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class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>McCulloch–Pitts (MCP) neuron</span> </div> </a> <ul id="toc-McCulloch–Pitts_(MCP)_neuron-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Biological_models" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Biological_models"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Biological models</span> </div> </a> <button aria-controls="toc-Biological_models-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle Biological models subsection</span> </button> <ul id="toc-Biological_models-sublist" class="vector-toc-list"> <li id="toc-Encoding" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Encoding"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.1</span> <span>Encoding</span> </div> </a> <ul id="toc-Encoding-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Physical_artificial_cells" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Physical_artificial_cells"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Physical artificial cells</span> </div> </a> <ul id="toc-Physical_artificial_cells-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-History" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#History"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>History</span> </div> </a> <ul id="toc-History-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Types_of_activation_function" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Types_of_activation_function"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>Types of activation function</span> </div> </a> <button aria-controls="toc-Types_of_activation_function-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle Types of activation function subsection</span> </button> <ul id="toc-Types_of_activation_function-sublist" class="vector-toc-list"> <li id="toc-Step_function" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Step_function"> <div class="vector-toc-text"> <span class="vector-toc-numb">6.1</span> <span>Step function</span> </div> </a> <ul id="toc-Step_function-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Linear_combination" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Linear_combination"> <div class="vector-toc-text"> <span class="vector-toc-numb">6.2</span> <span>Linear combination</span> </div> </a> <ul id="toc-Linear_combination-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Sigmoid" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Sigmoid"> <div class="vector-toc-text"> <span class="vector-toc-numb">6.3</span> <span>Sigmoid</span> </div> </a> <ul id="toc-Sigmoid-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Rectifier" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Rectifier"> <div class="vector-toc-text"> <span class="vector-toc-numb">6.4</span> <span>Rectifier</span> </div> </a> <ul id="toc-Rectifier-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Pseudocode_algorithm" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Pseudocode_algorithm"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>Pseudocode algorithm</span> </div> </a> <ul id="toc-Pseudocode_algorithm-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-See_also" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#See_also"> <div class="vector-toc-text"> <span class="vector-toc-numb">8</span> <span>See also</span> </div> </a> <ul id="toc-See_also-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-References" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#References"> <div class="vector-toc-text"> <span class="vector-toc-numb">9</span> <span>References</span> </div> </a> <ul id="toc-References-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Further_reading" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Further_reading"> <div class="vector-toc-text"> <span class="vector-toc-numb">10</span> <span>Further reading</span> </div> </a> <ul id="toc-Further_reading-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-External_links" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#External_links"> <div class="vector-toc-text"> <span class="vector-toc-numb">11</span> <span>External links</span> </div> </a> <ul id="toc-External_links-sublist" class="vector-toc-list"> </ul> </li> </ul> </div> </div> </nav> </div> </div> <div class="mw-content-container"> <main id="content" class="mw-body"> <header class="mw-body-header vector-page-titlebar"> <nav aria-label="Contents" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" title="Table of Contents" > <input type="checkbox" id="vector-page-titlebar-toc-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-titlebar-toc" class="vector-dropdown-checkbox " aria-label="Toggle the table of contents" > <label id="vector-page-titlebar-toc-label" for="vector-page-titlebar-toc-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-listBullet mw-ui-icon-wikimedia-listBullet"></span> <span class="vector-dropdown-label-text">Toggle the table of contents</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-titlebar-toc-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <h1 id="firstHeading" class="firstHeading mw-first-heading"><span class="mw-page-title-main">Artificial neuron</span></h1> <div id="p-lang-btn" class="vector-dropdown mw-portlet mw-portlet-lang" > <input type="checkbox" id="p-lang-btn-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-p-lang-btn" class="vector-dropdown-checkbox mw-interlanguage-selector" aria-label="Go to an article in another 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Available in 18 languages" > <label id="p-lang-btn-label" for="p-lang-btn-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--action-progressive mw-portlet-lang-heading-18" aria-hidden="true" ><span class="vector-icon mw-ui-icon-language-progressive mw-ui-icon-wikimedia-language-progressive"></span> <span class="vector-dropdown-label-text">18 languages</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D8%B9%D8%B5%D8%A8_%D8%A7%D8%B5%D8%B7%D9%86%D8%A7%D8%B9%D9%8A" title="عصب اصطناعي – Arabic" lang="ar" hreflang="ar" data-title="عصب اصطناعي" data-language-autonym="العربية" data-language-local-name="Arabic" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-az mw-list-item"><a href="https://az.wikipedia.org/wiki/S%C3%BCni_neyron" title="Süni neyron – Azerbaijani" lang="az" hreflang="az" data-title="Süni neyron" data-language-autonym="Azərbaycanca" data-language-local-name="Azerbaijani" class="interlanguage-link-target"><span>Azərbaycanca</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Neurona_artificial" title="Neurona artificial – Catalan" lang="ca" hreflang="ca" data-title="Neurona artificial" data-language-autonym="Català" data-language-local-name="Catalan" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-cv mw-list-item"><a href="https://cv.wikipedia.org/wiki/%D0%AE%D1%80%D0%B8%D0%BB%D0%BB%D0%B5_%D0%BD%D0%B5%D0%B9%D1%80%D0%BE%D0%BD" title="Юрилле нейрон – Chuvash" lang="cv" hreflang="cv" data-title="Юрилле нейрон" data-language-autonym="Чӑвашла" data-language-local-name="Chuvash" class="interlanguage-link-target"><span>Чӑвашла</span></a></li><li class="interlanguage-link interwiki-de badge-Q17437798 badge-goodarticle mw-list-item" title="good article badge"><a href="https://de.wikipedia.org/wiki/K%C3%BCnstliches_Neuron" title="Künstliches Neuron – German" lang="de" hreflang="de" data-title="Künstliches Neuron" data-language-autonym="Deutsch" data-language-local-name="German" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/Tehisneuron" title="Tehisneuron – Estonian" lang="et" hreflang="et" data-title="Tehisneuron" data-language-autonym="Eesti" data-language-local-name="Estonian" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Neurona_artificial" title="Neurona artificial – Spanish" lang="es" hreflang="es" data-title="Neurona artificial" data-language-autonym="Español" data-language-local-name="Spanish" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D8%B9%D8%B5%D8%A8_%D9%85%D8%B5%D9%86%D9%88%D8%B9%DB%8C" title="عصب مصنوعی – Persian" lang="fa" hreflang="fa" data-title="عصب مصنوعی" data-language-autonym="فارسی" data-language-local-name="Persian" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Neurone_formel" title="Neurone formel – French" lang="fr" hreflang="fr" data-title="Neurone formel" data-language-autonym="Français" data-language-local-name="French" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EC%9D%B8%EA%B3%B5_%EB%89%B4%EB%9F%B0" title="인공 뉴런 – Korean" lang="ko" hreflang="ko" data-title="인공 뉴런" data-language-autonym="한국어" data-language-local-name="Korean" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E4%BA%BA%E5%B7%A5%E7%A5%9E%E7%B5%8C" title="人工神経 – Japanese" lang="ja" hreflang="ja" data-title="人工神経" data-language-autonym="日本語" data-language-local-name="Japanese" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Sztuczny_neuron" title="Sztuczny neuron – Polish" lang="pl" hreflang="pl" data-title="Sztuczny neuron" data-language-autonym="Polski" data-language-local-name="Polish" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Neur%C3%B4nio_artificial" title="Neurônio artificial – Portuguese" lang="pt" hreflang="pt" data-title="Neurônio artificial" data-language-autonym="Português" data-language-local-name="Portuguese" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%98%D1%81%D0%BA%D1%83%D1%81%D1%81%D1%82%D0%B2%D0%B5%D0%BD%D0%BD%D1%8B%D0%B9_%D0%BD%D0%B5%D0%B9%D1%80%D0%BE%D0%BD" title="Искусственный нейрон – Russian" lang="ru" hreflang="ru" data-title="Искусственный нейрон" data-language-autonym="Русский" data-language-local-name="Russian" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/%D0%92%D0%B5%D1%88%D1%82%D0%B0%D1%87%D0%BA%D0%B8_%D0%BD%D0%B5%D1%83%D1%80%D0%BE%D0%BD" title="Вештачки неурон – Serbian" lang="sr" hreflang="sr" data-title="Вештачки неурон" data-language-autonym="Српски / srpski" data-language-local-name="Serbian" class="interlanguage-link-target"><span>Српски / srpski</span></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" title="செயற்கை நரம்பணு – Tamil" lang="ta" hreflang="ta" data-title="செயற்கை நரம்பணு" data-language-autonym="தமிழ்" data-language-local-name="Tamil" class="interlanguage-link-target"><span>தமிழ்</span></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%B8%D0%B9_%D0%BD%D0%B5%D0%B9%D1%80%D0%BE%D0%BD" title="Штучний нейрон – Ukrainian" lang="uk" hreflang="uk" data-title="Штучний нейрон" data-language-autonym="Українська" data-language-local-name="Ukrainian" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-zh-yue mw-list-item"><a href="https://zh-yue.wikipedia.org/wiki/%E4%BA%BA%E5%B7%A5%E7%A5%9E%E7%B6%93%E7%B4%B0%E8%83%9E" title="人工神經細胞 – Cantonese" lang="yue" hreflang="yue" data-title="人工神經細胞" data-language-autonym="粵語" data-language-local-name="Cantonese" class="interlanguage-link-target"><span>粵語</span></a></li> </ul> <div class="after-portlet after-portlet-lang"><span class="wb-langlinks-edit wb-langlinks-link"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q177058#sitelinks-wikipedia" title="Edit interlanguage links" class="wbc-editpage">Edit links</a></span></div> </div> </div> </div> </header> <div class="vector-page-toolbar"> <div class="vector-page-toolbar-container"> <div id="left-navigation"> <nav aria-label="Namespaces"> <div id="p-associated-pages" class="vector-menu vector-menu-tabs mw-portlet mw-portlet-associated-pages" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-nstab-main" class="selected vector-tab-noicon mw-list-item"><a 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<div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="en" dir="ltr"><div class="shortdescription nomobile noexcerpt noprint searchaux" style="display:none">Mathematical function conceived as a crude model</div> <figure typeof="mw:File/Thumb"><a href="/wiki/File:Artificial_neuron_structure.svg" class="mw-file-description"><img alt="Artificial neuron structure" src="//upload.wikimedia.org/wikipedia/commons/thumb/c/c6/Artificial_neuron_structure.svg/306px-Artificial_neuron_structure.svg.png" decoding="async" width="306" height="150" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/c6/Artificial_neuron_structure.svg/459px-Artificial_neuron_structure.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/c6/Artificial_neuron_structure.svg/612px-Artificial_neuron_structure.svg.png 2x" data-file-width="816" data-file-height="400" /></a><figcaption>Artificial neuron structure</figcaption></figure> <p>An <b>artificial neuron</b> is a <a href="/wiki/Function_(mathematics)" title="Function (mathematics)">mathematical function</a> conceived as a <a href="/wiki/Mathematical_model" title="Mathematical model">model</a> of a <a href="/wiki/Neuron" title="Neuron">biological neuron</a> in a <a href="/wiki/Neural_network" title="Neural network">neural network</a>. The artificial neuron is the elementary unit of an <i><a href="/wiki/Neural_network_(machine_learning)" title="Neural network (machine learning)">artificial neural network</a></i>.<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> </p><p>The design of the artificial neuron was inspired by biological <a href="/wiki/Neural_circuit" title="Neural circuit">neural circuitry</a>. Its inputs are analogous to <a href="/wiki/Excitatory_postsynaptic_potential" title="Excitatory postsynaptic potential">excitatory postsynaptic potentials</a> and <a href="/wiki/Inhibitory_postsynaptic_potential" title="Inhibitory postsynaptic potential">inhibitory postsynaptic potentials</a> at neural <a href="/wiki/Dendrite" title="Dendrite">dendrites</a>, or <style data-mw-deduplicate="TemplateStyles:r1238216509">.mw-parser-output .vanchor>:target~.vanchor-text{background-color:#b1d2ff}@media screen{html.skin-theme-clientpref-night .mw-parser-output .vanchor>:target~.vanchor-text{background-color:#0f4dc9}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .vanchor>:target~.vanchor-text{background-color:#0f4dc9}}</style><span class="vanchor"><span id="activation"></span><span class="vanchor-text">activation</span></span>. Its weights are analogous to <a href="/wiki/Synaptic_weight" title="Synaptic weight">synaptic weights</a>, and its output is analogous to a neuron's <a href="/wiki/Action_potential" title="Action potential">action potential</a> which is transmitted along its <a href="/wiki/Axon" title="Axon">axon</a>. </p><p>Usually, each input is separately <a href="/wiki/Weighting" title="Weighting">weighted</a>, and the sum is often added to a term known as a <i>bias</i> (loosely corresponding to the <a href="/wiki/Threshold_potential" title="Threshold potential">threshold potential</a>), before being passed through a <a href="/wiki/Nonlinear_system" title="Nonlinear system">nonlinear function</a> known as an <a href="/wiki/Activation_function" title="Activation function">activation function</a>. Depending on the task, these functions could have a <a href="/wiki/Sigmoid_function" title="Sigmoid function">sigmoid</a> shape (e.g. for <a href="/wiki/Binary_classification" title="Binary classification">binary classification</a>), but they may also take the form of other nonlinear functions, <a href="/wiki/Piecewise" class="mw-redirect" title="Piecewise">piecewise</a> linear functions, or <a href="#Step_function">step functions</a>. They are also often <a href="/wiki/Monotonic_function" title="Monotonic function">monotonically increasing</a>, <a href="/wiki/Continuous_function" title="Continuous function">continuous</a>, <a href="/wiki/Differentiable_function" title="Differentiable function">differentiable</a>, and <a href="/wiki/Bounded_function" title="Bounded function">bounded</a>. Non-monotonic, unbounded, and oscillating activation functions with multiple zeros that outperform sigmoidal and <a href="/wiki/Rectifier_(neural_networks)" title="Rectifier (neural networks)">ReLU-like</a> activation functions on many tasks have also been recently explored. The threshold function has inspired building <a href="/wiki/Logic_gate" title="Logic gate">logic gates</a> referred to as threshold logic; applicable to building <a href="/wiki/Logic_circuit" class="mw-redirect" title="Logic circuit">logic circuits</a> resembling brain processing. For example, new devices such as <a href="/wiki/Memristor" title="Memristor">memristors</a> have been extensively used to develop such logic.<sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> </p><p>The artificial neuron activation function should not be confused with a linear system's <a href="/wiki/Transfer_function" title="Transfer function">transfer function</a>. </p><p>An artificial neuron may be referred to as a <b>semi-linear unit</b>, <b>Nv neuron</b>, <b>binary neuron</b>, <b>linear threshold function</b>, or <b>McCulloch–Pitts</b> (<b>MCP</b>) <b>neuron</b>, depending on the structure used. </p><p>Simple artificial neurons, such as the McCulloch–Pitts model, are sometimes described as "caricature models", since they are intended to reflect one or more neurophysiological observations, but without regard to realism.<sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> Artificial neurons can also refer to <a href="/wiki/Artificial_cell" title="Artificial cell">artificial cells</a> in <a href="#Physical_artificial_cells">neuromorphic engineering</a> that are similar to natural physical neurons. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Basic_structure">Basic structure</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Artificial_neuron&action=edit&section=1" title="Edit section: Basic structure"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>For a given artificial neuron <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle k}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>k</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle k}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c3c9a2c7b599b37105512c5d570edc034056dd40" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.211ex; height:2.176ex;" alt="{\displaystyle k}" /></span>, let there be <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle m+1}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>m</mi> <mo>+</mo> <mn>1</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle m+1}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c6f7ed29a2b4a62d3b6af05cd91a58ffc6094201" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:6.043ex; height:2.343ex;" alt="{\displaystyle m+1}" /></span> inputs with signals <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle x_{0}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x_{0}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/86f21d0e31751534cd6584264ecf864a6aa792cf" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.384ex; height:2.009ex;" alt="{\displaystyle x_{0}}" /></span> through <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle x_{m}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>m</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x_{m}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7f12100e1dc5769ced8c9806b219abc06ab321d3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.005ex; height:2.009ex;" alt="{\displaystyle x_{m}}" /></span> and weights <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle w_{k0}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>w</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>k</mi> <mn>0</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle w_{k0}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/438f972438473237be323f95b3eb49d4cc2e690d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.575ex; height:2.009ex;" alt="{\displaystyle w_{k0}}" /></span> through <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle w_{km}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>w</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>k</mi> <mi>m</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle w_{km}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cc31b9803be8ab56fba475a4b5b75b35bb90b381" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:4.196ex; height:2.009ex;" alt="{\displaystyle w_{km}}" /></span>. Usually, the input <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle x_{0}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x_{0}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/86f21d0e31751534cd6584264ecf864a6aa792cf" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.384ex; height:2.009ex;" alt="{\displaystyle x_{0}}" /></span> is assigned the value +1, which makes it a bias input with <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle w_{k0}=b_{k}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>w</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>k</mi> <mn>0</mn> </mrow> </msub> <mo>=</mo> <msub> <mi>b</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>k</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle w_{k0}=b_{k}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/320f6dba0021ed537fce93b9f1229b606f850573" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:8.76ex; height:2.509ex;" alt="{\displaystyle w_{k0}=b_{k}}" /></span>. This leaves only <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle m}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>m</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle m}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0a07d98bb302f3856cbabc47b2b9016692e3f7bc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.04ex; height:1.676ex;" alt="{\displaystyle m}" /></span> actual inputs to the neuron: <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle x_{1}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x_{1}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a8788bf85d532fa88d1fb25eff6ae382a601c308" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.384ex; height:2.009ex;" alt="{\displaystyle x_{1}}" /></span> to <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle x_{m}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>m</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x_{m}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7f12100e1dc5769ced8c9806b219abc06ab321d3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.005ex; height:2.009ex;" alt="{\displaystyle x_{m}}" /></span>. </p><p>The output of the <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle k}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>k</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle k}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c3c9a2c7b599b37105512c5d570edc034056dd40" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.211ex; height:2.176ex;" alt="{\displaystyle k}" /></span>-th neuron is: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle y_{k}=\varphi \left(\sum _{j=0}^{m}w_{kj}x_{j}\right)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>k</mi> </mrow> </msub> <mo>=</mo> <mi>φ</mi> <mrow> <mo>(</mo> <mrow> <munderover> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> <mo>=</mo> <mn>0</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>m</mi> </mrow> </munderover> <msub> <mi>w</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>k</mi> <mi>j</mi> </mrow> </msub> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> </mrow> </msub> </mrow> <mo>)</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle y_{k}=\varphi \left(\sum _{j=0}^{m}w_{kj}x_{j}\right)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/be21980cc9e55ea0880327b9d4797f2a0da6d06e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.338ex; width:20.327ex; height:7.676ex;" alt="{\displaystyle y_{k}=\varphi \left(\sum _{j=0}^{m}w_{kj}x_{j}\right)}" /></span>,</dd></dl> <p>where <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \varphi }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>φ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \varphi }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/33ee699558d09cf9d653f6351f9fda0b2f4aaa3e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:1.52ex; height:2.176ex;" alt="{\displaystyle \varphi }" /></span> (phi) is the activation function. </p><p><span class="mw-default-size" typeof="mw:File"><a href="/wiki/File:Artificial_neuron.