurons with only such connections form a <a href="/wiki/Directed_acyclic_graph" title="Directed acyclic graph">directed acyclic graph</a> and are known as <a href="/wiki/Feedforward_neural_network" title="Feedforward neural network">feedforward networks</a>.<a href="#cite_note-Zell1994p73-118">[118]</a> Alternatively, networks that allow connections between neurons in the same or previous layers are known as <a href="/wiki/Recurrent_neural_network" title="Recurrent neural network">recurrent networks</a>.<a href="#cite_note-119">[119]</a> <div class="mw-heading mw-heading3"><h3 id="Hyperparameter">Hyperparameter</h3> <a role="button" href="/w/index.php?title=Neural_network_(machine_learning)&action=edit&section=12" title="Edit section: Hyperparameter" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> edit </a> </div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Hyperparameter_(machine_learning)" title="Hyperparameter (machine learning)">Hyperparameter (machine learning)</a></div> A <a href="/wiki/Hyperparameter_(machine_learning)" title="Hyperparameter (machine learning)">hyperparameter</a> is a constant <a href="/wiki/Parameter" title="Parameter">parameter</a> whose value is set before the learning process begins. The values of parameters are derived via learning. Examples of hyperparameters include <a href="/wiki/Learning_rate" title="Learning rate">learning rate</a>, the number of hidden layers and batch size.[<a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed">citation needed</a>] The values of some hyperparameters can be dependent on those of other hyperparameters. For example, the size of some layers can depend on the overall number of layers.[<a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed">citation needed</a>] <div class="mw-heading mw-heading3"><h3 id="Learning">Learning</h3> <a role="button" href="/w/index.php?title=Neural_network_(machine_learning)&action=edit&section=13" title="Edit section: Learning" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> edit </a> </div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1251242444"><table class="box-No_footnotes plainlinks metadata ambox ambox-style ambox-No_footnotes" role="presentation"><tbody><tr><td class="mbox-text"><div class="mbox-text-span">This section includes a <a href="/wiki/Wikipedia:Citing_sources" title="Wikipedia:Citing sources">list of references</a>, <a href="/wiki/Wikipedia:Further_reading" title="Wikipedia:Further reading">related reading</a>, or <a href="/wiki/Wikipedia:External_links" title="Wikipedia:External links">external links</a>, but its sources remain unclear because it lacks <a href="/wiki/Wikipedia:Citing_sources#Inline_citations" title="Wikipedia:Citing sources">inline citations</a>. Please help <a href="/wiki/Wikipedia:WikiProject_Fact_and_Reference_Check" class="mw-redirect" title="Wikipedia:WikiProject Fact and Reference Check">improve</a> this section by <a href="/wiki/Wikipedia:When_to_cite" title="Wikipedia:When to cite">introducing</a> more precise citations. (August 2019) (<a href="/wiki/Help:Maintenance_template_removal" title="Help:Maintenance template removal">Learn how and when to remove this message</a>)</div></td></tr></tbody></table><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">See also: <a href="/wiki/Mathematical_optimization" title="Mathematical optimization">Mathematical optimization</a>, <a href="/wiki/Estimation_theory" title="Estimation theory">Estimation theory</a>, and <a href="/wiki/Machine_learning" title="Machine learning">Machine learning</a></div> Learning is the adaptation of the network to better handle a task by considering sample observations. Learning involves adjusting the weights (and optional thresholds) of the network to improve the accuracy of the result. This is done by minimizing the observed errors. Learning is complete when examining additional observations does not usefully reduce the error rate. Even after learning, the error rate typically does not reach 0. If after learning, the error rate is too high, the network typically must be redesigned. Practically this is done by defining a <a href="/wiki/Loss_function" title="Loss function">cost function</a> that is evaluated periodically during learning. As long as its output continues to decline, learning continues. The cost is frequently defined as a <a href="/wiki/Statistic" title="Statistic">statistic</a> whose value can only be approximated. The outputs are actually numbers, so when the error is low, the difference between the output (almost certainly a cat) and the correct answer (cat) is small. Learning attempts to reduce the total of the differences across the observations. Most learning models can be viewed as a straightforward application of <a href="/wiki/Mathematical_optimization" title="Mathematical optimization">optimization</a> theory and <a href="/wiki/Statistical_estimation" class="mw-redirect" title="Statistical estimation">statistical estimation</a>.<a href="#cite_note-Zell1994ch5.2-112">[112]</a><a href="#cite_note-120">[120]</a> <div class="mw-heading mw-heading4"><h4 id="Learning_rate">Learning rate</h4> <a role="button" href="/w/index.php?title=Neural_network_(machine_learning)&action=edit&section=14" title="Edit section: Learning rate" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> edit </a> </div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Learning_rate" title="Learning rate">Learning rate</a></div> The learning rate defines the size of the corrective steps that the model takes to adjust for errors in each observation.<a href="#cite_note-121">[121]</a> A high learning rate shortens the training time, but with lower ultimate accuracy, while a lower learning rate takes longer, but with the potential for greater accuracy. Optimizations such as <a href="/wiki/Quickprop" title="Quickprop">Quickprop</a> are primarily aimed at speeding up error minimization, while other improvements mainly try to increase reliability. In order to avoid <a href="/wiki/Oscillation" title="Oscillation">oscillation</a> inside the network such as alternating connection weights, and to improve the rate of convergence, refinements use an <a href="/wiki/Adaptive_learning_rate" class="mw-redirect" title="Adaptive learning rate">adaptive learning rate</a> that increases or decreases as appropriate.<a href="#cite_note-122">[122]</a> The concept of momentum allows the balance between the gradient and the previous change to be weighted such that the weight adjustment depends to some degree on the previous change. A momentum close to 0 emphasizes the gradient, while a value close to 1 emphasizes the last change.[<a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed">citation needed</a>] <div class="mw-heading mw-heading4"><h4 id="Cost_function">Cost function</h4> <a role="button" href="/w/index.php?title=Neural_network_(machine_learning)&action=edit&section=15" title="Edit section: Cost function" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> edit </a> </div> While it is possible to define a cost function <a href="/wiki/Ad_hoc" title="Ad hoc">ad hoc</a>, frequently the choice is determined by the function's desirable properties (such as <a href="/wiki/Convex_function" title="Convex function">convexity</a>) or because it arises from the model (e.g. in a probabilistic model the model's <a href="/wiki/Posterior_probability" title="Posterior probability">posterior probability</a> can be used as an inverse cost).[<a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed">citation needed</a>] <div class="mw-heading mw-heading4"><h4 id="Backpropagation_2">Backpropagation</h4> <a role="button" href="/w/index.php?title=Neural_network_(machine_learning)&action=edit&section=16" title="Edit section: Backpropagation" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> edit </a> </div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Backpropagation" title="Backpropagation">Backpropagation</a></div> Backpropagation is a method used to adjust the connection weights to compensate for each error found during learning. The error amount is effectively divided among the connections. Technically, backprop calculates the <a href="/wiki/Gradient" title="Gradient">gradient</a> (the derivative) of the <a href="/wiki/Loss_function" title="Loss function">cost function</a> associated with a given state with respect to the weights. The weight updates can be done via <a href="/wiki/Stochastic_gradient_descent" title="Stochastic gradient descent">stochastic gradient descent</a> or other methods, such as <a href="/wiki/Extreme_learning_machine" title="Extreme learning machine">extreme learning machines</a>,<a href="#cite_note-123">[123]</a> "no-prop" networks,<a href="#cite_note-124">[124]</a> training without backtracking,<a href="#cite_note-125">[125]</a> "weightless" networks,<a href="#cite_note-RBMTRAIN-126">[126]</a><a href="#cite_note-127">[127]</a> and <a href="/wiki/Holographic_associative_memory" title="Holographic associative memory">non-connectionist neural networks</a>.[<a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed">citation needed</a>] <div class="mw-heading mw-heading3"><h3 id="Learning_paradigms">Learning paradigms</h3> <a role="button" href="/w/index.php?title=Neural_network_(machine_learning)&action=edit&section=17" title="Edit section: Learning paradigms" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> edit </a> </div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1251242444"><table class="box-No_footnotes plainlinks metadata ambox ambox-style ambox-No_footnotes" role="presentation"><tbody><tr><td class="mbox-text"><div class="mbox-text-span">This section includes a <a href="/wiki/Wikipedia:Citing_sources" title="Wikipedia:Citing sources">list of references</a>, <a href="/wiki/Wikipedia:Further_reading" title="Wikipedia:Further reading">related reading</a>, or <a href="/wiki/Wikipedia:External_links" title="Wikipedia:External links">external links</a>, but its sources remain unclear because it lacks <a href="/wiki/Wikipedia:Citing_sources#Inline_citations" title="Wikipedia:Citing sources">inline citations</a>. Please help <a href="/wiki/Wikipedia:WikiProject_Fact_and_Reference_Check" class="mw-redirect" title="Wikipedia:WikiProject Fact and Reference Check">improve</a> this section by <a href="/wiki/Wikipedia:When_to_cite" title="Wikipedia:When to cite">introducing</a> more precise citations. (August 2019) (<a href="/wiki/Help:Maintenance_template_removal" title="Help:Maintenance template removal">Learn how and when to remove this message</a>)</div></td></tr></tbody></table> Machine learning is commonly separated into three main learning paradigms, <a href="/wiki/Supervised_learning" title="Supervised learning">supervised learning</a>,<a href="#cite_note-128">[128]</a> <a href="/wiki/Unsupervised_learning" title="Unsupervised learning">unsupervised learning</a><a href="#cite_note-129">[129]</a> and <a href="/wiki/Reinforcement_learning" title="Reinforcement learning">reinforcement learning</a>.<a href="#cite_note-130">[130]</a> Each corresponds to a particular learning task. <div class="mw-heading mw-heading4"><h4 id="Supervised_learning">Supervised learning</h4> <a role="button" href="/w/index.php?title=Neural_network_(machine_learning)&action=edit&section=18" title="Edit section: Supervised learning" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> edit </a> </div> <a href="/wiki/Supervised_learning" title="Supervised learning">Supervised learning</a> uses a set of paired inputs and desired outputs. The learning task is to produce the desired output for each input. In this case, the cost function is related to eliminating incorrect deductions.<a href="#cite_note-131">[131]</a> A commonly used cost is the <a href="/wiki/Mean-squared_error" class="mw-redirect" title="Mean-squared error">mean-squared error</a>, which tries to minimize the average squared error between the network's output and the desired output. Tasks suited for supervised learning are <a href="/wiki/Pattern_recognition" title="Pattern recognition">pattern recognition</a> (also known as classification) and <a href="/wiki/Regression_analysis" title="Regression analysis">regression</a> (also known as function approximation). Supervised learning is also applicable to sequential data (e.g., for handwriting, speech and <a href="/wiki/Gesture_recognition" title="Gesture recognition">gesture recognition</a>). This can be thought of as learning with a "teacher", in the form of a function that provides continuous feedback on the quality of solutions obtained thus far. <div class="mw-heading mw-heading4"><h4 id="Unsupervised_learning">Unsupervised learning</h4> <a role="button" href="/w/index.php?title=Neural_network_(machine_learning)&action=edit&section=19" title="Edit section: Unsupervised learning" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> edit </a> </div> In <a href="/wiki/Unsupervised_learning" title="Unsupervised learning">unsupervised learning</a>, input data is given along with the cost function, some function of the data <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \textstyle x}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle displaystyle="false" scriptlevel="0"> <mi>x</mi> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \textstyle x}</annotation> </semantics> </math><noscript><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1bd1c9e87a24e459706fa8e63b9e5d94db4540b4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.33ex; height:1.676ex;" alt="{\displaystyle \textstyle x}"></noscript><span class="lazy-image-placeholder" style="width: 1.33ex;height: 1.676ex;vertical-align: -0.338ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1bd1c9e87a24e459706fa8e63b9e5d94db4540b4" data-alt="{\displaystyle \textstyle x}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert">  and the network's output. The cost function is dependent on the task (the model domain) and any <a href="/wiki/A_priori_and_a_posteriori" title="A priori and a posteriori">a priori</a> assumptions (the implicit properties of the model, its parameters and the observed variables). As a trivial example, consider the model <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \textstyle f(x)=a}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle displaystyle="false" scriptlevel="0"> <mi>f</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mi>a</mi> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \textstyle f(x)=a}</annotation> </semantics> </math><noscript><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a0e4cc2a7c5c4f65d59b669d64c7759623c648c5" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:8.746ex; height:2.843ex;" alt="{\displaystyle \textstyle f(x)=a}"></noscript><span class="lazy-image-placeholder" style="width: 8.746ex;height: 2.843ex;vertical-align: -0.838ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a0e4cc2a7c5c4f65d59b669d64c7759623c648c5" data-alt="{\displaystyle \textstyle f(x)=a}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert">  where <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \textstyle a}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle displaystyle="false" scriptlevel="0"> <mi>a</mi> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \textstyle a}</annotation> </semantics> </math><noscript><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7abc4e8a2ef67ff9b7ad050afa4cf286c3ec0cd3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.23ex; height:1.676ex;" alt="{\displaystyle \textstyle a}"></noscript><span class="lazy-image-placeholder" style="width: 1.23ex;height: 1.676ex;vertical-align: -0.338ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7abc4e8a2ef67ff9b7ad050afa4cf286c3ec0cd3" data-alt="{\displaystyle \textstyle a}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert">  is a constant and the cost <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \textstyle C=E[(x-f(x))^{2}]}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle displaystyle="false" scriptlevel="0"> <mi>C</mi> <mo>=</mo> <mi>E</mi> <mo stretchy="false">[</mo> <mo stretchy="false">(</mo> <mi>x</mi> <mo>−</mo> <mi>f</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo stretchy="false">]</mo> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \textstyle C=E[(x-f(x))^{2}]}</annotation> </semantics> </math><noscript><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2929ecb1606fdfeaddc55477d9671e11c034e21c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:19.385ex; height:3.009ex;" alt="{\displaystyle \textstyle C=E[(x-f(x))^{2}]}"></noscript><span class="lazy-image-placeholder" style="width: 19.385ex;height: 3.009ex;vertical-align: -0.838ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2929ecb1606fdfeaddc55477d9671e11c034e21c" data-alt="{\displaystyle \textstyle C=E[(x-f(x))^{2}]}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> . Minimizing this cost produces a value of <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \textstyle a}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle displaystyle="false" scriptlevel="0"> <mi>a</mi> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \textstyle a}</annotation> </semantics> </math><noscript><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7abc4e8a2ef67ff9b7ad050afa4cf286c3ec0cd3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.23ex; height:1.676ex;" alt="{\displaystyle \textstyle a}"></noscript><span class="lazy-image-placeholder" style="width: 1.23ex;height: 1.676ex;vertical-align: -0.338ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7abc4e8a2ef67ff9b7ad050afa4cf286c3ec0cd3" data-alt="{\displaystyle \textstyle a}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert">  that is equal to the mean of the data. The cost function can be much more complicated. Its form depends on the application: for example, in <a href="/wiki/Data_compression" title="Data compression">compression</a> it could be related to the <a href="/wiki/Mutual_information" title="Mutual information">mutual information</a> between <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \textstyle x}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle displaystyle="false" scriptlevel="0"> <mi>x</mi> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \textstyle x}</annotation> </semantics> </math><noscript><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1bd1c9e87a24e459706fa8e63b9e5d94db4540b4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.33ex; height:1.676ex;" alt="{\displaystyle \textstyle x}"></noscript><span class="lazy-image-placeholder" style="width: 1.33ex;height: 1.676ex;vertical-align: -0.338ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1bd1c9e87a24e459706fa8e63b9e5d94db4540b4" data-alt="{\displaystyle \textstyle x}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert">  and <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \textstyle f(x)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle displaystyle="false" scriptlevel="0"> <mi>f</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \textstyle f(x)}</annotation> </semantics> </math><noscript><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e0fa998ae55408f7f94d08ee08a04fcf92330878" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:4.418ex; height:2.843ex;" alt="{\displaystyle \textstyle f(x)}"></noscript><span class="lazy-image-placeholder" style="width: 4.418ex;height: 2.843ex;vertical-align: -0.838ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e0fa998ae55408f7f94d08ee08a04fcf92330878" data-alt="{\displaystyle \textstyle f(x)}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> , whereas in statistical modeling, it could be related to the <a href="/wiki/Posterior_probability" title="Posterior probability">posterior probability</a> of the model given the data (note that in both of those examples, those quantities would be maximized rather than minimized). Tasks that fall within the paradigm of unsupervised learning are in general <a href="/wiki/Approximation" title="Approximation">estimation</a> problems; the applications include <a href="/wiki/Data_clustering" class="mw-redirect" title="Data clustering">clustering</a>, the estimation of <a href="/wiki/Statistical_distributions" class="mw-redirect" title="Statistical distributions">statistical distributions</a>, <a href="/wiki/Data_compression" title="Data compression">compression</a> and <a href="/wiki/Bayesian_spam_filtering" class="mw-redirect" title="Bayesian spam filtering">filtering</a>. <div class="mw-heading mw-heading4"><h4 id="Reinforcement_learning">Reinforcement learning</h4> <a role="button" href="/w/index.php?title=Neural_network_(machine_learning)&action=edit&section=20" title="Edit section: Reinforcement learning" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> edit </a> </div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Reinforcement_learning" title="Reinforcement learning">Reinforcement learning</a></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">See also: <a href="/wiki/Stochastic_control" title="Stochastic control">Stochastic control</a></div> In applications such as playing video games, an actor takes a string of actions, receiving a generally unpredictable response from the environment after each one. The goal is to win the game, i.e., generate the most positive (lowest cost) responses. In <a href="/wiki/Reinforcement_learning" title="Reinforcement learning">reinforcement learning</a>, the aim is to weight the network (devise a policy) to perform actions that minimize long-term (expected cumulative) cost. At each point in time the agent performs an action and the environment generates an observation and an <a href="/wiki/Instant" title="Instant">instantaneous</a> cost, according to some (usually unknown) rules. The rules and the long-term cost usually only can be estimated. At any juncture, the agent decides whether to explore new actions to uncover their costs or to exploit prior learning to proceed more quickly. Formally the environment is modeled as a <a href="/wiki/Markov_decision_process" title="Markov decision process">Markov decision process</a> (MDP) with states <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \textstyle {s_{1},...,s_{n}}\in S}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle displaystyle="false" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>s</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>,</mo> <mo>.</mo> <mo>.</mo> <mo>.</mo> <mo>,</mo> <msub> <mi>s</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> </mrow> <mo>∈</mo> <mi>S</mi> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \textstyle {s_{1},...,s_{n}}\in S}</annotation> </semantics> </math><noscript><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/594ab196af08f0326623318ae24ea08359f03c2f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:13.963ex; height:2.509ex;" alt="{\displaystyle \textstyle {s_{1},...,s_{n}}\in S}"></noscript><span class="lazy-image-placeholder" style="width: 13.963ex;height: 2.509ex;vertical-align: -0.671ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/594ab196af08f0326623318ae24ea08359f03c2f" data-alt="{\displaystyle \textstyle {s_{1},...,s_{n}}\in S}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert">  and actions <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \textstyle {a_{1},...,a_{m}}\in A}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle displaystyle="false" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>,</mo> <mo>.</mo> <mo>.</mo> <mo>.</mo> <mo>,</mo> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>m</mi> </mrow> </msub> </mrow> <mo>∈</mo> <mi>A</mi> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \textstyle {a_{1},...,a_{m}}\in A}</annotation> </semantics> </math><noscript><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c1a2b52db3ad57568da895b2171c90ae6e0de377" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:14.942ex; height:2.509ex;" alt="{\displaystyle \textstyle {a_{1},...,a_{m}}\in A}"></noscript><span class="lazy-image-placeholder" style="width: 14.942ex;height: 2.509ex;vertical-align: -0.671ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c1a2b52db3ad57568da895b2171c90ae6e0de377" data-alt="{\displaystyle \textstyle {a_{1},...,a_{m}}\in A}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> . Because the state transitions are not known, probability distributions are used instead: the instantaneous cost distribution <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \textstyle P(c_{t}|s_{t})}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle displaystyle="false" scriptlevel="0"> <mi>P</mi> <mo stretchy="false">(</mo> <msub> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>t</mi> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <msub> <mi>s</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>t</mi> </mrow> </msub> <mo stretchy="false">)</mo> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \textstyle P(c_{t}|s_{t})}</annotation> </semantics> </math><noscript><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d64a75ad0caf0be43f971b53a2c16b637bf8bb20" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:7.951ex; height:2.843ex;" alt="{\displaystyle \textstyle P(c_{t}|s_{t})}"></noscript><span class="lazy-image-placeholder" style="width: 7.951ex;height: 2.843ex;vertical-align: -0.838ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d64a75ad0caf0be43f971b53a2c16b637bf8bb20" data-alt="{\displaystyle \textstyle P(c_{t}|s_{t})}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> , the observation distribution <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \textstyle P(x_{t}|s_{t})}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle displaystyle="false" scriptlevel="0"> <mi>P</mi> <mo stretchy="false">(</mo> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>t</mi> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <msub> <mi>s</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>t</mi> </mrow> </msub> <mo stretchy="false">)</mo> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \textstyle P(x_{t}|s_{t})}</annotation> </semantics> </math><noscript><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/591cc95a2eb71b92b0fc200675bc8037094a37f0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:8.274ex; height:2.843ex;" alt="{\displaystyle \textstyle P(x_{t}|s_{t})}"></noscript><span class="lazy-image-placeholder" style="width: 8.274ex;height: 2.843ex;vertical-align: -0.838ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/591cc95a2eb71b92b0fc200675bc8037094a37f0" data-alt="{\displaystyle \textstyle P(x_{t}|s_{t})}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert">  and the transition distribution <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \textstyle P(s_{t+1}|s_{t},a_{t})}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle displaystyle="false" scriptlevel="0"> <mi>P</mi> <mo stretchy="false">(</mo> <msub> <mi>s</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>t</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <msub> <mi>s</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>t</mi> </mrow> </msub> <mo>,</mo> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>t</mi> </mrow> </msub> <mo stretchy="false">)</mo> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \textstyle P(s_{t+1}|s_{t},a_{t})}</annotation> </semantics> </math><noscript><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0200f5e1c5ad6c6114027fd0f660399c8b584d71" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:13.225ex; height:2.843ex;" alt="{\displaystyle \textstyle P(s_{t+1}|s_{t},a_{t})}"></noscript><span class="lazy-image-placeholder" style="width: 13.225ex;height: 2.843ex;vertical-align: -0.838ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0200f5e1c5ad6c6114027fd0f660399c8b584d71" data-alt="{\displaystyle \textstyle P(s_{t+1}|s_{t},a_{t})}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> , while a policy is defined as the conditional distribution over actions given the observations. Taken together, the two define a <a href="/wiki/Markov_chain" title="Markov chain">Markov chain</a> (MC). The aim is to discover the lowest-cost MC. ANNs serve as the learning component in such applications.<a href="#cite_note-132">[132]</a><a href="#cite_note-133">[133]</a> <a href="/wiki/Dynamic_programming" title="Dynamic programming">Dynamic programming</a> coupled with ANNs (giving <a href="/wiki/Neural_oscillation" title="Neural oscillation">neurodynamic</a> programming)<a href="#cite_note-134">[134]</a> has been applied to problems such as those involved in <a href="/wiki/Vehicle_routing" class="mw-redirect" title="Vehicle routing">vehicle routing</a>,<a href="#cite_note-135">[135]</a> video games, <a href="/wiki/Natural_resource_management" title="Natural resource management">natural resource management</a><a href="#cite_note-136">[136]</a><a href="#cite_note-137">[137]</a> and <a href="/wiki/Medicine" title="Medicine">medicine</a><a href="#cite_note-138">[138]</a> because of ANNs ability to mitigate losses of accuracy even when reducing the <a href="/wiki/Discretization" title="Discretization">discretization</a> grid density for numerically approximating the solution of control problems. Tasks that fall within the paradigm of reinforcement learning are control problems, <a href="/wiki/Game" title="Game">games</a> and other sequential decision making tasks. <div class="mw-heading mw-heading4"><h4 id="Self-learning">Self-learning</h4> <a role="button" href="/w/index.php?title=Neural_network_(machine_learning)&action=edit&section=21" title="Edit section: Self-learning" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> edit </a> </div> Self-learning in neural networks was introduced in 1982 along with a neural network capable of self-learning named crossbar adaptive array (CAA).<a href="#cite_note-139">[139]</a> It is a system with only one input, situation s, and only one output, action (or behavior) a. It has neither external advice input nor external reinforcement input from the environment. The CAA computes, in a crossbar fashion, both decisions about actions and emotions (feelings) about encountered situations. The system is driven by the interaction between cognition and emotion.<a href="#cite_note-140">[140]</a> Given the memory matrix, W =||w(a,s)||, the crossbar self-learning algorithm in each iteration performs the following computation: <pre> In situation s perform action a; Receive consequence situation s'; Compute emotion of being in consequence situation v(s'); Update crossbar memory w'(a,s) = w(a,s) + v(s'). </pre> The backpropagated value (secondary reinforcement) is the emotion toward the consequence situation. The CAA exists in two environments, one is behavioral environment where it behaves, and the other is genetic environment, where from it initially and only once receives initial emotions about to be encountered situations in the behavioral environment. Having received the genome vector (species vector) from the genetic environment, the CAA will learn a goal-seeking behavior, in the behavioral environment that contains both desirable and undesirable situations.<a href="#cite_note-141">[141]</a> <div class="mw-heading mw-heading4"><h4 id="Neuroevolution">Neuroevolution</h4> <a role="button" href="/w/index.php?title=Neural_network_(machine_learning)&action=edit&section=22" title="Edit section: Neuroevolution" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> edit </a> </div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Neuroevolution" title="Neuroevolution">Neuroevolution</a></div> <a href="/wiki/Neuroevolution" title="Neuroevolution">Neuroevolution</a> can create neural network topologies and weights using <a href="/wiki/Evolutionary_computation" title="Evolutionary computation">evolutionary computation</a>. It is competitive with sophisticated gradient descent approaches.<a href="#cite_note-142">[142]</a><a href="#cite_note-143">[143]</a> One advantage of neuroevolution is that it may be less prone to get caught in "dead ends".<a href="#cite_note-144">[144]</a> <div class="mw-heading mw-heading3"><h3 id="Stochastic_neural_network">Stochastic neural network</h3> <a role="button" href="/w/index.php?title=Neural_network_(machine_learning)&action=edit&section=23" title="Edit section: Stochastic neural network" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> edit </a> </div> Stochastic neural networks originating from <a href="/wiki/Spin_glass#Sherrington%E2%80%93Kirkpatrick_model" title="Spin glass">Sherrington–Kirkpatrick models</a> are a type of artificial neural network built by introducing random variations into the network, either by giving the network's <a href="/wiki/Artificial_neuron" title="Artificial neuron">artificial neurons</a> <a href="/wiki/Stochastic_process" title="Stochastic process">stochastic</a> transfer functions [<a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed">citation needed</a>], or by giving them stochastic weights. This makes them useful tools for <a href="/wiki/Optimization_(mathematics)" class="mw-redirect" title="Optimization (mathematics)">optimization</a> problems, since the random fluctuations help the network escape from <a href="/wiki/Maxima_and_minima" class="mw-redirect" title="Maxima and minima">local minima</a>.<a href="#cite_note-145">[145]</a> Stochastic neural networks trained using a Bayesian approach are known as Bayesian neural networks.<a href="#cite_note-146">[146]</a> <div class="mw-heading mw-heading3"><h3 id="Other">Other</h3> <a role="button" href="/w/index.php?title=Neural_network_(machine_learning)&action=edit&section=24" title="Edit section: Other" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> edit </a> </div> In a <a href="/wiki/Bayesian_probability" title="Bayesian probability">Bayesian</a> framework, a distribution over the set of allowed models is chosen to minimize the cost. <a href="/wiki/Evolutionary_methods" class="mw-redirect" title="Evolutionary methods">Evolutionary methods</a>,<a href="#cite_note-147">[147]</a> <a href="/wiki/Gene_expression_programming" title="Gene expression programming">gene expression programming</a>,<a href="#cite_note-148">[148]</a> <a href="/wiki/Simulated_annealing" title="Simulated annealing">simulated annealing</a>,<a href="#cite_note-149">[149]</a> <a href="/wiki/Expectation%E2%80%93maximization_algorithm" title="Expectation–maximization algorithm">expectation–maximization</a>, <a href="/wiki/Non-parametric_methods" class="mw-redirect" title="Non-parametric methods">non-parametric methods</a> and <a href="/wiki/Particle_swarm_optimization" title="Particle swarm optimization">particle swarm optimization</a><a href="#cite_note-150">[150]</a> are other learning algorithms. Convergent recursion is a learning algorithm for <a href="/wiki/Cerebellar_model_articulation_controller" title="Cerebellar model articulation controller">cerebellar model articulation controller</a> (CMAC) neural networks.<a href="#cite_note-Qin1-151">[151]</a><a href="#cite_note-Qin2-152">[152]</a> <div class="mw-heading mw-heading4"><h4 id="Modes">Modes</h4> <a role="button" href="/w/index.php?title=Neural_network_(machine_learning)&action=edit&section=25" title="Edit section: Modes" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> edit </a> </div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1251242444"><table class="box-No_footnotes plainlinks metadata ambox ambox-style ambox-No_footnotes" role="presentation"><tbody><tr><td class="mbox-text"><div class="mbox-text-span">This section includes a <a href="/wiki/Wikipedia:Citing_sources" title="Wikipedia:Citing sources">list of references</a>, <a href="/wiki/Wikipedia:Further_reading" title="Wikipedia:Further reading">related reading</a>, or <a href="/wiki/Wikipedia:External_links" title="Wikipedia:External links">external links</a>, but its sources remain unclear because it lacks <a href="/wiki/Wikipedia:Citing_sources#Inline_citations" title="Wikipedia:Citing sources">inline citations</a>. Please help <a href="/wiki/Wikipedia:WikiProject_Fact_and_Reference_Check" class="mw-redirect" title="Wikipedia:WikiProject Fact and Reference Check">improve</a> this section by <a href="/wiki/Wikipedia:When_to_cite" title="Wikipedia:When to cite">introducing</a> more precise citations. (August 2019) (<a href="/wiki/Help:Maintenance_template_removal" title="Help:Maintenance template removal">Learn how and when to remove this message</a>)</div></td></tr></tbody></table> Two modes of learning are available: <a href="/wiki/Stochastic_gradient_descent" title="Stochastic gradient descent">stochastic</a> and batch. In stochastic learning, each input creates a weight adjustment. In batch learning weights are adjusted based on a batch of inputs, accumulating errors over the batch. Stochastic learning introduces "noise" into the process, using the local gradient calculated from one data point; this reduces the chance of the network getting stuck in local minima. However, batch learning typically yields a faster, more stable descent to a local minimum, since each update is performed in the direction of the batch's average error. A common compromise is to use "mini-batches", small batches with samples in each batch selected stochastically from the entire data set. </section><div class="mw-heading mw-heading2 section-heading" onclick="mfTempOpenSection(4)"><h2 id="Types">Types</h2> <a role="button" href="/w/index.php?title=Neural_network_(machine_learning)&action=edit&section=26" title="Edit section: Types" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> edit </a> </div><section class="mf-section-4 collapsible-block" id="mf-section-4"> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Types_of_artificial_neural_networks" title="Types of artificial neural networks">Types of artificial neural networks</a></div> ANNs have evolved into a broad family of techniques that have advanced the state of the art across multiple domains. The simplest types have one or more static components, including number of units, number of layers, unit weights and <a href="/wiki/Topology" title="Topology">topology</a>. Dynamic types allow one or more of these to evolve via learning. The latter is much more complicated but can shorten learning periods and produce better results. Some types allow/require learning to be "supervised" by the operator, while others operate independently. Some types operate purely in hardware, while others are purely software and run on general purpose computers. Some of the main breakthroughs include: <ul><li><a href="/wiki/Convolutional_neural_network" title="Convolutional neural network">Convolutional neural networks</a> that have proven particularly successful in processing visual and other two-dimensional data;<a href="#cite_note-153">[153]</a><a href="#cite_note-lecun2016slides-154">[154]</a> where long short-term memory avoids the <a href="/wiki/Vanishing_gradient_problem" title="Vanishing gradient problem">vanishing gradient problem</a><a href="#cite_note-:03-155">[155]</a> and can handle signals that have a mix of low and high frequency components aiding large-vocabulary speech recognition,<a href="#cite_note-sak2014-156">[156]</a><a href="#cite_note-liwu2015-157">[157]</a> text-to-speech synthesis,<a href="#cite_note-158">[158]</a><a href="#cite_note-scholarpedia2-159">[159]</a><a href="#cite_note-zen2015-160">[160]</a> and photo-real talking heads;<a href="#cite_note-fan2015-161">[161]</a></li> <li>Competitive networks such as <a href="/wiki/Generative_adversarial_network" title="Generative adversarial network">generative adversarial networks</a> in which multiple networks (of varying structure) compete with each other, on tasks such as winning a game<a href="#cite_note-preprint-162">[162]</a> or on deceiving the opponent about the authenticity of an input.<a href="#cite_note-GANnips-94">[94]</a></li></ul> </section><div class="mw-heading mw-heading2 section-heading" onclick="mfTempOpenSection(5)"><h2 id="Network_design">Network design</h2> <a role="button" href="/w/index.php?title=Neural_network_(machine_learning)&action=edit&section=27" title="Edit section: Network design" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> edit </a> </div><section class="mf-section-5 collapsible-block" id="mf-section-5"> Using artificial neural networks requires an understanding of their characteristics. <ul><li>Choice of model: This depends on the data representation and the application. Model parameters include the number, type, and connectedness of network layers, as well as the size of each and the connection type (full, pooling, etc. ). Overly complex models learn slowly.</li> <li><a href="/wiki/Machine_learning" title="Machine learning">Learning algorithm</a>: Numerous trade-offs exist between learning algorithms. Almost any algorithm will work well with the correct hyperparameters<a href="#cite_note-163">[163]</a> for training on a particular data set. However, selecting and tuning an algorithm for training on unseen data requires significant experimentation.</li> <li><a href="/wiki/Robustness" title="Robustness">Robustness</a>: If the model, cost function and learning algorithm are selected appropriately, the resulting ANN can become robust.</li></ul> <a href="/wiki/Neural_architecture_search" title="Neural architecture search">Neural architecture search</a> (NAS) uses machine learning to automate ANN design. Various approaches to NAS have designed networks that compare well with hand-designed systems. The basic search algorithm is to propose a candidate model, evaluate it against a dataset, and use the results as feedback to teach the NAS network.<a href="#cite_note-164">[164]</a> Available systems include <a href="/wiki/Automated_machine_learning" title="Automated machine learning">AutoML</a> and AutoKeras.<a href="#cite_note-165">[165]</a> <a href="/wiki/Scikit-learn" title="Scikit-learn">scikit-learn library</a> provides functions to help with building a deep network from scratch. We can then implement a deep network with <a href="/wiki/TensorFlow" title="TensorFlow">TensorFlow</a> or <a href="/wiki/Keras" title="Keras">Keras</a>. Hyperparameters must also be defined as part of the design (they are not learned), governing matters such as how many neurons are in each layer, learning rate, step, stride, depth, receptive field and padding (for CNNs), etc.<a href="#cite_note-abs1502.02127-166">[166]</a> The <a href="/wiki/Python_(programming_language)" title="Python (programming language)">Python</a> code snippet provides an overview of the training function, which uses the training dataset, number of hidden layer units, learning rate, and number of iterations as parameters:<div class="mw-highlight mw-highlight-lang-python3 mw-content-ltr mw-highlight-lines" dir="ltr"><pre>def train(X, y, n_hidden, learning_rate, n_iter): m, n_input = X.shape # 1. random initialize weights and biases w1 = np.random.randn(n_input, n_hidden) b1 = np.zeros((1, n_hidden)) w2 = np.random.randn(n_hidden, 1) b2 = np.zeros((1, 1)) # 2. in each iteration, feed all layers with the latest weights and biases for i in range(n_iter + 1): z2 = np.dot(X, w1) + b1 a2 = sigmoid(z2) z3 = np.dot(a2, w2) + b2 a3 = z3 dz3 = a3 - y dw2 = np.dot(a2.T, dz3) db2 = np.sum(dz3, axis=0, keepdims=True) dz2 = np.dot(dz3, w2.T) * sigmoid_derivative(z2) dw1 = np.dot(X.T, dz2) db1 = np.sum(dz2, axis=0) # 3. update weights and biases with gradients w1 -= learning_rate * dw1 / m w2 -= learning_rate * dw2 / m b1 -= learning_rate * db1 / m b2 -= learning_rate * db2 / m if i % 1000 == 0: print("Epoch", i, "loss: ", np.mean(np.square(dz3))) model = {"w1": w1, "b1": b1, "w2": w2, "b2": b2} return model </pre></div>[<a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed">citation needed</a>] </section><div class="mw-heading mw-heading2 section-heading" onclick="mfTempOpenSection(6)"><h2 id="Applications">Applications</h2> <a role="button" href="/w/index.php?title=Neural_network_(machine_learning)&action=edit&section=28" title="Edit section: Applications" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> edit </a> </div><section class="mf-section-6 collapsible-block" id="mf-section-6"> Because of their ability to reproduce and model nonlinear processes, artificial neural networks have found applications in many disciplines. These include: <ul><li><a href="/wiki/Function_approximation" title="Function approximation">Function approximation</a>,<a href="#cite_note-167">[167]</a> or <a href="/wiki/Regression_analysis" title="Regression analysis">regression analysis</a>,<a href="#cite_note-168">[168]</a> (including <a href="/wiki/Time_series#Prediction_and_forecasting" title="Time series">time series prediction</a>, <a href="/wiki/Fitness_approximation" title="Fitness approximation">fitness approximation</a>,<a href="#cite_note-169">[169]</a> and modeling)</li> <li><a href="/wiki/Data_processing" title="Data processing">Data processing</a><a href="#cite_note-170">[170]</a> (including filtering, clustering, <a href="/wiki/Blind_source_separation" class="mw-redirect" title="Blind source separation">blind source separation</a>,<a href="#cite_note-171">[171]</a> and compression)</li> <li><a href="/wiki/Nonlinear_system_identification" title="Nonlinear system identification">Nonlinear system identification</a><a href="#cite_note-SAB1-93">[93]</a> and control (including vehicle control, trajectory prediction,<a href="#cite_note-172">[172]</a> <a href="/wiki/Adaptive_control" title="Adaptive control">adaptive control</a>, <a href="/wiki/Process_control" class="mw-redirect" title="Process control">process control</a>, and <a href="/wiki/Natural_resource_management" title="Natural resource management">natural resource management</a>)</li> <li><a href="/wiki/Pattern_recognition" title="Pattern recognition">Pattern recognition</a> (including radar systems, <a href="/wiki/Facial_recognition_system" title="Facial recognition system">face identification</a>, signal classification,<a href="#cite_note-173">[173]</a> <a href="/wiki/Novelty_detection" title="Novelty detection">novelty detection</a>, <a href="/wiki/3D_reconstruction" title="3D reconstruction">3D reconstruction</a>,<a href="#cite_note-174">[174]</a> object recognition, and sequential decision making<a href="#cite_note-TurekNeuralNet-175">[175]</a>)</li> <li>Sequence recognition (including <a href="/wiki/Gesture_recognition" title="Gesture recognition">gesture</a>, <a href="/wiki/Speech_recognition" title="Speech recognition">speech</a>, and <a href="/wiki/Handwriting_recognition" title="Handwriting recognition">handwritten</a> and printed text recognition<a href="#cite_note-176">[176]</a>)</li> <li>Sensor data analysis<a href="#cite_note-177">[177]</a> (including <a href="/wiki/Image_analysis" title="Image analysis">image analysis</a>)</li> <li><a href="/wiki/Robotics" title="Robotics">Robotics</a> (including directing manipulators and <a href="/wiki/Prosthesis" title="Prosthesis">prostheses</a>)</li> <li><a href="/wiki/Data_mining" title="Data mining">Data mining</a> (including <a href="/wiki/Knowledge_discovery_in_databases" class="mw-redirect" title="Knowledge discovery in databases">knowledge discovery in databases</a>)</li> <li>Finance<a href="#cite_note-178">[178]</a> (such as <a href="/wiki/Ex-ante" title="Ex-ante">ex-ante</a> models for specific financial long-run forecasts and <a href="/wiki/Artificial_financial_market" class="mw-redirect" title="Artificial financial market">artificial financial markets</a>)</li> <li><a href="/wiki/Quantum_chemistry" title="Quantum chemistry">Quantum chemistry</a><a href="#cite_note-Balabin_2009-179">[179]</a></li> <li><a href="/wiki/General_game_playing" title="General game playing">General game playing</a><a href="#cite_note-180">[180]</a></li> <li><a href="/wiki/Generative_AI" class="mw-redirect" title="Generative AI">Generative AI</a><a href="#cite_note-181">[181]</a></li> <li><a href="/wiki/Data_visualization" class="mw-redirect" title="Data visualization">Data visualization</a></li> <li><a href="/wiki/Machine_translation" title="Machine translation">Machine translation</a></li> <li>Social network filtering<a href="#cite_note-182">[182]</a></li> <li><a href="/wiki/E-mail_spam" class="mw-redirect" title="E-mail spam">E-mail spam</a> filtering</li> <li><a href="/wiki/Medical_diagnosis" title="Medical diagnosis">Medical diagnosis</a><a href="#cite_note-Ciaramella-183">[183]</a></li></ul> ANNs have been used to diagnose several types of cancers<a href="#cite_note-184">[184]</a><a href="#cite_note-185">[185]</a> and to distinguish highly invasive cancer cell lines from less invasive lines using only cell shape information.<a href="#cite_note-186">[186]</a><a href="#cite_note-187">[187]</a> ANNs have been used to accelerate reliability analysis of infrastructures subject to natural disasters<a href="#cite_note-188">[188]</a><a href="#cite_note-189">[189]</a> and to predict foundation settlements.<a href="#cite_note-190">[190]</a> It can also be useful to mitigate flood by the use of ANNs for modelling rainfall-runoff.<a href="#cite_note-191">[191]</a> ANNs have also been used for building black-box models in <a href="/wiki/Geoscience" class="mw-redirect" title="Geoscience">geoscience</a>: <a href="/wiki/Hydrology" title="Hydrology">hydrology</a>,<a href="#cite_note-192">[192]</a><a href="#cite_note-193">[193]</a> ocean modelling and <a href="/wiki/Coastal_engineering" title="Coastal engineering">coastal engineering</a>,<a href="#cite_note-194">[194]</a><a href="#cite_note-195">[195]</a> and <a href="/wiki/Geomorphology" title="Geomorphology">geomorphology</a>.<a href="#cite_note-196">[196]</a> ANNs have been employed in <a href="/wiki/Computer_security" title="Computer security">cybersecurity</a>, with the objective to discriminate between legitimate activities and malicious ones. For example, machine learning has been used for classifying Android malware,<a href="#cite_note-197">[197]</a> for identifying domains belonging to threat actors and for detecting URLs posing a security risk.