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/b/b0/Artificial_neuron.png" decoding="async" width="272" height="187" class="mw-file-element" data-file-width="272" data-file-height="187" /></a></span> </p><p>The output is analogous to the <a href="/wiki/Axon" title="Axon">axon</a> of a biological neuron, and its value propagates to the input of the next layer, through a synapse. It may also exit the system, possibly as part of an output <a href="/wiki/Vector_(mathematics_and_physics)" title="Vector (mathematics and physics)">vector</a>. </p><p>It has no learning process as such. Its activation function weights are calculated, and its threshold value is predetermined. </p> <div class="mw-heading mw-heading2"><h2 id="McCulloch–Pitts_(MCP)_neuron"><span id="McCulloch.E2.80.93Pitts_.28MCP.29_neuron"></span>McCulloch–Pitts (MCP) neuron</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Artificial_neuron&action=edit&section=2" title="Edit section: McCulloch–Pitts (MCP) neuron"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style 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">Main article: <a href="/wiki/Perceptron" title="Perceptron">Perceptron</a></div> <p>An MCP neuron is a kind of restricted artificial neuron which operates in discrete time-steps. Each has zero or more inputs, and are written as <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle x_{1},...,x_{n}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>,</mo> <mo>.</mo> <mo>.</mo> <mo>.</mo> <mo>,</mo> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x_{1},...,x_{n}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5f979c14353ba9d99b39d68265ad6db58c5faaae" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:10.102ex; height:2.009ex;" alt="{\displaystyle x_{1},...,x_{n}}" /></span>. It has one output, written as <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle y}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>y</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle y}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b8a6208ec717213d4317e666f1ae872e00620a0d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.155ex; height:2.009ex;" alt="{\displaystyle y}" /></span>. Each input can be either <i>excitatory</i> or <i>inhibitory</i>. The output can either be <i>quiet</i> or <i>firing</i>. An MCP neuron also has a threshold <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle b\in \{0,1,2,...\}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>b</mi> <mo>∈</mo> <mo fence="false" stretchy="false">{</mo> <mn>0</mn> <mo>,</mo> <mn>1</mn> <mo>,</mo> <mn>2</mn> <mo>,</mo> <mo>.</mo> <mo>.</mo> <mo>.</mo> <mo fence="false" stretchy="false">}</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle b\in \{0,1,2,...\}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f5f96628f893e481699387d506be7df9670bccc2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:15.854ex; height:2.843ex;" alt="{\displaystyle b\in \{0,1,2,...\}}" /></span>. </p><p>In an MCP neural network, all the neurons operate in synchronous discrete time-steps of <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle t=0,1,2,3,...}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>t</mi> <mo>=</mo> <mn>0</mn> <mo>,</mo> <mn>1</mn> <mo>,</mo> <mn>2</mn> <mo>,</mo> <mn>3</mn> <mo>,</mo> <mo>.</mo> <mo>.</mo> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle t=0,1,2,3,...}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b4c1cda85a425c4a1a62511d32881a134a174c0f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:15.438ex; height:2.509ex;" alt="{\displaystyle t=0,1,2,3,...}" /></span>. At time <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle t+1}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>t</mi> <mo>+</mo> <mn>1</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle t+1}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ab2785d8415d6902b0c93efe1419c4bc3ce4643d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:4.842ex; height:2.343ex;" alt="{\displaystyle t+1}" /></span>, the output of the neuron is <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle y(t+1)=1}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>y</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo>+</mo> <mn>1</mn> <mo stretchy="false">)</mo> <mo>=</mo> <mn>1</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle y(t+1)=1}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/19f8f1dba0e828a16217e2d73f3f62077a3116f0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:12.068ex; height:2.843ex;" alt="{\displaystyle y(t+1)=1}" /></span> if the number of firing excitatory inputs is at least equal to the threshold, and no inhibitory inputs are firing; <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle y(t+1)=0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>y</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo>+</mo> <mn>1</mn> <mo stretchy="false">)</mo> <mo>=</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle y(t+1)=0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5d124605aebe8b995aeafa51e605f52e5fb14524" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:12.068ex; height:2.843ex;" alt="{\displaystyle y(t+1)=0}" /></span> otherwise. </p><p>Each output can be the input to an arbitrary number of neurons, including itself (i.e., self-loops are possible). However, an output cannot connect more than once with a single neuron. Self-loops do not cause contradictions, since the network operates in synchronous discrete time-steps. </p><p>As a simple example, consider a single neuron with threshold 0, and a single inhibitory self-loop. Its output would oscillate between 0 and 1 at every step, acting as a "clock". </p><p>Any <a href="/wiki/Finite-state_machine" title="Finite-state machine">finite state machine</a> can be simulated by a MCP neural network.<sup id="cite_ref-:0_4-0" class="reference"><a href="#cite_note-:0-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> Furnished with an infinite tape, MCP neural networks can simulate any <a href="/wiki/Turing_machine" title="Turing machine">Turing machine</a>.<sup id="cite_ref-5" class="reference"><a href="#cite_note-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Biological_models">Biological models</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Artificial_neuron&action=edit&section=3" title="Edit section: Biological models"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></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/Biological_neuron_model" title="Biological neuron model">Biological neuron model</a></div> <figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Neuron3.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/a/ac/Neuron3.svg/400px-Neuron3.svg.png" decoding="async" width="400" height="222" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/ac/Neuron3.svg/600px-Neuron3.