<a href="#cite_note-198">[198]</a> Research is underway on ANN systems designed for penetration testing, for detecting botnets,<a href="#cite_note-199">[199]</a> credit cards frauds<a href="#cite_note-200">[200]</a> and network intrusions. ANNs have been proposed as a tool to solve <a href="/wiki/Partial_differential_equation" title="Partial differential equation">partial differential equations</a> in physics<a href="#cite_note-201">[201]</a><a href="#cite_note-202">[202]</a><a href="#cite_note-203">[203]</a> and simulate the properties of many-body <a href="/wiki/Open_quantum_system" title="Open quantum system">open quantum systems</a>.<a href="#cite_note-204">[204]</a><a href="#cite_note-205">[205]</a><a href="#cite_note-206">[206]</a><a href="#cite_note-207">[207]</a> In brain research ANNs have studied short-term behavior of <a href="/wiki/Biological_neuron_models" class="mw-redirect" title="Biological neuron models">individual neurons</a>,<a href="#cite_note-208">[208]</a> the dynamics of neural circuitry arise from interactions between individual neurons and how behavior can arise from abstract neural modules that represent complete subsystems. Studies considered long-and short-term plasticity of neural systems and their relation to learning and memory from the individual neuron to the system level. It is possible to create a profile of a user's interests from pictures, using artificial neural networks trained for object recognition.<a href="#cite_note-209">[209]</a> Beyond their traditional applications, artificial neural networks are increasingly being utilized in interdisciplinary research, such as materials science. For instance, graph neural networks (GNNs) have demonstrated their capability in scaling deep learning for the discovery of new stable materials by efficiently predicting the total energy of crystals. This application underscores the adaptability and potential of ANNs in tackling complex problems beyond the realms of predictive modeling and artificial intelligence, opening new pathways for scientific discovery and innovation.<a href="#cite_note-210">[210]</a> </section><div class="mw-heading mw-heading2 section-heading" onclick="mfTempOpenSection(7)"><h2 id="Theoretical_properties">Theoretical properties</h2> <a role="button" href="/w/index.php?title=Neural_network_(machine_learning)&action=edit&section=29" title="Edit section: Theoretical properties" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> edit </a> </div><section class="mf-section-7 collapsible-block" id="mf-section-7"> <div class="mw-heading mw-heading3"><h3 id="Computational_power">Computational power</h3> <a role="button" href="/w/index.php?title=Neural_network_(machine_learning)&action=edit&section=30" title="Edit section: Computational power" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> edit </a> </div> The <a href="/wiki/Multilayer_perceptron" title="Multilayer perceptron">multilayer perceptron</a> is a <a href="/wiki/UTM_theorem" title="UTM theorem">universal function</a> approximator, as proven by the <a href="/wiki/Universal_approximation_theorem" title="Universal approximation theorem">universal approximation theorem</a>. However, the proof is not constructive regarding the number of neurons required, the network topology, the weights and the learning parameters. A specific recurrent architecture with <a href="/wiki/Rational_number" title="Rational number">rational</a>-valued weights (as opposed to full precision <a href="/wiki/Real_number" title="Real number">real number</a>-valued weights) has the power of a <a href="/wiki/Universal_Turing_machine" title="Universal Turing machine">universal Turing machine</a>,<a href="#cite_note-211">[211]</a> using a finite number of neurons and standard linear connections. Further, the use of <a href="/wiki/Irrational_number" title="Irrational number">irrational</a> values for weights results in a machine with <a href="/wiki/Hypercomputation" title="Hypercomputation">super-Turing</a> power.<a href="#cite_note-212">[212]</a><a href="#cite_note-213">[213]</a>[<a href="/wiki/Wikipedia:Verifiability" title="Wikipedia:Verifiability">failed verification</a>] <div class="mw-heading mw-heading3"><h3 id="Capacity">Capacity</h3> <a role="button" href="/w/index.php?title=Neural_network_(machine_learning)&action=edit&section=31" title="Edit section: Capacity" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> edit </a> </div> A model's "capacity" property corresponds to its ability to model any given function. It is related to the amount of information that can be stored in the network and to the notion of complexity. Two notions of capacity are known by the community. The information capacity and the VC Dimension. The information capacity of a perceptron is intensively discussed in Sir David MacKay's book<a href="#cite_note-auto-214">[214]</a> which summarizes work by Thomas Cover.<a href="#cite_note-215">[215]</a> The capacity of a network of standard neurons (not convolutional) can be derived by four rules<a href="#cite_note-216">[216]</a> that derive from understanding a neuron as an electrical element. The information capacity captures the functions modelable by the network given any data as input. The second notion, is the <a href="/wiki/VC_dimension" class="mw-redirect" title="VC dimension">VC dimension</a>. VC Dimension uses the principles of <a href="/wiki/Measure_theory" class="mw-redirect" title="Measure theory">measure theory</a> and finds the maximum capacity under the best possible circumstances. This is, given input data in a specific form. As noted in,<a href="#cite_note-auto-214">[214]</a> the VC Dimension for arbitrary inputs is half the information capacity of a Perceptron. The VC Dimension for arbitrary points is sometimes referred to as Memory Capacity.<a href="#cite_note-217">[217]</a> <div class="mw-heading mw-heading3"><h3 id="Convergence">Convergence</h3> <a role="button" href="/w/index.php?title=Neural_network_(machine_learning)&action=edit&section=32" title="Edit section: Convergence" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> edit </a> </div> Models may not consistently converge on a single solution, firstly because local minima may exist, depending on the cost function and the model. Secondly, the optimization method used might not guarantee to converge when it begins far from any local minimum. Thirdly, for sufficiently large data or parameters, some methods become impractical. Another issue worthy to mention is that training may cross some <a href="/wiki/Saddle_point" title="Saddle point">Saddle point</a> which may lead the convergence to the wrong direction. The convergence behavior of certain types of ANN architectures are more understood than others. When the width of network approaches to infinity, the ANN is well described by its first order Taylor expansion throughout training, and so inherits the convergence behavior of <a href="/wiki/Linear_model" title="Linear model">affine models</a>.<a href="#cite_note-218">[218]</a><a href="#cite_note-219">[219]</a> Another example is when parameters are small, it is observed that ANNs often fits target functions from low to high frequencies. This behavior is referred to as the spectral bias, or frequency principle, of neural networks.<a href="#cite_note-220">[220]</a><a href="#cite_note-221">[221]</a><a href="#cite_note-222">[222]</a><a href="#cite_note-223">[223]</a> This phenomenon is the opposite to the behavior of some well studied iterative numerical schemes such as <a href="/wiki/Jacobi_method" title="Jacobi method">Jacobi method</a>. Deeper neural networks have been observed to be more biased towards low frequency functions.<a href="#cite_note-224">[224]</a> <div class="mw-heading mw-heading3"><h3 id="Generalization_and_statistics">Generalization and statistics</h3> <a role="button" href="/w/index.php?title=Neural_network_(machine_learning)&action=edit&section=33" title="Edit section: Generalization and statistics" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> edit </a> </div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1251242444"><table class="box-No_footnotes plainlinks metadata ambox ambox-style ambox-No_footnotes" role="presentation"><tbody><tr><td class="mbox-text"><div class="mbox-text-span">This section includes a <a href="/wiki/Wikipedia:Citing_sources" title="Wikipedia:Citing sources">list of references</a>, <a href="/wiki/Wikipedia:Further_reading" title="Wikipedia:Further reading">related reading</a>, or <a href="/wiki/Wikipedia:External_links" title="Wikipedia:External links">external links</a>, but its sources remain unclear because it lacks <a href="/wiki/Wikipedia:Citing_sources#Inline_citations" title="Wikipedia:Citing sources">inline citations</a>. Please help <a href="/wiki/Wikipedia:WikiProject_Fact_and_Reference_Check" class="mw-redirect" title="Wikipedia:WikiProject Fact and Reference Check">improve</a> this section by <a href="/wiki/Wikipedia:When_to_cite" title="Wikipedia:When to cite">introducing</a> more precise citations. (August 2019) (<a href="/wiki/Help:Maintenance_template_removal" title="Help:Maintenance template removal">Learn how and when to remove this message</a>)</div></td></tr></tbody></table> Applications whose goal is to create a system that generalizes well to unseen examples, face the possibility of over-training. This arises in convoluted or over-specified systems when the network capacity significantly exceeds the needed free parameters. Two approaches address over-training. The first is to use <a href="/wiki/Cross-validation_(statistics)" title="Cross-validation (statistics)">cross-validation</a> and similar techniques to check for the presence of over-training and to select hyperparameters to minimize the generalization error. The second is to use some form of <a href="/wiki/Regularization_(mathematics)" title="Regularization (mathematics)">regularization</a>. This concept emerges in a probabilistic (Bayesian) framework, where regularization can be performed by selecting a larger prior probability over simpler models; but also in statistical learning theory, where the goal is to minimize over two quantities: the 'empirical risk' and the 'structural risk', which roughly corresponds to the error over the training set and the predicted error in unseen data due to overfitting. <figure class="mw-default-size mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Synapse_deployment.jpg" class="mw-file-description"><noscript><img src="//upload.wikimedia.org/wikipedia/commons/thumb/2/22/Synapse_deployment.jpg/250px-Synapse_deployment.jpg" decoding="async" width="250" height="192" class="mw-file-element" data-file-width="1024" data-file-height="786"></noscript><span class="lazy-image-placeholder" style="width: 250px;height: 192px;" data-src="//upload.wikimedia.org/wikipedia/commons/thumb/2/22/Synapse_deployment.jpg/250px-Synapse_deployment.jpg" data-width="250" data-height="192" data-srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/22/Synapse_deployment.jpg/375px-Synapse_deployment.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/2/22/Synapse_deployment.jpg/500px-Synapse_deployment.jpg 2x" data-class="mw-file-element"> </a><figcaption>Confidence analysis of a neural network</figcaption></figure> Supervised neural networks that use a <a href="/wiki/Mean_squared_error" title="Mean squared error">mean squared error</a> (MSE) cost function can use formal statistical methods to determine the confidence of the trained model. The MSE on a validation set can be used as an estimate for variance. This value can then be used to calculate the <a href="/wiki/Confidence_interval" title="Confidence interval">confidence interval</a> of network output, assuming a <a href="/wiki/Normal_distribution" title="Normal distribution">normal distribution</a>. A confidence analysis made this way is statistically valid as long as the output <a href="/wiki/Probability_distribution" title="Probability distribution">probability distribution</a> stays the same and the network is not modified. By assigning a <a href="/wiki/Softmax_activation_function" class="mw-redirect" title="Softmax activation function">softmax activation function</a>, a generalization of the <a href="/wiki/Logistic_function" title="Logistic function">logistic function</a>, on the output layer of the neural network (or a softmax component in a component-based network) for categorical target variables, the outputs can be interpreted as posterior probabilities. This is useful in classification as it gives a certainty measure on classifications. The softmax activation function is: <dl><dd><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle y_{i}={\frac {e^{x_{i}}}{\sum _{j=1}^{c}e^{x_{j}}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mrow> </msup> <mrow> <munderover> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>c</mi> </mrow> </munderover> <msup> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> </mrow> </msub> </mrow> </msup> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle y_{i}={\frac {e^{x_{i}}}{\sum _{j=1}^{c}e^{x_{j}}}}}</annotation> </semantics> </math><noscript><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/481884e3588b192020e8d0aafe16b41c0ed26007" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.171ex; width:14.695ex; height:6.509ex;" alt="{\displaystyle y_{i}={\frac {e^{x_{i}}}{\sum _{j=1}^{c}e^{x_{j}}}}}"></noscript><span class="lazy-image-placeholder" style="width: 14.695ex;height: 6.509ex;vertical-align: -3.171ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/481884e3588b192020e8d0aafe16b41c0ed26007" data-alt="{\displaystyle y_{i}={\frac {e^{x_{i}}}{\sum _{j=1}^{c}e^{x_{j}}}}}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </dd></dl> </section><div class="mw-heading mw-heading2 section-heading" onclick="mfTempOpenSection(8)"><h2 id="Criticism">Criticism</h2> <a role="button" href="/w/index.php?title=Neural_network_(machine_learning)&action=edit&section=34" title="Edit section: Criticism" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> edit </a> </div><section class="mf-section-8 collapsible-block" id="mf-section-8"> <div class="mw-heading mw-heading3"><h3 id="Training_2">Training</h3> <a role="button" href="/w/index.php?title=Neural_network_(machine_learning)&action=edit&section=35" title="Edit section: Training" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> edit </a> </div> A common criticism of neural networks, particularly in robotics, is that they require too many training samples for real-world operation.<a href="#cite_note-225">[225]</a> Any learning machine needs sufficient representative examples in order to capture the underlying structure that allows it to generalize to new cases. Potential solutions include randomly shuffling training examples, by using a numerical optimization algorithm that does not take too large steps when changing the network connections following an example, grouping examples in so-called mini-batches and/or introducing a recursive least squares algorithm for <a href="/wiki/Cerebellar_model_articulation_controller" title="Cerebellar model articulation controller">CMAC</a>.<a href="#cite_note-Qin1-151">[151]</a> Dean Pomerleau uses a neural network to train a robotic vehicle to drive on multiple types of roads (single lane, multi-lane, dirt, etc.), and a large amount of his research is devoted to extrapolating multiple training scenarios from a single training experience, and preserving past training diversity so that the system does not become overtrained (if, for example, it is presented with a series of right turns—it should not learn to always turn right).<a href="#cite_note-226">[226]</a> <div class="mw-heading mw-heading3"><h3 id="Theory">Theory</h3> <a role="button" href="/w/index.php?title=Neural_network_(machine_learning)&action=edit&section=36" title="Edit section: Theory" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> edit </a> </div> A central claim[<a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed">citation needed</a>] of ANNs is that they embody new and powerful general principles for processing information. These principles are ill-defined. It is often claimed[<a href="/wiki/Wikipedia:Manual_of_Style/Words_to_watch#Unsupported_attributions" title="Wikipedia:Manual of Style/Words to watch">by whom?</a>] that they are <a href="/wiki/Emergent_properties" class="mw-redirect" title="Emergent properties">emergent</a> from the network itself. This allows simple statistical association (the basic function of artificial neural networks) to be described as learning or recognition. In 1997, <a href="/wiki/Alexander_Dewdney" class="mw-redirect" title="Alexander Dewdney">Alexander Dewdney</a>, a former <a href="/wiki/Scientific_American" title="Scientific American">Scientific American</a> columnist, commented that as a result, artificial neural networks have a "something-for-nothing quality, one that imparts a peculiar aura of laziness and a distinct lack of curiosity about just how good these computing systems are. No human hand (or mind) intervenes; solutions are found as if by magic; and no one, it seems, has learned anything".