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/ac/Neuron3.svg/800px-Neuron3.svg.png 2x" data-file-width="450" data-file-height="250" /></a><figcaption>Neuron and myelinated axon, with signal flow from inputs at dendrites to outputs at axon terminals</figcaption></figure> <p>Artificial neurons are designed to mimic aspects of their biological counterparts. However a significant performance gap exists between biological and artificial neural networks. In particular single biological neurons in the human brain with oscillating activation function capable of learning the <a href="/wiki/Exclusive_or" title="Exclusive or">XOR function</a> have been discovered.<sup id="cite_ref-6" class="reference"><a href="#cite_note-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> </p> <ul><li><a href="/wiki/Dendrites" class="mw-redirect" title="Dendrites">Dendrites</a> – in biological neurons, dendrites act as the input vector. These dendrites allow the cell to receive signals from a large (>1000) number of neighboring neurons. As in the above mathematical treatment, each dendrite is able to perform "multiplication" by that dendrite's "weight value." The multiplication is accomplished by increasing or decreasing the ratio of synaptic neurotransmitters to signal chemicals introduced into the dendrite in response to the synaptic neurotransmitter. A negative multiplication effect can be achieved by transmitting signal inhibitors (i.e. oppositely charged ions) along the dendrite in response to the reception of synaptic neurotransmitters.</li> <li><a href="/wiki/Soma_(biology)" title="Soma (biology)">Soma</a> – in biological neurons, the soma acts as the summation function, seen in the above mathematical description. As positive and negative signals (exciting and inhibiting, respectively) arrive in the soma from the dendrites, the positive and negative ions are effectively added in summation, by simple virtue of being mixed together in the solution inside the cell's body.</li> <li><a href="/wiki/Axon" title="Axon">Axon</a> – the axon gets its signal from the summation behavior which occurs inside the soma. The opening to the axon essentially samples the electrical potential of the solution inside the soma. Once the soma reaches a certain potential, the axon will transmit an all-in signal pulse down its length. In this regard, the axon behaves as the ability for us to connect our artificial neuron to other artificial neurons.</li></ul> <p>Unlike most artificial neurons, however, biological neurons fire in discrete pulses. Each time the electrical potential inside the soma reaches a certain threshold, a pulse is transmitted down the axon. This pulsing can be translated into continuous values. The rate (activations per second, etc.) at which an axon fires converts directly into the rate at which neighboring cells get signal ions introduced into them. The faster a biological neuron fires, the faster nearby neurons accumulate electrical potential (or lose electrical potential, depending on the "weighting" of the dendrite that connects to the neuron that fired). It is this conversion that allows computer scientists and mathematicians to simulate biological neural networks using artificial neurons which can output distinct values (often from −1 to 1). </p> <div class="mw-heading mw-heading3"><h3 id="Encoding">Encoding</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Artificial_neuron&action=edit&section=4" title="Edit section: Encoding"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Research has shown that <a href="/wiki/Unary_coding" title="Unary coding">unary coding</a> is used in the neural circuits responsible for <a href="/wiki/Birdsong" class="mw-redirect" title="Birdsong">birdsong</a> production.<sup id="cite_ref-7" class="reference"><a href="#cite_note-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-8" class="reference"><a href="#cite_note-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> The use of unary in biological networks is presumably due to the inherent simplicity of the coding. Another contributing factor could be that unary coding provides a certain degree of error correction.<sup id="cite_ref-9" class="reference"><a href="#cite_note-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Physical_artificial_cells">Physical artificial cells</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Artificial_neuron&action=edit&section=5" title="Edit section: Physical artificial cells"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>There is research and development into physical artificial neurons – organic and inorganic. </p><p>For example, some artificial neurons can receive<sup id="cite_ref-knowablemagazineorganic_10-0" class="reference"><a href="#cite_note-knowablemagazineorganic-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-11" class="reference"><a href="#cite_note-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup> and release <a href="/wiki/Dopamine" title="Dopamine">dopamine</a> (<a href="/wiki/Neurotransmitter" title="Neurotransmitter">chemical signals</a> rather than electrical signals) and communicate with natural rat <a href="/wiki/Soft_robot" class="mw-redirect" title="Soft robot">muscle</a> and <a href="/wiki/Brain_cell" title="Brain cell">brain cells</a>, with potential for use in <a href="/wiki/Brain%E2%80%93computer_interface" title="Brain–computer interface">BCIs</a>/<a href="/wiki/Wetware_computer#Future_applications" title="Wetware computer">prosthetics</a>.<sup id="cite_ref-12" class="reference"><a href="#cite_note-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-13" class="reference"><a href="#cite_note-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup> </p><p>Low-power biocompatible <a href="/wiki/Memristor" title="Memristor">memristors</a> may enable construction of artificial neurons which function at voltages of biological <a href="/wiki/Action_potential" title="Action potential">action potentials</a> and could be used to directly process <a href="/wiki/Biosensor" title="Biosensor">biosensing signals</a>, for <a href="/wiki/Neuromorphic_computing" title="Neuromorphic computing">neuromorphic computing</a> and/or <a href="/wiki/Brain%E2%80%93computer_interface" title="Brain–computer interface">direct communication with biological neurons</a>.<sup id="cite_ref-14" class="reference"><a href="#cite_note-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-15" class="reference"><a href="#cite_note-15"><span class="cite-bracket">[</span>15<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-16" class="reference"><a href="#cite_note-16"><span class="cite-bracket">[</span>16<span class="cite-bracket">]</span></a></sup> </p><p>Organic neuromorphic circuits made out of <a href="/wiki/Polymer" title="Polymer">polymers</a>, coated with an ion-rich gel to enable a material to carry an electric charge like <a href="/wiki/Neuron" title="Neuron">real neurons</a>, have been built into a robot, enabling it to learn sensorimotorically within the real world, rather than via simulations or virtually.<sup id="cite_ref-sciame_17-0" class="reference"><a href="#cite_note-sciame-17"><span class="cite-bracket">[</span>17<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-18" class="reference"><a href="#cite_note-18"><span class="cite-bracket">[</span>18<span class="cite-bracket">]</span></a></sup> Moreover, artificial spiking neurons made of soft matter (polymers) can operate in biologically relevant environments and enable the synergetic communication between the artificial and biological domains.