<a href="#cite_note-227">[227]</a> One response to Dewdney is that neural networks have been successfully used to handle many complex and diverse tasks, ranging from autonomously flying aircraft<a href="#cite_note-228">[228]</a> to detecting credit card fraud to mastering the game of <a href="/wiki/Go_(game)" title="Go (game)">Go</a>. Technology writer Roger Bridgman commented: <style data-mw-deduplicate="TemplateStyles:r1244412712">.mw-parser-output .templatequote{overflow:hidden;margin:1em 0;padding:0 32px}.mw-parser-output .templatequotecite{line-height:1.5em;text-align:left;margin-top:0}@media(min-width:500px){.mw-parser-output .templatequotecite{padding-left:1.6em}}</style><blockquote class="templatequote">Neural networks, for instance, are in the dock not only because they have been hyped to high heaven, (what hasn't?) but also because you could create a successful net without understanding how it worked: the bunch of numbers that captures its behaviour would in all probability be "an opaque, unreadable table...valueless as a scientific resource". In spite of his emphatic declaration that science is not technology, Dewdney seems here to pillory neural nets as bad science when most of those devising them are just trying to be good engineers. An unreadable table that a useful machine could read would still be well worth having.<a href="#cite_note-229">[229]</a> </blockquote> Although it is true that analyzing what has been learned by an artificial neural network is difficult, it is much easier to do so than to analyze what has been learned by a biological neural network. Moreover, recent emphasis on the <a href="/wiki/Explainable_artificial_intelligence" title="Explainable artificial intelligence">explainability</a> of AI has contributed towards the development of methods, notably those based on <a href="/wiki/Attention_(machine_learning)" title="Attention (machine learning)">attention</a> mechanisms, for visualizing and explaining learned neural networks. Furthermore, researchers involved in exploring learning algorithms for neural networks are gradually uncovering generic principles that allow a learning machine to be successful. For example, Bengio and LeCun (2007) wrote an article regarding local vs non-local learning, as well as shallow vs deep architecture.<a href="#cite_note-230">[230]</a> Biological brains use both shallow and deep circuits as reported by brain anatomy,<a href="#cite_note-VanEssen1991-231">[231]</a> displaying a wide variety of invariance. Weng<a href="#cite_note-Weng2012-232">[232]</a> argued that the brain self-wires largely according to signal statistics and therefore, a serial cascade cannot catch all major statistical dependencies. <div class="mw-heading mw-heading3"><h3 id="Hardware">Hardware</h3> <a role="button" href="/w/index.php?title=Neural_network_(machine_learning)&action=edit&section=37" title="Edit section: Hardware" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> edit </a> </div> Large and effective neural networks require considerable computing resources.<a href="#cite_note-:0-233">[233]</a> While the brain has hardware tailored to the task of processing signals through a <a href="/wiki/Graph_(discrete_mathematics)" title="Graph (discrete mathematics)">graph</a> of neurons, simulating even a simplified neuron on <a href="/wiki/Von_Neumann_architecture" title="Von Neumann architecture">von Neumann architecture</a> may consume vast amounts of <a href="/wiki/Random-access_memory" title="Random-access memory">memory</a> and storage. Furthermore, the designer often needs to transmit signals through many of these connections and their associated neurons – which require enormous <a href="/wiki/Central_processing_unit" title="Central processing unit">CPU</a> power and time.[<a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed">citation needed</a>] Some argue that the resurgence of neural networks in the twenty-first century is largely attributable to advances in hardware: from 1991 to 2015, computing power, especially as delivered by <a href="/wiki/General-purpose_computing_on_graphics_processing_units" title="General-purpose computing on graphics processing units">GPGPUs</a> (on <a href="/wiki/Graphics_processing_unit" title="Graphics processing unit">GPUs</a>), has increased around a million-fold, making the standard backpropagation algorithm feasible for training networks that are several layers deeper than before.<a href="#cite_note-SCHIDHUB4-38">[38]</a> The use of accelerators such as <a href="/wiki/Field-programmable_gate_array" title="Field-programmable gate array">FPGAs</a> and GPUs can reduce training times from months to days.<a href="#cite_note-:0-233">[233]</a><a href="#cite_note-234">[234]</a> <a href="/wiki/Neuromorphic_engineering" class="mw-redirect" title="Neuromorphic engineering">Neuromorphic engineering</a> or a <a href="/wiki/Physical_neural_network" title="Physical neural network">physical neural network</a> addresses the hardware difficulty directly, by constructing non-von-Neumann chips to directly implement neural networks in circuitry. Another type of chip optimized for neural network processing is called a <a href="/wiki/Tensor_Processing_Unit" title="Tensor Processing Unit">Tensor Processing Unit</a>, or TPU.<a href="#cite_note-235">[235]</a> <div class="mw-heading mw-heading3"><h3 id="Practical_counterexamples">Practical counterexamples</h3> <a role="button" href="/w/index.php?title=Neural_network_(machine_learning)&action=edit&section=38" title="Edit section: Practical counterexamples" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> edit </a> </div> Analyzing what has been learned by an ANN is much easier than analyzing what has been learned by a biological neural network. Furthermore, researchers involved in exploring learning algorithms for neural networks are gradually uncovering general principles that allow a learning machine to be successful. For example, local vs. non-local learning and shallow vs. deep architecture.<a href="#cite_note-236">[236]</a> <div class="mw-heading mw-heading3"><h3 id="Hybrid_approaches">Hybrid approaches</h3> <a role="button" href="/w/index.php?title=Neural_network_(machine_learning)&action=edit&section=39" title="Edit section: Hybrid approaches" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> edit </a> </div> Advocates of <a href="/wiki/Hybrid_neural_network" title="Hybrid neural network">hybrid</a> models (combining neural networks and symbolic approaches) say that such a mixture can better capture the mechanisms of the human mind.<a href="#cite_note-237">[237]</a><a href="#cite_note-238">[238]</a> <div class="mw-heading mw-heading3"><h3 id="Dataset_bias">Dataset bias</h3> <a role="button" href="/w/index.php?title=Neural_network_(machine_learning)&action=edit&section=40" title="Edit section: Dataset bias" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> edit </a> </div> Neural networks are dependent on the quality of the data they are trained on, thus low quality data with imbalanced representativeness can lead to the model learning and perpetuating societal biases.<a href="#cite_note-:010-239">[239]</a><a href="#cite_note-:17-240">[240]</a> These inherited biases become especially critical when the ANNs are integrated into real-world scenarios where the training data may be imbalanced due to the scarcity of data for a specific race, gender or other attribute.<a href="#cite_note-:010-239">[239]</a> This imbalance can result in the model having inadequate representation and understanding of underrepresented groups, leading to discriminatory outcomes that exacerbate societal inequalities, especially in applications like <a href="/wiki/Facial_recognition_system" title="Facial recognition system">facial recognition</a>, hiring processes, and <a href="/wiki/Law_enforcement" title="Law enforcement">law enforcement</a>.<a href="#cite_note-:17-240">[240]</a><a href="#cite_note-:22-241">[241]</a> For example, in 2018, <a href="/wiki/Amazon_(company)" title="Amazon (company)">Amazon</a> had to scrap a recruiting tool because the model favored men over women for jobs in software engineering due to the higher number of male workers in the field.<a href="#cite_note-:22-241">[241]</a> The program would penalize any resume with the word "woman" or the name of any women's college. However, the use of <a href="/wiki/Synthetic_data" title="Synthetic data">synthetic data</a> can help reduce dataset bias and increase representation in datasets.<a href="#cite_note-242">[242]</a> </section><div class="mw-heading mw-heading2 section-heading" onclick="mfTempOpenSection(9)"><h2 id="Gallery">Gallery</h2> <a role="button" href="/w/index.php?title=Neural_network_(machine_learning)&action=edit&section=41" title="Edit section: Gallery" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> edit </a> </div><section class="mf-section-9 collapsible-block" id="mf-section-9"> <ul class="gallery mw-gallery-traditional"> <li class="gallerybox" style="width: 255px"> <div class="thumb" style="width: 250px; height: 150px;"><a href="/wiki/File:Single_layer_ann.svg" class="mw-file-description" title="A single-layer feedforward artificial neural network. Arrows originating from '"`UNIQ--postMath-0000000E-QINU`"' are omitted for clarity. There are p inputs to this network and q outputs. In this system, the value of the qth output, '"`UNIQ--postMath-0000000F-QINU`"', is calculated as '"`UNIQ--postMath-00000010-QINU`"'"><noscript><img alt="A single-layer feedforward artificial neural network. Arrows originating from '"`UNIQ--postMath-0000000E-QINU`"' are omitted for clarity. There are p inputs to this network and q outputs. In this system, the value of the qth output, '"`UNIQ--postMath-0000000F-QINU`"', is calculated as '"`UNIQ--postMath-00000010-QINU`"'" src="//upload.wikimedia.org/wikipedia/commons/thumb/b/be/Single_layer_ann.svg/172px-Single_layer_ann.svg.png" decoding="async" width="172" height="120" class="mw-file-element" data-file-width="329" data-file-height="230"></noscript><span class="lazy-image-placeholder" style="width: 172px;height: 120px;" data-src="//upload.wikimedia.org/wikipedia/commons/thumb/b/be/Single_layer_ann.svg/172px-Single_layer_ann.svg.png" data-alt="A single-layer feedforward artificial neural network. Arrows originating from '"`UNIQ--postMath-0000000E-QINU`"' are omitted for clarity. There are p inputs to this network and q outputs. In this system, the value of the qth output, '"`UNIQ--postMath-0000000F-QINU`"', is calculated as '"`UNIQ--postMath-00000010-QINU`"'" data-width="172" data-height="120" data-srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/be/Single_layer_ann.svg/258px-Single_layer_ann.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/be/Single_layer_ann.svg/344px-Single_layer_ann.svg.png 2x" data-class="mw-file-element"> </a></div> <div class="gallerytext">A single-layer feedforward artificial neural network. Arrows originating from <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \scriptstyle x_{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle displaystyle="false" scriptlevel="1"> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \scriptstyle x_{2}}</annotation> </semantics> </math><noscript><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e758ff5bf928d44a755aa0e87d3b97a28f5fd50e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:1.772ex; height:1.509ex;" alt="{\displaystyle \scriptstyle x_{2}}"></noscript><span class="lazy-image-placeholder" style="width: 1.772ex;height: 1.509ex;vertical-align: -0.505ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e758ff5bf928d44a755aa0e87d3b97a28f5fd50e" data-alt="{\displaystyle \scriptstyle x_{2}}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert">  are omitted for clarity. There are p inputs to this network and q outputs. In this system, the value of the qth output, <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle y_{q}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>q</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle y_{q}}</annotation> </semantics> </math><noscript><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/62e77051e3953cdf3818c7c8458d4f515eb5f79c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:2.128ex; height:2.343ex;" alt="{\displaystyle y_{q}}"></noscript><span class="lazy-image-placeholder" style="width: 2.128ex;height: 2.343ex;vertical-align: -1.005ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/62e77051e3953cdf3818c7c8458d4f515eb5f79c" data-alt="{\displaystyle y_{q}}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> , is calculated as <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \scriptstyle y_{q}=K*(\sum _{i}(x_{i}*w_{iq})-b_{q}).}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle displaystyle="false" scriptlevel="1"> <msub> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>q</mi> </mrow> </msub> <mo>=</mo> <mi>K</mi> <mo>∗</mo> <mo stretchy="false">(</mo> <munder> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </munder> <mo stretchy="false">(</mo> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo>∗</mo> <msub> <mi>w</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mi>q</mi> </mrow> </msub> <mo stretchy="false">)</mo> <mo>−</mo> <msub> <mi>b</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>q</mi> </mrow> </msub> <mo stretchy="false">)</mo> <mo>.</mo> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \scriptstyle y_{q}=K*(\sum _{i}(x_{i}*w_{iq})-b_{q}).}</annotation> </semantics> </math><noscript><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4acabcd3a2df465f6bb9a5747d5b431e339b61d9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:18.086ex; height:2.343ex;" alt="{\displaystyle \scriptstyle y_{q}=K*(\sum _{i}(x_{i}*w_{iq})-b_{q}).}"></noscript><span class="lazy-image-placeholder" style="width: 18.086ex;height: 2.343ex;vertical-align: -0.838ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4acabcd3a2df465f6bb9a5747d5b431e339b61d9" data-alt="{\displaystyle \scriptstyle y_{q}=K*(\sum _{i}(x_{i}*w_{iq})-b_{q}).}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </div> </li> <li class="gallerybox" style="width: 255px"> <div class="thumb" style="width: 250px; height: 150px;"><a href="/wiki/File:Two_layer_ann.svg" class="mw-file-description" title="A two-layer feedforward artificial neural network"><noscript><img alt="A two-layer feedforward artificial neural network" src="//upload.wikimedia.org/wikipedia/commons/thumb/7/7f/Two_layer_ann.svg/94px-Two_layer_ann.svg.png" decoding="async" width="94" height="120" class="mw-file-element" data-file-width="331" data-file-height="421"></noscript><span class="lazy-image-placeholder" style="width: 94px;height: 120px;" data-src="//upload.wikimedia.org/wikipedia/commons/thumb/7/7f/Two_layer_ann.svg/94px-Two_layer_ann.svg.png" data-alt="A two-layer feedforward artificial neural network" data-width="94" data-height="120" data-srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/7f/Two_layer_ann.svg/141px-Two_layer_ann.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/7f/Two_layer_ann.svg/189px-Two_layer_ann.svg.png 2x" data-class="mw-file-element"> </a></div> <div class="gallerytext">A two-layer feedforward artificial neural network</div> </li> <li class="gallerybox" style="width: 255px"> <div class="thumb" style="width: 250px; height: 150px;"><a href="/wiki/File:Artificial_neural_network.svg" class="mw-file-description" title="An artificial neural network"><noscript><img alt="An artificial neural network" src="//upload.wikimedia.org/wikipedia/commons/thumb/e/e4/Artificial_neural_network.svg/134px-Artificial_neural_network.svg.png" decoding="async" width="134" height="120" class="mw-file-element" data-file-width="560" data-file-height="500"></noscript><span class="lazy-image-placeholder" style="width: 134px;height: 120px;" data-src="//upload.wikimedia.org/wikipedia/commons/thumb/e/e4/Artificial_neural_network.svg/134px-Artificial_neural_network.svg.png" data-alt="An artificial neural network" data-width="134" data-height="120" data-srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/e4/Artificial_neural_network.svg/202px-Artificial_neural_network.