<sup id="cite_ref-19" class="reference"><a href="#cite_note-19"><span class="cite-bracket">[</span>19<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-20" class="reference"><a href="#cite_note-20"><span class="cite-bracket">[</span>20<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="History">History</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Artificial_neuron&action=edit&section=6" title="Edit section: History"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The first artificial neuron was the Threshold Logic Unit (TLU), or Linear Threshold Unit,<sup id="cite_ref-Anthony2001_21-0" class="reference"><a href="#cite_note-Anthony2001-21"><span class="cite-bracket">[</span>21<span class="cite-bracket">]</span></a></sup> first proposed by <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> in 1943 in <i><a href="/wiki/A_Logical_Calculus_of_the_Ideas_Immanent_in_Nervous_Activity" title="A Logical Calculus of the Ideas Immanent in Nervous Activity">A logical calculus of the ideas immanent in nervous activity</a></i>. The model was specifically targeted as a computational model of the "nerve net" in the brain.<sup id="cite_ref-Aggarwal2014_22-0" class="reference"><a href="#cite_note-Aggarwal2014-22"><span class="cite-bracket">[</span>22<span class="cite-bracket">]</span></a></sup> As an activation function, it employed a threshold, equivalent to using the <a href="/wiki/Heaviside_step_function" title="Heaviside step function">Heaviside step function</a>. Initially, only a simple model was considered, with binary inputs and outputs, some restrictions on the possible weights, and a more flexible threshold value. Since the beginning it was already noticed that any <a href="/wiki/Boolean_function" title="Boolean function">Boolean function</a> could be implemented by networks of such devices, what is easily seen from the fact that one can implement the AND and OR functions, and use them in the <a href="/wiki/Disjunctive_normal_form" title="Disjunctive normal form">disjunctive</a> or the <a href="/wiki/Conjunctive_normal_form" title="Conjunctive normal form">conjunctive normal form</a>. Researchers also soon realized that cyclic networks, with <a href="/wiki/Feedback" title="Feedback">feedbacks</a> through neurons, could define dynamical systems with memory, but most of the research concentrated (and still does) on strictly <a href="/wiki/Feed-forward_network" class="mw-redirect" title="Feed-forward network">feed-forward networks</a> because of the smaller difficulty they present. </p><p>One important and pioneering artificial neural network that used the linear threshold function was the <a href="/wiki/Perceptron" title="Perceptron">perceptron</a>, developed by <a href="/wiki/Frank_Rosenblatt" title="Frank Rosenblatt">Frank Rosenblatt</a>. This model already considered more flexible weight values in the neurons, and was used in machines with adaptive capabilities. The representation of the threshold values as a bias term was introduced by <a href="/wiki/Bernard_Widrow" title="Bernard Widrow">Bernard Widrow</a> in 1960 – see <a href="/wiki/ADALINE" title="ADALINE">ADALINE</a>. </p><p>In the late 1980s, when research on neural networks regained strength, neurons with more continuous shapes started to be considered. The possibility of differentiating the activation function allows the direct use of the <a href="/wiki/Gradient_descent" title="Gradient descent">gradient descent</a> and other optimization algorithms for the adjustment of the weights. Neural networks also started to be used as a general <a href="/wiki/Function_approximation" title="Function approximation">function approximation</a> model. The best known training algorithm called <a href="/wiki/Backpropagation" title="Backpropagation">backpropagation</a> has been rediscovered several times but its first development goes back to the work of <a href="/wiki/Paul_Werbos" title="Paul Werbos">Paul Werbos</a>.<sup id="cite_ref-23" class="reference"><a href="#cite_note-23"><span class="cite-bracket">[</span>23<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-24" class="reference"><a href="#cite_note-24"><span class="cite-bracket">[</span>24<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Types_of_activation_function">Types of activation function</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Artificial_neuron&action=edit&section=7" title="Edit section: Types of activation function"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></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/Activation_function" title="Activation function">Activation function</a></div> <p>The activation function of a neuron is chosen to have a number of properties which either enhance or simplify the network containing the neuron. Crucially, for instance, any <a href="/wiki/Multilayer_perceptron" title="Multilayer perceptron">multilayer perceptron</a> using a linear activation function has an equivalent single-layer network; a <i>non</i>-linear function is therefore necessary to gain the advantages of a multi-layer network.<sup class="noprint Inline-Template Template-Fact" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed"><span title="This claim needs references to reliable sources. (May 2018)">citation needed</span></a></i>]</sup> </p><p>Below, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle u}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>u</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle u}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c3e6bb763d22c20916ed4f0bb6bd49d7470cffd8" 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 u}" /></span> refers in all cases to the weighted sum of all the inputs to the neuron, i.e. for <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle n}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a601995d55609f2d9f5e233e36fbe9ea26011b3b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.395ex; height:1.676ex;" alt="{\displaystyle n}" /></span> inputs, </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle u=\sum _{i=1}^{n}w_{i}x_{i}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>u</mi> <mo>=</mo> <munderover> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </munderover> <msub> <mi>w</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle u=\sum _{i=1}^{n}w_{i}x_{i}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8773ce7afe8e89c86732f0b59beb83f41f23c832" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:12.763ex; height:6.843ex;" alt="{\displaystyle u=\sum _{i=1}^{n}w_{i}x_{i}}" /></span></dd></dl> <p>where <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle w}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>w</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle w}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/88b1e0c8e1be5ebe69d18a8010676fa42d7961e6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.664ex; height:1.676ex;" alt="{\displaystyle w}" /></span> is a vector of synaptic weights and <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle x}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>x</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/87f9e315fd7e2ba406057a97300593c4802b53e4" 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 x}" /></span> is a vector of inputs. </p> <div class="mw-heading mw-heading3"><h3 id="Step_function">Step function</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Artificial_neuron&action=edit&section=8" title="Edit section: Step function"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></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/Step_function" title="Step function">Step function</a></div> <p>The output <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle y}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>y</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle y}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b8a6208ec717213d4317e666f1ae872e00620a0d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.155ex; height:2.009ex;" alt="{\displaystyle y}" /></span> of this activation function is binary, depending on whether the input meets a specified threshold, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \theta }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>θ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \theta }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6e5ab2664b422d53eb0c7df3b87e1360d75ad9af" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.09ex; height:2.176ex;" alt="{\displaystyle \theta }" /></span> (theta). The "signal" is sent, i.e. the output is set to 1, if the activation meets or exceeds the threshold. </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle y={\begin{cases}1&{\text{if }}u\geq \theta \\0&{\text{if }}u<\theta \end{cases}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>y</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo>{</mo> <mtable columnalign="left left" rowspacing=".2em" columnspacing="1em" displaystyle="false"> <mtr> <mtd> <mn>1</mn> </mtd> <mtd> <mrow class="MJX-TeXAtom-ORD"> <mtext>if </mtext> </mrow> <mi>u</mi> <mo>≥</mo> <mi>θ</mi> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mrow class="MJX-TeXAtom-ORD"> <mtext>if </mtext> </mrow> <mi>u</mi> <mo><</mo> <mi>θ</mi> </mtd> </mtr> </mtable> <mo fence="true" stretchy="true" symmetric="true"></mo> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle y={\begin{cases}1&{\text{if }}u\geq \theta \\0&{\text{if }}u<\theta \end{cases}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9dd1436c7b0c1fa2ad911c56f237fd23d925cca3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:17.692ex; height:6.176ex;" alt="{\displaystyle y={\begin{cases}1&{\text{if }}u\geq \theta \\0&{\text{if }}u<\theta \end{cases}}}" /></span></dd></dl> <p>This function is used in <a href="/wiki/Perceptron" title="Perceptron">perceptrons</a>, and appears in many other models. It performs a division of the <a href="/wiki/Vector_space" title="Vector space">space</a> of inputs by a <a href="/wiki/Hyperplane" title="Hyperplane">hyperplane</a>. It is specially useful in the last layer of a network, intended for example to perform binary classification of the inputs. </p> <div class="mw-heading mw-heading3"><h3 id="Linear_combination">Linear combination</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Artificial_neuron&action=edit&section=9" title="Edit section: Linear combination"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></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/Linear_combination" title="Linear combination">Linear combination</a></div> <p>In this case, the output unit is simply the weighted sum of its inputs, plus a bias term. A number of such linear neurons perform a linear transformation of the input vector. This is usually more useful in the early layers of a network. A number of analysis tools exist based on linear models, such as <a href="/wiki/Harmonic_analysis" title="Harmonic analysis">harmonic analysis</a>, and they can all be used in neural networks with this linear neuron. The bias term allows us to make <a href="/wiki/Homogeneous_coordinates" title="Homogeneous coordinates">affine transformations</a> to the data. </p> <div class="mw-heading mw-heading3"><h3 id="Sigmoid">Sigmoid</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Artificial_neuron&action=edit&section=10" title="Edit section: Sigmoid"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></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/Sigmoid_function" title="Sigmoid function">Sigmoid function</a></div> <p>A fairly simple nonlinear function, the <a href="/wiki/Sigmoid_function" title="Sigmoid function">sigmoid function</a> such as the logistic function also has an easily calculated derivative, which can be important when calculating the weight updates in the network. It thus makes the network more easily manipulable mathematically, and was attractive to early computer scientists who needed to minimize the computational load of their simulations. It was previously commonly seen in <a href="/wiki/Multilayer_perceptron" title="Multilayer perceptron">multilayer perceptrons</a>. However, recent work has shown sigmoid neurons to be less effective than <a href="/wiki/Rectifier_(neural_networks)" title="Rectifier (neural networks)">rectified linear</a> neurons. The reason is that the gradients computed by the <a href="/wiki/Backpropagation" title="Backpropagation">backpropagation</a> algorithm tend to diminish towards zero as activations propagate through layers of sigmoidal neurons, making it difficult to optimize neural networks using multiple layers of sigmoidal neurons. </p> <div class="mw-heading mw-heading3"><h3 id="Rectifier">Rectifier</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Artificial_neuron&action=edit&section=11" title="Edit section: Rectifier"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></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/Rectifier_(neural_networks)" title="Rectifier (neural networks)">Rectifier (neural networks)</a></div> <p>In the context of <a href="/wiki/Artificial_neural_network" class="mw-redirect" title="Artificial neural network">artificial neural networks</a>, the <b>rectifier</b> or <b>ReLU (Rectified Linear Unit)</b> is an <a href="/wiki/Activation_function" title="Activation function">activation function</a> defined as the positive part of its argument: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle f(x)=x^{+}=\max(0,x),}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>f</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> <mo>=</mo> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>+</mo> </mrow> </msup> <mo>=</mo> <mo movablelimits="true" form="prefix">max</mo> <mo stretchy="false">(</mo> <mn>0</mn> <mo>,</mo> <mi>x</mi> <mo stretchy="false">)</mo> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle f(x)=x^{+}=\max(0,x),}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e9c5f17dbc2be5cb379c1894b3a43561f296cf5c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:23.763ex; height:3.009ex;" alt="{\displaystyle f(x)=x^{+}=\max(0,x),}" /></span></dd></dl> <p>where <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle x}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>x</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/87f9e315fd7e2ba406057a97300593c4802b53e4" 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 x}" /></span> is the input to a neuron. This is also known as a <a href="/wiki/Ramp_function" title="Ramp function">ramp function</a> and is analogous to <a href="/wiki/Half-wave_rectification" class="mw-redirect" title="Half-wave rectification">half-wave rectification</a> in electrical engineering. This <a href="/wiki/Activation_function" title="Activation function">activation function</a> was first introduced to a dynamical network by Hahnloser et al. in a 2000 paper in <i><a href="/wiki/Nature_(journal)" title="Nature (journal)">Nature</a></i><sup id="cite_ref-Hahnloser2000_25-0" class="reference"><a href="#cite_note-Hahnloser2000-25"><span class="cite-bracket">[</span>25<span class="cite-bracket">]</span></a></sup> with strong <a href="/wiki/Biological" class="mw-redirect" title="Biological">biological</a> motivations and mathematical justifications.<sup id="cite_ref-Hahnloser2001_26-0" class="reference"><a href="#cite_note-Hahnloser2001-26"><span class="cite-bracket">[</span>26<span class="cite-bracket">]</span></a></sup> It has been demonstrated for the first time in 2011 to enable better training of deeper networks,<sup id="cite_ref-glorot2011_27-0" class="reference"><a href="#cite_note-glorot2011-27"><span class="cite-bracket">[</span>27<span class="cite-bracket">]</span></a></sup> compared to the widely used activation functions prior to 2011, i.e., the <a href="/wiki/Logistic_function" title="Logistic function">logistic sigmoid</a> (which is inspired by <a href="/wiki/Probability_theory" title="Probability theory">probability theory</a>; see <a href="/wiki/Logistic_regression" title="Logistic regression">logistic regression</a>) and its more practical<sup id="cite_ref-28" class="reference"><a href="#cite_note-28"><span class="cite-bracket">[</span>28<span class="cite-bracket">]</span></a></sup> counterpart, the <a href="/wiki/Hyperbolic_tangent" class="mw-redirect" title="Hyperbolic tangent">hyperbolic tangent</a>. </p><p>A commonly used variant of the ReLU activation function is the Leaky ReLU which allows a small, positive gradient when the unit is not active: </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle f(x)={\begin{cases}x&{\text{if }}x>0,\\ax&{\text{otherwise}}.