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/e4/Artificial_neural_network.svg/269px-Artificial_neural_network.svg.png 2x" data-class="mw-file-element"> </a></div> <div class="gallerytext">An artificial neural network</div> </li> <li class="gallerybox" style="width: 255px"> <div class="thumb" style="width: 250px; height: 150px;"><a href="/wiki/File:Ann_dependency_(graph).svg" class="mw-file-description" title="An ANN dependency graph"><noscript><img alt="An ANN dependency graph" src="//upload.wikimedia.org/wikipedia/commons/thumb/d/dd/Ann_dependency_%28graph%29.svg/168px-Ann_dependency_%28graph%29.svg.png" decoding="async" width="168" height="120" class="mw-file-element" data-file-width="178" data-file-height="127"></noscript><span class="lazy-image-placeholder" style="width: 168px;height: 120px;" data-src="//upload.wikimedia.org/wikipedia/commons/thumb/d/dd/Ann_dependency_%28graph%29.svg/168px-Ann_dependency_%28graph%29.svg.png" data-alt="An ANN dependency graph" data-width="168" data-height="120" data-srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/dd/Ann_dependency_%28graph%29.svg/252px-Ann_dependency_%28graph%29.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/d/dd/Ann_dependency_%28graph%29.svg/337px-Ann_dependency_%28graph%29.svg.png 2x" data-class="mw-file-element"> </a></div> <div class="gallerytext">An ANN dependency graph</div> </li> <li class="gallerybox" style="width: 255px"> <div class="thumb" style="width: 250px; height: 150px;"><a href="/wiki/File:Single-layer_feedforward_artificial_neural_network.png" class="mw-file-description" title="A single-layer feedforward artificial neural network with 4 inputs, 6 hidden nodes and 2 outputs. Given position state and direction, it outputs wheel based control values."><noscript><img alt="A single-layer feedforward artificial neural network with 4 inputs, 6 hidden nodes and 2 outputs. Given position state and direction, it outputs wheel based control values." src="//upload.wikimedia.org/wikipedia/commons/thumb/3/32/Single-layer_feedforward_artificial_neural_network.png/214px-Single-layer_feedforward_artificial_neural_network.png" decoding="async" width="214" height="120" class="mw-file-element" data-file-width="1280" data-file-height="720"></noscript><span class="lazy-image-placeholder" style="width: 214px;height: 120px;" data-src="//upload.wikimedia.org/wikipedia/commons/thumb/3/32/Single-layer_feedforward_artificial_neural_network.png/214px-Single-layer_feedforward_artificial_neural_network.png" data-alt="A single-layer feedforward artificial neural network with 4 inputs, 6 hidden nodes and 2 outputs. Given position state and direction, it outputs wheel based control values." data-width="214" data-height="120" data-srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/32/Single-layer_feedforward_artificial_neural_network.png/320px-Single-layer_feedforward_artificial_neural_network.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/32/Single-layer_feedforward_artificial_neural_network.png/427px-Single-layer_feedforward_artificial_neural_network.png 2x" data-class="mw-file-element"> </a></div> <div class="gallerytext">A single-layer feedforward artificial neural network with 4 inputs, 6 hidden nodes and 2 outputs. Given position state and direction, it outputs wheel based control values.</div> </li> <li class="gallerybox" style="width: 255px"> <div class="thumb" style="width: 250px; height: 150px;"><a href="/wiki/File:Two-layer_feedforward_artificial_neural_network.png" class="mw-file-description" title="A two-layer feedforward artificial neural network with 8 inputs, 2x8 hidden nodes and 2 outputs. Given position state, direction and other environment values, it outputs thruster based control values."><noscript><img alt="A two-layer feedforward artificial neural network with 8 inputs, 2x8 hidden nodes and 2 outputs. Given position state, direction and other environment values, it outputs thruster based control values." src="//upload.wikimedia.org/wikipedia/commons/thumb/5/58/Two-layer_feedforward_artificial_neural_network.png/214px-Two-layer_feedforward_artificial_neural_network.png" decoding="async" width="214" height="120" class="mw-file-element" data-file-width="1280" data-file-height="720"></noscript><span class="lazy-image-placeholder" style="width: 214px;height: 120px;" data-src="//upload.wikimedia.org/wikipedia/commons/thumb/5/58/Two-layer_feedforward_artificial_neural_network.png/214px-Two-layer_feedforward_artificial_neural_network.png" data-alt="A two-layer feedforward artificial neural network with 8 inputs, 2x8 hidden nodes and 2 outputs. Given position state, direction and other environment values, it outputs thruster based control values." data-width="214" data-height="120" data-srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/58/Two-layer_feedforward_artificial_neural_network.png/320px-Two-layer_feedforward_artificial_neural_network.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/58/Two-layer_feedforward_artificial_neural_network.png/427px-Two-layer_feedforward_artificial_neural_network.png 2x" data-class="mw-file-element"> </a></div> <div class="gallerytext">A two-layer feedforward artificial neural network with 8 inputs, 2x8 hidden nodes and 2 outputs. Given position state, direction and other environment values, it outputs thruster based control values.</div> </li> <li class="gallerybox" style="width: 255px"> <div class="thumb" style="width: 250px; height: 150px;"><a href="/wiki/File:Cmac.jpg" class="mw-file-description" title="Parallel pipeline structure of CMAC neural network. This learning algorithm can converge in one step."><noscript><img alt="Parallel pipeline structure of CMAC neural network. This learning algorithm can converge in one step." src="//upload.wikimedia.org/wikipedia/commons/thumb/6/6d/Cmac.jpg/177px-Cmac.jpg" decoding="async" width="177" height="120" class="mw-file-element" data-file-width="899" data-file-height="609"></noscript><span class="lazy-image-placeholder" style="width: 177px;height: 120px;" data-src="//upload.wikimedia.org/wikipedia/commons/thumb/6/6d/Cmac.jpg/177px-Cmac.jpg" data-alt="Parallel pipeline structure of CMAC neural network. This learning algorithm can converge in one step." data-width="177" data-height="120" data-srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/6d/Cmac.jpg/266px-Cmac.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/6d/Cmac.jpg/355px-Cmac.jpg 2x" data-class="mw-file-element"> </a></div> <div class="gallerytext">Parallel pipeline structure of CMAC neural network. This learning algorithm can converge in one step. </div> </li> </ul> </section><div class="mw-heading mw-heading2 section-heading" onclick="mfTempOpenSection(10)"><h2 id="Recent_advancements_and_future_directions">Recent advancements and future directions</h2> <a role="button" href="/w/index.php?title=Neural_network_(machine_learning)&action=edit&section=42" title="Edit section: Recent advancements and future directions" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> edit </a> </div><section class="mf-section-10 collapsible-block" id="mf-section-10"> Artificial neural networks (ANNs) have undergone significant advancements, particularly in their ability to model complex systems, handle large data sets, and adapt to various types of applications. Their evolution over the past few decades has been marked by a broad range of applications in fields such as image processing, speech recognition, natural language processing, finance, and medicine.[<a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed">citation needed</a>] <div class="mw-heading mw-heading3"><h3 id="Image_processing">Image processing</h3> <a role="button" href="/w/index.php?title=Neural_network_(machine_learning)&action=edit&section=43" title="Edit section: Image processing" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> edit </a> </div> In the realm of image processing, ANNs are employed in tasks such as image classification, object recognition, and image segmentation. For instance, deep convolutional neural networks (CNNs) have been important in handwritten digit recognition, achieving state-of-the-art performance.<a href="#cite_note-:07-243">[243]</a> This demonstrates the ability of ANNs to effectively process and interpret complex visual information, leading to advancements in fields ranging from automated surveillance to medical imaging.<a href="#cite_note-:07-243">[243]</a> <div class="mw-heading mw-heading3"><h3 id="Speech_recognition">Speech recognition</h3> <a role="button" href="/w/index.php?title=Neural_network_(machine_learning)&action=edit&section=44" title="Edit section: Speech recognition" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> edit </a> </div> By modeling speech signals, ANNs are used for tasks like speaker identification and speech-to-text conversion. Deep neural network architectures have introduced significant improvements in large vocabulary continuous speech recognition, outperforming traditional techniques.<a href="#cite_note-:07-243">[243]</a><a href="#cite_note-:15-244">[244]</a> These advancements have enabled the development of more accurate and efficient voice-activated systems, enhancing user interfaces in technology products.[<a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed">citation needed</a>] <div class="mw-heading mw-heading3"><h3 id="Natural_language_processing">Natural language processing</h3> <a role="button" href="/w/index.php?title=Neural_network_(machine_learning)&action=edit&section=45" title="Edit section: Natural language processing" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> edit </a> </div> In natural language processing, ANNs are used for tasks such as text classification, sentiment analysis, and machine translation. They have enabled the development of models that can accurately translate between languages, understand the context and sentiment in textual data, and categorize text based on content.<a href="#cite_note-:07-243">[243]</a><a href="#cite_note-:15-244">[244]</a> This has implications for automated customer service, content moderation, and language understanding technologies.[<a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed">citation needed</a>] <div class="mw-heading mw-heading3"><h3 id="Control_systems">Control systems</h3> <a role="button" href="/w/index.php?title=Neural_network_(machine_learning)&action=edit&section=46" title="Edit section: Control systems" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> edit </a> </div> In the domain of control systems, ANNs are used to model dynamic systems for tasks such as system identification, control design, and optimization. For instance, deep feedforward neural networks are important in system identification and control applications.[<a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed">citation needed</a>] <div class="mw-heading mw-heading3"><h3 id="Finance">Finance</h3> <a role="button" href="/w/index.php?title=Neural_network_(machine_learning)&action=edit&section=47" title="Edit section: Finance" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> edit </a> </div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Further information: <a href="/wiki/Applications_of_artificial_intelligence#Trading_and_investment" title="Applications of artificial intelligence">Applications of artificial intelligence § Trading and investment</a></div> ANNs are used for <a href="/wiki/Quantitative_investing" class="mw-redirect" title="Quantitative investing">stock market prediction</a> and <a href="/wiki/Credit_scoring" class="mw-redirect" title="Credit scoring">credit scoring</a>: <ul><li>In investing, ANNs can process vast amounts of financial data, recognize complex patterns, and forecast stock market trends, aiding investors and risk managers in making informed decisions.<a href="#cite_note-:07-243">[243]</a></li> <li>In credit scoring, ANNs offer data-driven, personalized assessments of creditworthiness, improving the accuracy of default predictions and automating the lending process.<a href="#cite_note-:15-244">[244]</a></li></ul> ANNs require high-quality data and careful tuning, and their "black-box" nature can pose challenges in interpretation. Nevertheless, ongoing advancements suggest that ANNs continue to play a role in finance, offering valuable insights and enhancing <a href="/wiki/Financial_risk_management" title="Financial risk management">risk management strategies</a>.[<a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed">citation needed</a>] <div class="mw-heading mw-heading3"><h3 id="Medicine">Medicine</h3> <a role="button" href="/w/index.php?title=Neural_network_(machine_learning)&action=edit&section=48" title="Edit section: Medicine" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> edit </a> </div> ANNs are able to process and analyze vast medical datasets. They enhance diagnostic accuracy, especially by interpreting complex <a href="/wiki/Medical_imaging" title="Medical imaging">medical imaging</a> for early disease detection, and by predicting patient outcomes for personalized treatment planning.<a href="#cite_note-:15-244">[244]</a> In drug discovery, ANNs speed up the identification of potential drug candidates and predict their efficacy and safety, significantly reducing development time and costs.<a href="#cite_note-:07-243">[243]</a> Additionally, their application in personalized medicine and healthcare data analysis allows tailored therapies and efficient patient care management.<a href="#cite_note-:15-244">[244]</a> Ongoing research is aimed at addressing remaining challenges such as data privacy and model interpretability, as well as expanding the scope of ANN applications in medicine.[<a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed">citation needed</a>] <div class="mw-heading mw-heading3"><h3 id="Content_creation">Content creation</h3> <a role="button" href="/w/index.php?title=Neural_network_(machine_learning)&action=edit&section=49" title="Edit section: Content creation" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> edit </a> </div> ANNs such as generative adversarial networks (<a href="/wiki/Generative_adversarial_network" title="Generative adversarial network">GAN</a>) and <a href="/wiki/Transformer_(machine_learning_model)" class="mw-redirect" title="Transformer (machine learning model)">transformers</a> are used for content creation across numerous industries.<a href="#cite_note-:09-245">[245]</a> This is because deep learning models are able to learn the style of an artist or musician from huge datasets and generate completely new artworks and music compositions. For instance, <a href="/wiki/DALL-E" title="DALL-E">DALL-E</a> is a deep neural network trained on 650 million pairs of images and texts across the internet that can create artworks based on text entered by the user.<a href="#cite_note-246">[246]</a> In the field of music, transformers are used to create original music for commercials and documentaries through companies such as <a href="/wiki/AIVA" title="AIVA">AIVA</a> and <a href="/wiki/Jukedeck" title="Jukedeck">Jukedeck</a>.<a href="#cite_note-247">[247]</a> In the marketing industry generative models are used to create personalized advertisements for consumers.<a href="#cite_note-:09-245">[245]</a> Additionally, major film companies are partnering with technology companies to analyze the financial success of a film, such as the partnership between Warner Bros and technology company Cinelytic established in 2020.<a href="#cite_note-248">[248]</a> Furthermore, neural networks have found uses in video game creation, where Non Player Characters (NPCs) can make decisions based on all the characters currently in the game.<a href="#cite_note-249">[249]</a> </section><div class="mw-heading mw-heading2 section-heading" onclick="mfTempOpenSection(11)"><h2 id="See_also">See also</h2> <a role="button" href="/w/index.php?title=Neural_network_(machine_learning)&action=edit&section=50" title="Edit section: See also" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> edit </a> </div><section class="mf-section-11 collapsible-block" id="mf-section-11"> <style data-mw-deduplicate="TemplateStyles:r1184024115">.mw-parser-output .div-col{margin-top:0.3em;column-width:30em}.mw-parser-output .div-col-small{font-size:90%}.mw-parser-output .div-col-rules{column-rule:1px solid #aaa}.mw-parser-output .div-col dl,.mw-parser-output .div-col ol,.mw-parser-output .div-col ul{margin-top:0}.mw-parser-output .div-col li,.mw-parser-output .div-col dd{page-break-inside:avoid;break-inside:avoid-column}</style><div class="div-col" style="column-width: 18em;"> <ul><li><a href="/wiki/ADALINE" title="ADALINE">ADALINE</a></li> <li><a href="/wiki/Autoencoder" title="Autoencoder">Autoencoder</a></li> <li><a href="/wiki/Bio-inspired_computing" title="Bio-inspired computing">Bio-inspired computing</a></li> <li><a href="/wiki/Blue_Brain_Project" title="Blue Brain Project">Blue Brain Project</a></li> <li><a href="/wiki/Catastrophic_interference" title="Catastrophic interference">Catastrophic interference</a></li> <li><a href="/wiki/Cognitive_architecture" title="Cognitive architecture">Cognitive architecture</a></li> <li><a href="/wiki/Connectionist_expert_system" title="Connectionist expert system">Connectionist expert system</a></li> <li><a href="/wiki/Connectomics" title="Connectomics">Connectomics</a></li> <li><a href="/wiki/Deep_image_prior" title="Deep image prior">Deep image prior</a></li> <li><a href="/wiki/Digital_morphogenesis" title="Digital morphogenesis">Digital morphogenesis</a></li> <li><a href="/wiki/Efficiently_updatable_neural_network" title="Efficiently updatable neural network">Efficiently updatable neural network</a></li> <li><a href="/wiki/Evolutionary_algorithm" title="Evolutionary algorithm">Evolutionary algorithm</a></li> <li><a href="/wiki/Genetic_algorithm" title="Genetic algorithm">Genetic algorithm</a></li> <li><a href="/wiki/Hyperdimensional_computing" title="Hyperdimensional computing">Hyperdimensional computing</a></li> <li><a href="/wiki/In_situ_adaptive_tabulation" title="In situ adaptive tabulation">In situ adaptive tabulation</a></li> <li><a href="/wiki/Large_width_limits_of_neural_networks" title="Large width limits of neural networks">Large width limits of neural networks</a></li> <li><a href="/wiki/List_of_machine_learning_concepts" class="mw-redirect" title="List of machine learning concepts">List of machine learning concepts</a></li> <li><a href="/wiki/Memristor" title="Memristor">Memristor</a></li> <li><a href="/wiki/Neural_gas" title="Neural gas">Neural gas</a></li> <li><a href="/wiki/Neural_network_software" title="Neural network software">Neural network software</a></li> <li><a href="/wiki/Optical_neural_network" title="Optical neural network">Optical neural network</a></li> <li><a href="/wiki/Parallel_distributed_processing" class="mw-redirect" title="Parallel distributed processing">Parallel distributed processing</a></li> <li><a href="/wiki/Philosophy_of_artificial_intelligence" title="Philosophy of artificial intelligence">Philosophy of artificial intelligence</a></li> <li><a href="/wiki/Predictive_analytics" title="Predictive analytics">Predictive analytics</a></li> <li><a href="/wiki/Quantum_neural_network" title="Quantum neural network">Quantum neural network</a></li> <li><a href="/wiki/Support_vector_machine" title="Support vector machine">Support vector machine</a></li> <li><a href="/wiki/Spiking_neural_network" title="Spiking neural network">Spiking neural network</a></li> <li><a href="/wiki/Stochastic_parrot" title="Stochastic parrot">Stochastic parrot</a></li> <li><a href="/wiki/Tensor_product_network" title="Tensor product network">Tensor product network</a></li></ul> </div> </section><div class="mw-heading mw-heading2 section-heading" onclick="mfTempOpenSection(12)"><h2 id="References">References</h2> <a role="button" href="/w/index.php?title=Neural_network_(machine_learning)&action=edit&section=51" title="Edit section: References" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> edit </a> </div><section class="mf-section-12 collapsible-block" id="mf-section-12"> <style data-mw-deduplicate="TemplateStyles:r1239543626">.mw-parser-output .reflist{margin-bottom:0.5em;list-style-type:decimal}@media screen{.mw-parser-output .reflist{font-size:90%}}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}</style><div class="reflist reflist-columns references-column-width" style="column-width: 30em;"> <ol class="references"> <li id="cite_note-1"><a href="#cite_ref-1">^</a> <style data-mw-deduplicate="TemplateStyles:r1238218222">.mw-parser-output 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a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-limited a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-registration a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-subscription a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .cs1-ws-icon a{background-size:contain;padding:0 1em 0 0}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:#085;margin-left:0.3em}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}@media screen{.mw-parser-output .cs1-format{font-size:95%}html.skin-theme-clientpref-night .mw-parser-output .cs1-maint{color:#18911f}}@media screen and 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(15 January 2001). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=NWOcMVA64aAC">"Gradient flow in recurrent nets: the difficulty of learning long-term dependencies"</a>. In Kolen JF, Kremer SC (eds.). A Field Guide to Dynamical Recurrent Networks. John Wiley & Sons. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-7803-5369-5" title="Special:BookSources/978-0-7803-5369-5"><bdi>978-0-7803-5369-5</bdi></a>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20240519081124/https://books.google.com/books?id=NWOcMVA64aAC">Archived</a> from the original on 19 May 2024. Retrieved 26 June 2017.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Gradient+flow+in+recurrent+nets%3A+the+difficulty+of+learning+long-term+dependencies&rft.btitle=A+Field+Guide+to+Dynamical+Recurrent+Networks&rft.pub=John+Wiley+%26+Sons&rft.date=2001-01-15&rft.isbn=978-0-7803-5369-5&rft.aulast=Hochreiter&rft.aufirst=S.&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DNWOcMVA64aAC&rfr_id=info%3Asid%2Fen.wikipedia.org%3ANeural+network+%28machine+learning%29" class="Z3988"> </li> <li id="cite_note-75"><a href="#cite_ref-75">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFSepp_HochreiterJürgen_Schmidhuber1995" class="citation cs2"><a href="/wiki/Sepp_Hochreiter" title="Sepp Hochreiter">Sepp Hochreiter</a>, <a href="/wiki/J%C3%BCrgen_Schmidhuber" title="Jürgen Schmidhuber">Jürgen Schmidhuber</a> (21 August 1995), <a rel="nofollow" class="external text" href="ftp://ftp.idsia.ch/pub/juergen/fki-207-95.ps.gz">Long Short Term Memory</a>, <a href="/wiki/WDQ_(identifier)" class="mw-redirect" title="WDQ (identifier)">Wikidata</a> <a href="https://www.wikidata.org/wiki/Q98967430" class="extiw" title="d:Q98967430">Q98967430</a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Long+Short+Term+Memory&rft.date=1995-08-21&rft.au=Sepp+Hochreiter&rft.au=J%C3%BCrgen+Schmidhuber&rft_id=ftp%3A%2F%2Fftp.idsia.ch%2Fpub%2Fjuergen%2Ffki-207-95.ps.gz&rfr_id=info%3Asid%2Fen.wikipedia.org%3ANeural+network+%28machine+learning%29" class="Z3988"> </li> <li id="cite_note-lstm2-76"><a href="#cite_ref-lstm2_76-0">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFHochreiterSchmidhuber1997" class="citation journal cs1"><a href="/wiki/Sepp_Hochreiter" title="Sepp Hochreiter">Hochreiter S</a>, Schmidhuber J (1 November 1997). 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Neural Computation. 9 (8): 1735–1780. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1162%2Fneco.1997.9.8.1735">10.1162/neco.1997.9.8.1735</a>. <a href="/wiki/PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/9377276">9377276</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:1915014">1915014</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Neural+Computation&rft.atitle=Long+Short-Term+Memory&rft.volume=9&rft.issue=8&rft.pages=1735-1780&rft.date=1997-11-01&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A1915014%23id-name%3DS2CID&rft_id=info%3Apmid%2F9377276&rft_id=info%3Adoi%2F10.1162%2Fneco.1997.9.8.1735&rft.aulast=Hochreiter&rft.aufirst=Sepp&rft.au=Schmidhuber%2C+J%C3%BCrgen&rfr_id=info%3Asid%2Fen.wikipedia.org%3ANeural+network+%28machine+learning%29" class="Z3988"> </li> <li id="cite_note-lstm1999-77"><a href="#cite_ref-lstm1999_77-0">^</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFGersSchmidhuberCummins1999" class="citation book cs1">Gers F, Schmidhuber J, Cummins F (1999). 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Van Nostrand Reinhold. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-442-00461-3" title="Special:BookSources/978-0-442-00461-3"><bdi>978-0-442-00461-3</bdi></a>. <a href="/wiki/OCLC_(identifier)" class="mw-redirect" title="OCLC (identifier)">OCLC</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/oclc/27429729">27429729</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Advanced+methods+in+neural+computing&rft.pub=Van+Nostrand+Reinhold&rft.date=1993&rft_id=info%3Aoclcnum%2F27429729&rft.isbn=978-0-442-00461-3&rft.aulast=Wasserman&rft.aufirst=Philip+D.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ANeural+network+%28machine+learning%29" class="Z3988"></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFWilson2018" class="citation book cs1">Wilson H (2018). Artificial intelligence. Grey House Publishing. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1-68217-867-6" title="Special:BookSources/978-1-68217-867-6"><bdi>978-1-68217-867-6</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Artificial+intelligence&rft.pub=Grey+House+Publishing&rft.date=2018&rft.isbn=978-1-68217-867-6&rft.aulast=Wilson&rft.aufirst=Halsey&rfr_id=info%3Asid%2Fen.wikipedia.org%3ANeural+network+%28machine+learning%29" class="Z3988"></li></ul> </div> </section><div class="mw-heading mw-heading2 section-heading" onclick="mfTempOpenSection(14)"><h2 id="External_links">External links</h2> <a role="button" href="/w/index.php?title=Neural_network_(machine_learning)&action=edit&section=53" title="Edit section: External links" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> edit </a> </div><section class="mf-section-14 collapsible-block" id="mf-section-14"> <style data-mw-deduplicate="TemplateStyles:r1235611614">.mw-parser-output .spoken-wikipedia{border:1px solid #a2a9b1;background-color:var(--background-color-interactive-subtle,#f8f9fa);margin:0.5em 0;padding:0.2em;line-height:1.5em;font-size:90%}.mw-parser-output .spoken-wikipedia-header{text-align:center}.mw-parser-output .spoken-wikipedia-listen-to{font-weight:bold}.mw-parser-output .spoken-wikipedia-files{text-align:center;margin-top:10px;margin-bottom:0.4em}.mw-parser-output .spoken-wikipedia-icon{float:left;margin-left:5px;margin-top:10px}.mw-parser-output .spoken-wikipedia-disclaimer{margin-left:60px;margin-top:10px;font-size:95%;line-height:1.4em}.mw-parser-output .spoken-wikipedia-footer{margin-top:10px;text-align:center}@media(min-width:720px){.mw-parser-output .spoken-wikipedia{width:20em;float:right;clear:right;margin-left:1em}}</style><div class="spoken-wikipedia noprint haudio"><div class="spoken-wikipedia-header">Listen to this article (31 minutes)</div><div class="spoken-wikipedia-files"><figure class="mw-halign-center" typeof="mw:File"><audio id="mwe_player_0" controls="" preload="none" data-mw-tmh="" class="mw-file-element" width="200" style="width:200px;" data-durationhint="1883" data-mwtitle="En-Neural_network.ogg" data-mwprovider="wikimediacommons"><source src="//upload.wikimedia.org/wikipedia/commons/a/a3/En-Neural_network.ogg" type='audio/ogg; codecs="vorbis"' data-width="0" data-height="0"></source><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/a/a3/En-Neural_network.ogg/En-Neural_network.ogg.mp3" type="audio/mpeg" data-transcodekey="mp3" data-width="0" data-height="0"></source></audio><figcaption></figcaption></figure> </div><div class="spoken-wikipedia-icon"><noscript><img alt="Spoken Wikipedia icon" src="//upload.wikimedia.org/wikipedia/commons/thumb/4/47/Sound-icon.svg/45px-Sound-icon.svg.png" decoding="async" width="45" height="34" class="mw-file-element" data-file-width="128" data-file-height="96"></noscript><span class="lazy-image-placeholder" style="width: 45px;height: 34px;" data-src="//upload.wikimedia.org/wikipedia/commons/thumb/4/47/Sound-icon.svg/45px-Sound-icon.svg.png" data-alt="Spoken Wikipedia icon" data-width="45" data-height="34" data-srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/47/Sound-icon.svg/68px-Sound-icon.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/47/Sound-icon.svg/90px-Sound-icon.svg.png 2x" data-class="mw-file-element"> </div><div class="spoken-wikipedia-disclaimer"><a href="/wiki/File:En-Neural_network.ogg" title="File:En-Neural network.ogg">This audio file</a> was created from a revision of this article dated 27 November 2011 (2011-11-27), and does not reflect subsequent edits.</div><div class="spoken-wikipedia-footer">(<a href="/wiki/Wikipedia:Media_help" class="mw-redirect" title="Wikipedia:Media help">Audio help</a> · <a href="/wiki/Wikipedia:Spoken_articles" title="Wikipedia:Spoken articles">More spoken articles</a>)</div></div> <ul><li><a rel="nofollow" class="external text" href="http://www.dkriesel.com/en/science/neural_networks">A Brief Introduction to Neural Networks (D. Kriesel)</a> – Illustrated, bilingual manuscript about artificial neural networks; Topics so far: Perceptrons, Backpropagation, Radial Basis Functions, Recurrent Neural Networks, Self Organizing Maps, Hopfield Networks.</li> <li><a rel="nofollow" class="external text" href="http://www.msm.cam.ac.uk/phase-trans/abstracts/neural.review.html">Review of Neural Networks in Materials Science</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20150607101310/http://www.msm.cam.ac.uk/phase-trans/abstracts/neural.review.html">Archived</a> 7 June 2015 at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a></li> <li><a rel="nofollow" class="external text" href="https://web.archive.org/web/20090318133122/http://www.gc.ssr.upm.es/inves/neural/ann1/anntutorial.html">Artificial Neural Networks Tutorial in three languages (Univ. Politécnica de Madrid)</a></li> <li><a rel="nofollow" class="external text" href="https://web.archive.org/web/20091216110504/http://www.doc.ic.ac.uk/~nd/surprise_96/journal/vol4/cs11/report.html">Another introduction to ANN</a></li> <li><a rel="nofollow" class="external text" href="https://www.youtube.com/watch?v=AyzOUbkUf3M">Next Generation of Neural Networks</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20110124234328/http://www.youtube.com/watch?v=AyzOUbkUf3M">Archived</a> 24 January 2011 at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a> – Google Tech Talks</li> <li><a rel="nofollow" class="external text" href="http://www.msm.cam.ac.uk/phase-trans/2009/performance.html">Performance of Neural Networks</a></li> <li><a rel="nofollow" class="external text" href="http://www.msm.cam.ac.uk/phase-trans/2009/review_Bhadeshia_SADM.pdf">Neural Networks and Information</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20090709153828/http://www.msm.cam.ac.uk/phase-trans/2009/review_Bhadeshia_SADM.pdf">Archived</a> 9 July 2009 at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFSanderson2017" class="citation web cs1">Sanderson G (5 October 2017). <a rel="nofollow" class="external text" href="https://www.youtube.com/watch?v=aircAruvnKk&list=PLZHQObOWTQDNU6R1_67000Dx_ZCJB-3pi">"But what is a Neural Network?"</a>. <a href="/wiki/3Blue1Brown" title="3Blue1Brown">3Blue1Brown</a>. <a rel="nofollow" class="external text" href="https://ghostarchive.org/varchive/youtube/20211107/aircAruvnKk">Archived</a> from the original on 7 November 2021 – via <a href="/wiki/YouTube" title="YouTube">YouTube</a>.</cite><span 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href="https://ar.wikipedia.org/wiki/%D8%B4%D8%A8%D9%83%D8%A9_%D8%B9%D8%B5%D8%A8%D9%88%D9%86%D9%8A%D8%A9_%D8%A7%D8%B5%D8%B7%D9%86%D8%A7%D8%B9%D9%8A%D8%A9" title="شبكة عصبونية اصطناعية – Arabic" lang="ar" hreflang="ar" data-title="شبكة عصبونية اصطناعية" data-language-autonym="العربية" data-language-local-name="Arabic" class="interlanguage-link-target">العربية</a></li><li class="interlanguage-link interwiki-hyw mw-list-item"><a href="https://hyw.wikipedia.org/wiki/%D4%B1%D6%80%D5%B0%D5%A5%D5%BD%D5%BF%D5%A1%D5%AF%D5%A1%D5%B6_%D5%8B%D5%B2%D5%A1%D5%A2%D5%BB%D5%AB%D5%BB%D5%A1%D5%B5%D5%AB%D5%B6_%D5%91%D5%A1%D5%B6%D6%81" title="Արհեստական Ջղաբջիջային Ցանց – Western Armenian" lang="hyw" hreflang="hyw" data-title="Արհեստական Ջղաբջիջային Ցանց" data-language-autonym="Արեւմտահայերէն" data-language-local-name="Western Armenian" class="interlanguage-link-target">Արեւմտահայերէն</a></li><li class="interlanguage-link interwiki-az mw-list-item"><a href="https://az.wikipedia.org/wiki/S%C3%BCni_neyron_%C5%9F%C9%99b%C9%99k%C9%99l%C9%99r" title="Süni neyron şəbəkələr – Azerbaijani" lang="az" hreflang="az" data-title="Süni neyron şəbəkələr" data-language-autonym="Azərbaycanca" data-language-local-name="Azerbaijani" class="interlanguage-link-target">Azərbaycanca</a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%95%E0%A7%83%E0%A6%A4%E0%A7%8D%E0%A6%B0%E0%A6%BF%E0%A6%AE_%E0%A6%A8%E0%A6%BF%E0%A6%89%E0%A6%B0%E0%A6%BE%E0%A6%B2_%E0%A6%A8%E0%A7%87%E0%A6%9F%E0%A6%93%E0%A6%AF%E0%A6%BC%E0%A6%BE%E0%A6%B0%E0%A7%8D%E0%A6%95" title="কৃত্রিম নিউরাল নেটওয়ার্ক – Bangla" lang="bn" hreflang="bn" data-title="কৃত্রিম নিউরাল নেটওয়ার্ক" data-language-autonym="বাংলা" data-language-local-name="Bangla" class="interlanguage-link-target">বাংলা</a></li><li class="interlanguage-link interwiki-zh-min-nan mw-list-item"><a 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href="https://el.wikipedia.org/wiki/%CE%9D%CE%B5%CF%85%CF%81%CF%89%CE%BD%CE%B9%CE%BA%CF%8C_%CE%B4%CE%AF%CE%BA%CF%84%CF%85%CE%BF" title="Νευρωνικό δίκτυο – Greek" lang="el" hreflang="el" data-title="Νευρωνικό δίκτυο" data-language-autonym="Ελληνικά" data-language-local-name="Greek" class="interlanguage-link-target">Ελληνικά</a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Red_neuronal_artificial" title="Red neuronal artificial – Spanish" lang="es" hreflang="es" data-title="Red neuronal artificial" data-language-autonym="Español" data-language-local-name="Spanish" class="interlanguage-link-target">Español</a></li><li class="interlanguage-link interwiki-eo mw-list-item"><a href="https://eo.wikipedia.org/wiki/Artefarita_ne%C5%ADra_reto" title="Artefarita neŭra reto – Esperanto" lang="eo" hreflang="eo" data-title="Artefarita neŭra reto" data-language-autonym="Esperanto" data-language-local-name="Esperanto" class="interlanguage-link-target">Esperanto</a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Neurona-sare_artifizial" title="Neurona-sare artifizial – Basque" lang="eu" hreflang="eu" data-title="Neurona-sare artifizial" data-language-autonym="Euskara" data-language-local-name="Basque" class="interlanguage-link-target">Euskara</a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D8%B4%D8%A8%DA%A9%D9%87_%D8%B9%D8%B5%D8%A8%DB%8C_%D9%85%D8%B5%D9%86%D9%88%D8%B9%DB%8C" title="شبکه عصبی مصنوعی – Persian" lang="fa" hreflang="fa" data-title="شبکه عصبی مصنوعی" data-language-autonym="فارسی" data-language-local-name="Persian" class="interlanguage-link-target">فارسی</a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/R%C3%A9seau_de_neurones_artificiels" title="Réseau de neurones artificiels – French" lang="fr" hreflang="fr" data-title="Réseau de neurones artificiels" data-language-autonym="Français" data-language-local-name="French" class="interlanguage-link-target">Français</a></li><li class="interlanguage-link interwiki-ga mw-list-item"><a href="https://ga.wikipedia.org/wiki/L%C3%ADonra_n%C3%A9arach_saorga" title="Líonra néarach saorga – Irish" lang="ga" hreflang="ga" data-title="Líonra néarach saorga" data-language-autonym="Gaeilge" data-language-local-name="Irish" class="interlanguage-link-target">Gaeilge</a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/Rede_neural_artificial" title="Rede neural artificial – Galician" lang="gl" hreflang="gl" data-title="Rede neural artificial" data-language-autonym="Galego" data-language-local-name="Galician" class="interlanguage-link-target">Galego</a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EC%9D%B8%EA%B3%B5_%EC%8B%A0%EA%B2%BD%EB%A7%9D" title="인공 신경망 – Korean" lang="ko" hreflang="ko" data-title="인공 신경망" data-language-autonym="한국어" data-language-local-name="Korean" class="interlanguage-link-target">한국어</a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%D4%B1%D6%80%D5%B0%D5%A5%D5%BD%D5%BF%D5%A1%D5%AF%D5%A1%D5%B6_%D5%B6%D5%A5%D5%B5%D6%80%D5%B8%D5%B6%D5%A1%D5%B5%D5%AB%D5%B6_%D6%81%D5%A1%D5%B6%D6%81" title="Արհեստական նեյրոնային ցանց – Armenian" lang="hy" hreflang="hy" data-title="Արհեստական նեյրոնային ցանց" data-language-autonym="Հայերեն" data-language-local-name="Armenian" class="interlanguage-link-target">Հայերեն</a></li><li class="interlanguage-link interwiki-hi mw-list-item"><a href="https://hi.wikipedia.org/wiki/%E0%A4%95%E0%A5%83%E0%A4%A4%E0%A5%8D%E0%A4%B0%E0%A4%BF%E0%A4%AE_%E0%A4%A4%E0%A4%82%E0%A4%A4%E0%A5%8D%E0%A4%B0%E0%A4%BF%E0%A4%95%E0%A4%BE_%E0%A4%A8%E0%A5%87%E0%A4%9F%E0%A4%B5%E0%A4%B0%E0%A5%8D%E0%A4%95" title="कृत्रिम तंत्रिका नेटवर्क – Hindi" lang="hi" hreflang="hi" data-title="कृत्रिम तंत्रिका नेटवर्क" data-language-autonym="हिन्दी" data-language-local-name="Hindi" class="interlanguage-link-target">हिन्दी</a></li><li class="interlanguage-link interwiki-hr mw-list-item"><a href="https://hr.wikipedia.org/wiki/Umjetna_neuronska_mre%C5%BEa" title="Umjetna neuronska mreža – Croatian" lang="hr" hreflang="hr" data-title="Umjetna neuronska mreža" data-language-autonym="Hrvatski" data-language-local-name="Croatian" class="interlanguage-link-target">Hrvatski</a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Jaringan_saraf_tiruan" title="Jaringan saraf tiruan – Indonesian" lang="id" hreflang="id" data-title="Jaringan saraf tiruan" data-language-autonym="Bahasa Indonesia" data-language-local-name="Indonesian" class="interlanguage-link-target">Bahasa Indonesia</a></li><li class="interlanguage-link interwiki-ia mw-list-item"><a href="https://ia.wikipedia.org/wiki/Rete_neural_artificial" title="Rete neural artificial – Interlingua" lang="ia" hreflang="ia" data-title="Rete neural artificial" data-language-autonym="Interlingua" data-language-local-name="Interlingua" class="interlanguage-link-target">Interlingua</a></li><li class="interlanguage-link interwiki-is mw-list-item"><a href="https://is.wikipedia.org/wiki/Gervitauganet" title="Gervitauganet – Icelandic" lang="is" hreflang="is" data-title="Gervitauganet" data-language-autonym="Íslenska" data-language-local-name="Icelandic" class="interlanguage-link-target">Íslenska</a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Rete_neurale_artificiale" title="Rete neurale artificiale – Italian" lang="it" hreflang="it" data-title="Rete neurale artificiale" data-language-autonym="Italiano" data-language-local-name="Italian" class="interlanguage-link-target">Italiano</a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%A8%D7%A9%D7%AA_%D7%A2%D7%A6%D7%91%D7%99%D7%AA_%D7%9E%D7%9C%D7%90%D7%9B%D7%95%D7%AA%D7%99%D7%AA" title="רשת עצבית מלאכותית – Hebrew" lang="he" hreflang="he" data-title="רשת עצבית מלאכותית" data-language-autonym="עברית" data-language-local-name="Hebrew" class="interlanguage-link-target">עברית</a></li><li class="interlanguage-link interwiki-ka mw-list-item"><a href="https://ka.wikipedia.org/wiki/%E1%83%AE%E1%83%94%E1%83%9A%E1%83%9D%E1%83%95%E1%83%9C%E1%83%A3%E1%83%A0%E1%83%98_%E1%83%9C%E1%83%94%E1%83%98%E1%83%A0%E1%83%9D%E1%83%9C%E1%83%A3%E1%83%9A%E1%83%98_%E1%83%A5%E1%83%A1%E1%83%94%E1%83%9A%E1%83%98" title="ხელოვნური ნეირონული ქსელი – Georgian" lang="ka" hreflang="ka" data-title="ხელოვნური ნეირონული ქსელი" data-language-autonym="ქართული" data-language-local-name="Georgian" class="interlanguage-link-target">ქართული</a></li><li class="interlanguage-link interwiki-la mw-list-item"><a href="https://la.wikipedia.org/wiki/Rete_neurale_artificiale" title="Rete neurale artificiale – Latin" lang="la" hreflang="la" data-title="Rete neurale artificiale" data-language-autonym="Latina" data-language-local-name="Latin" class="interlanguage-link-target">Latina</a></li><li class="interlanguage-link interwiki-lv mw-list-item"><a href="https://lv.wikipedia.org/wiki/M%C4%81ksl%C4%ABgais_neironu_t%C4%ABkls" title="Mākslīgais neironu tīkls – Latvian" lang="lv" hreflang="lv" data-title="Mākslīgais neironu tīkls" data-language-autonym="Latviešu" data-language-local-name="Latvian" class="interlanguage-link-target">Latviešu</a></li><li class="interlanguage-link interwiki-lt mw-list-item"><a href="https://lt.wikipedia.org/wiki/Dirbtinis_neuroninis_tinklas" title="Dirbtinis neuroninis tinklas – Lithuanian" lang="lt" hreflang="lt" data-title="Dirbtinis neuroninis tinklas" data-language-autonym="Lietuvių" data-language-local-name="Lithuanian" class="interlanguage-link-target">Lietuvių</a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Mesters%C3%A9ges_neur%C3%A1lis_h%C3%A1l%C3%B3zat" title="Mesterséges neurális hálózat – Hungarian" lang="hu" hreflang="hu" data-title="Mesterséges neurális hálózat" data-language-autonym="Magyar" data-language-local-name="Hungarian" class="interlanguage-link-target">Magyar</a></li><li class="interlanguage-link interwiki-mk mw-list-item"><a href="https://mk.wikipedia.org/wiki/%D0%92%D0%B5%D1%88%D1%82%D0%B0%D1%87%D0%BA%D0%B0_%D0%BD%D0%B5%D0%B2%D1%80%D0%BE%D0%BD%D1%81%D0%BA%D0%B0_%D0%BC%D1%80%D0%B5%D0%B6%D0%B0" title="Вештачка невронска мрежа – Macedonian" lang="mk" hreflang="mk" data-title="Вештачка невронска мрежа" data-language-autonym="Македонски" data-language-local-name="Macedonian" class="interlanguage-link-target">Македонски</a></li><li class="interlanguage-link interwiki-mg mw-list-item"><a href="https://mg.wikipedia.org/wiki/Tambajotra_ner%C3%B4nina" title="Tambajotra nerônina – Malagasy" lang="mg" hreflang="mg" data-title="Tambajotra nerônina" data-language-autonym="Malagasy" data-language-local-name="Malagasy" class="interlanguage-link-target">Malagasy</a></li><li class="interlanguage-link interwiki-ml mw-list-item"><a href="https://ml.wikipedia.org/wiki/%E0%B4%95%E0%B5%83%E0%B4%A4%E0%B5%8D%E0%B4%B0%E0%B4%BF%E0%B4%AE_%E0%B4%A8%E0%B4%BE%E0%B4%A1%E0%B5%80%E0%B4%B5%E0%B5%8D%E0%B4%AF%E0%B5%82%E0%B4%B9%E0%B4%82" title="കൃത്രിമ നാഡീവ്യൂഹം – Malayalam" lang="ml" hreflang="ml" data-title="കൃത്രിമ നാഡീവ്യൂഹം" data-language-autonym="മലയാളം" data-language-local-name="Malayalam" class="interlanguage-link-target">മലയാളം</a></li><li class="interlanguage-link interwiki-ms mw-list-item"><a href="https://ms.wikipedia.org/wiki/Rangkaian_neural_buatan" title="Rangkaian neural buatan – Malay" lang="ms" hreflang="ms" data-title="Rangkaian neural buatan" data-language-autonym="Bahasa Melayu" data-language-local-name="Malay" class="interlanguage-link-target">Bahasa Melayu</a></li><li class="interlanguage-link interwiki-nl badge-Q70894304 mw-list-item" title=""><a href="https://nl.wikipedia.org/wiki/Kunstmatig_neural_netwerk" title="Kunstmatig neural netwerk – Dutch" lang="nl" hreflang="nl" data-title="Kunstmatig neural netwerk" data-language-autonym="Nederlands" data-language-local-name="Dutch" class="interlanguage-link-target">Nederlands</a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E3%83%8B%E3%83%A5%E3%83%BC%E3%83%A9%E3%83%AB%E3%83%8D%E3%83%83%E3%83%88%E3%83%AF%E3%83%BC%E3%82%AF" title="ニューラルネットワーク – Japanese" lang="ja" hreflang="ja" data-title="ニューラルネットワーク" data-language-autonym="日本語" data-language-local-name="Japanese" class="interlanguage-link-target">日本語</a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Kunstig_nevralt_nettverk" title="Kunstig nevralt nettverk – Norwegian Bokmål" lang="nb" hreflang="nb" data-title="Kunstig nevralt nettverk" data-language-autonym="Norsk bokmål" data-language-local-name="Norwegian Bokmål" class="interlanguage-link-target">Norsk bokmål</a></li><li class="interlanguage-link interwiki-nn mw-list-item"><a href="https://nn.wikipedia.org/wiki/Kunstig_nevralt_nettverk" title="Kunstig nevralt nettverk – Norwegian Nynorsk" lang="nn" hreflang="nn" data-title="Kunstig nevralt nettverk" data-language-autonym="Norsk nynorsk" data-language-local-name="Norwegian Nynorsk" class="interlanguage-link-target">Norsk nynorsk</a></li><li class="interlanguage-link interwiki-or mw-list-item"><a href="https://or.wikipedia.org/wiki/%E0%AC%86%E0%AC%B0%E0%AD%8D%E0%AC%9F%E0%AC%BF%E0%AC%AB%E0%AC%BF%E0%AC%B8%E0%AC%BF%E0%AC%86%E0%AC%B2_%E0%AC%A8%E0%AD%8D%E0%AD%9F%E0%AD%81%E0%AC%B0%E0%AC%BE%E0%AC%B2_%E0%AC%A8%E0%AD%87%E0%AC%9F%E0%AD%B1%E0%AC%B0%E0%AD%8D%E0%AC%95" title="ଆର୍ଟିଫିସିଆଲ ନ୍ୟୁରାଲ ନେଟୱର୍କ – Odia" lang="or" hreflang="or" data-title="ଆର୍ଟିଫିସିଆଲ ନ୍ୟୁରାଲ ନେଟୱର୍କ" data-language-autonym="ଓଡ଼ିଆ" data-language-local-name="Odia" class="interlanguage-link-target">ଓଡ଼ିଆ</a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Sie%C4%87_neuronowa" title="Sieć neuronowa – Polish" lang="pl" hreflang="pl" data-title="Sieć neuronowa" data-language-autonym="Polski" data-language-local-name="Polish" class="interlanguage-link-target">Polski</a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Rede_neural_artificial" title="Rede neural artificial – Portuguese" lang="pt" hreflang="pt" data-title="Rede neural artificial" data-language-autonym="Português" data-language-local-name="Portuguese" class="interlanguage-link-target">Português</a></li><li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/Re%C8%9Bea_neural%C4%83" title="Rețea neurală – Romanian" lang="ro" hreflang="ro" data-title="Rețea neurală" data-language-autonym="Română" data-language-local-name="Romanian" class="interlanguage-link-target">Română</a></li><li class="interlanguage-link interwiki-qu mw-list-item"><a href="https://qu.wikipedia.org/wiki/Kapchisqa_ankucha_llika" title="Kapchisqa ankucha llika – Quechua" lang="qu" hreflang="qu" data-title="Kapchisqa ankucha llika" data-language-autonym="Runa Simi" data-language-local-name="Quechua" class="interlanguage-link-target">Runa Simi</a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%9D%D0%B5%D0%B9%D1%80%D0%BE%D0%BD%D0%BD%D0%B0%D1%8F_%D1%81%D0%B5%D1%82%D1%8C" title="Нейронная сеть – Russian" lang="ru" hreflang="ru" data-title="Нейронная сеть" data-language-autonym="Русский" data-language-local-name="Russian" class="interlanguage-link-target">Русский</a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Artificial_neural_network" title="Artificial neural network – Simple English" lang="en-simple" hreflang="en-simple" data-title="Artificial neural network" data-language-autonym="Simple English" data-language-local-name="Simple English" class="interlanguage-link-target">Simple English</a></li><li class="interlanguage-link interwiki-sk mw-list-item"><a href="https://sk.wikipedia.org/wiki/Umel%C3%A1_neur%C3%B3nov%C3%A1_sie%C5%A5" title="Umelá neurónová sieť – Slovak" lang="sk" hreflang="sk" data-title="Umelá neurónová sieť" data-language-autonym="Slovenčina" data-language-local-name="Slovak" class="interlanguage-link-target">Slovenčina</a></li><li class="interlanguage-link interwiki-szl mw-list-item"><a href="https://szl.wikipedia.org/wiki/Neuronowy_nec" title="Neuronowy nec – Silesian" lang="szl" hreflang="szl" data-title="Neuronowy nec" data-language-autonym="Ślůnski" data-language-local-name="Silesian" class="interlanguage-link-target">Ślůnski</a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/Ve%C5%A1ta%C4%8Dka_neuronska_mre%C5%BEa" title="Veštačka neuronska mreža – Serbian" lang="sr" hreflang="sr" data-title="Veštačka neuronska mreža" data-language-autonym="Српски / srpski" data-language-local-name="Serbian" class="interlanguage-link-target">Српски / srpski</a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Neuroverkot" title="Neuroverkot – Finnish" lang="fi" hreflang="fi" data-title="Neuroverkot" data-language-autonym="Suomi" data-language-local-name="Finnish" class="interlanguage-link-target">Suomi</a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Artificiellt_neuronn%C3%A4t" title="Artificiellt neuronnät – Swedish" lang="sv" hreflang="sv" data-title="Artificiellt neuronnät" data-language-autonym="Svenska" data-language-local-name="Swedish" class="interlanguage-link-target">Svenska</a></li><li class="interlanguage-link interwiki-ta mw-list-item"><a href="https://ta.wikipedia.org/wiki/%E0%AE%9A%E0%AF%86%E0%AE%AF%E0%AE%B1%E0%AF%8D%E0%AE%95%E0%AF%88_%E0%AE%A8%E0%AE%B0%E0%AE%AE%E0%AF%8D%E0%AE%AA%E0%AE%A3%E0%AF%81%E0%AE%AA%E0%AF%8D_%E0%AE%AA%E0%AE%BF%E0%AE%A3%E0%AF%88%E0%AE%AF%E0%AE%AE%E0%AF%8D" title="செயற்கை நரம்பணுப் பிணையம் – Tamil" lang="ta" hreflang="ta" data-title="செயற்கை நரம்பணுப் பிணையம்" data-language-autonym="தமிழ்" data-language-local-name="Tamil" class="interlanguage-link-target">தமிழ்</a></li><li class="interlanguage-link interwiki-th mw-list-item"><a href="https://th.wikipedia.org/wiki/%E0%B9%82%E0%B8%84%E0%B8%A3%E0%B8%87%E0%B8%82%E0%B9%88%E0%B8%B2%E0%B8%A2%E0%B8%9B%E0%B8%A3%E0%B8%B0%E0%B8%AA%E0%B8%B2%E0%B8%97%E0%B9%80%E0%B8%97%E0%B8%B5%E0%B8%A2%E0%B8%A1" title="โครงข่ายประสาทเทียม – Thai" lang="th" hreflang="th" data-title="โครงข่ายประสาทเทียม" data-language-autonym="ไทย" data-language-local-name="Thai" class="interlanguage-link-target">ไทย</a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/Yapay_sinir_a%C4%9Flar%C4%B1" title="Yapay sinir ağları – Turkish" lang="tr" hreflang="tr" data-title="Yapay sinir ağları" data-language-autonym="Türkçe" data-language-local-name="Turkish" class="interlanguage-link-target">Türkçe</a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%A8%D1%82%D1%83%D1%87%D0%BD%D0%B0_%D0%BD%D0%B5%D0%B9%D1%80%D0%BE%D0%BD%D0%BD%D0%B0_%D0%BC%D0%B5%D1%80%D0%B5%D0%B6%D0%B0" title="Штучна нейронна мережа – Ukrainian" lang="uk" hreflang="uk" data-title="Штучна нейронна мережа" data-language-autonym="Українська" data-language-local-name="Ukrainian" class="interlanguage-link-target">Українська</a></li><li class="interlanguage-link interwiki-ur mw-list-item"><a href="https://ur.wikipedia.org/wiki/%D8%A7%D8%B5%D8%B7%D9%86%D8%A7%D8%B9%DB%8C_%D8%B9%D8%B5%D8%A8%DB%8C_%D8%AC%D8%A7%D9%84%DA%A9%D8%A7%D8%B1" title="اصطناعی عصبی جالکار – Urdu" lang="ur" hreflang="ur" 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