\end{cases}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>f</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo>{</mo> <mtable columnalign="left left" rowspacing=".2em" columnspacing="1em" displaystyle="false"> <mtr> <mtd> <mi>x</mi> </mtd> <mtd> <mrow class="MJX-TeXAtom-ORD"> <mtext>if </mtext> </mrow> <mi>x</mi> <mo>></mo> <mn>0</mn> <mo>,</mo> </mtd> </mtr> <mtr> <mtd> <mi>a</mi> <mi>x</mi> </mtd> <mtd> <mrow class="MJX-TeXAtom-ORD"> <mtext>otherwise</mtext> </mrow> <mo>.</mo> </mtd> </mtr> </mtable> <mo fence="true" stretchy="true" symmetric="true"></mo> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle f(x)={\begin{cases}x&{\text{if }}x>0,\\ax&{\text{otherwise}}.\end{cases}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fda8917e3cf15d50f5d783e0580eb19366e961d9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:25.117ex; height:6.176ex;" alt="{\displaystyle f(x)={\begin{cases}x&{\text{if }}x>0,\\ax&{\text{otherwise}}.\end{cases}}}" /></span> </p><p>where <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle x}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>x</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/87f9e315fd7e2ba406057a97300593c4802b53e4" 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 x}" /></span> is the input to the neuron and <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle a}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>a</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ffd2487510aa438433a2579450ab2b3d557e5edc" 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 a}" /></span> is a small positive constant (set to 0.01 in the original paper).<sup id="cite_ref-maas2014_29-0" class="reference"><a href="#cite_note-maas2014-29"><span class="cite-bracket">[</span>29<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Pseudocode_algorithm">Pseudocode algorithm</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Artificial_neuron&action=edit&section=12" title="Edit section: Pseudocode algorithm"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The following is a simple <a href="/wiki/Pseudocode" title="Pseudocode">pseudocode</a> implementation<sup class="noprint Inline-Template Template-Fact" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed"><span title="This claim needs references to reliable sources. (September 2024)">citation needed</span></a></i>]</sup> of a single Threshold Logic Unit (TLU) which takes <a href="/wiki/Boolean_data_type" title="Boolean data type">Boolean</a> inputs (true or false), and returns a single Boolean output when activated. An <a href="/wiki/Object_oriented" class="mw-redirect" title="Object oriented">object-oriented</a> model is used. No method of training is defined, since several exist. If a purely functional model were used, the class TLU below would be replaced with a function TLU with input parameters threshold, weights, and inputs that returned a Boolean value. </p> <pre><b>class</b> TLU <b>defined as:</b> <b>data member</b> threshold <b>:</b> number <b>data member</b> weights <b>: list of</b> numbers <b>of size</b> X <b>function member</b> fire(inputs <b>: list of</b> booleans <b>of size</b> X) <b>:</b> boolean <b>defined as:</b> <b>variable</b> T <b>:</b> number T <b>←</b> 0 <b>for each</b> i <b>in</b> 1 <b>to</b> X <b>do</b> <b>if</b> inputs(i) <b>is</b> true <b>then</b> T <b>←</b> T + weights(i) <b>end if</b> <b>end for each</b> <b>if</b> T > threshold <b>then</b> <b>return</b> true <b>else:</b> <b>return</b> false <b>end if</b> <b>end function</b> <b>end class</b> </pre> <div class="mw-heading mw-heading2"><h2 id="See_also">See also</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Artificial_neuron&action=edit&section=13" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Binding_neuron" title="Binding neuron">Binding neuron</a></li> <li><a href="/wiki/Connectionism" title="Connectionism">Connectionism</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="References">References</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Artificial_neuron&action=edit&section=14" title="Edit section: References"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <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"> <div class="mw-references-wrap mw-references-columns"><ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-1">^</a></b></span> <span class="reference-text"><style data-mw-deduplicate="TemplateStyles:r1238218222">.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free.id-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited.id-lock-limited a,.mw-parser-output .id-lock-registration.id-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription.id-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-free 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 (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .cs1-maint{color:#18911f}}</style><cite id="CITEREFRami_A._AlzahraniAlice_C._Parker" class="citation conference cs1">Rami A. Alzahrani; Alice C. Parker. "Neuromorphic Circuits With Neural Modulation Enhancing the Information Content of Neural Signaling". <i>Proceedings of International Conference on Neuromorphic Systems 2020</i>. Art. 19. New York: Association for Computing Machinery. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.1145%2F3407197.3407204">10.1145/3407197.3407204</a></span>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1-4503-8851-1" title="Special:BookSources/978-1-4503-8851-1"><bdi>978-1-4503-8851-1</bdi></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:220794387">220794387</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=conference&rft.atitle=Neuromorphic+Circuits+With+Neural+Modulation+Enhancing+the+Information+Content+of+Neural+Signaling&rft.btitle=Proceedings+of+International+Conference+on+Neuromorphic+Systems+2020&rft.place=New+York&rft.pub=Association+for+Computing+Machinery&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A220794387%23id-name%3DS2CID&rft_id=info%3Adoi%2F10.1145%2F3407197.3407204&rft.isbn=978-1-4503-8851-1&rft.au=Rami+A.+Alzahrani&rft.au=Alice+C.+Parker&rfr_id=info%3Asid%2Fen.wikipedia.org%3AArtificial+neuron" class="Z3988"></span></span> </li> <li id="cite_note-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-2">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFMaanJayadeviJames2016" class="citation journal cs1">Maan, A. K.; Jayadevi, D. A.; James, A. P. (1 January 2016). "A Survey of Memristive Threshold Logic Circuits". <i>IEEE Transactions on Neural Networks and Learning Systems</i>. <b>PP</b> (99): <span class="nowrap">1734–</span>1746. <a href="/wiki/ArXiv_(identifier)" class="mw-redirect" title="ArXiv (identifier)">arXiv</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://arxiv.org/abs/1604.07121">1604.07121</a></span>. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2016arXiv160407121M">2016arXiv160407121M</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1109%2FTNNLS.2016.2547842">10.1109/TNNLS.2016.2547842</a>. <a href="/wiki/ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/2162-237X">2162-237X</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/27164608">27164608</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:1798273">1798273</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=IEEE+Transactions+on+Neural+Networks+and+Learning+Systems&rft.atitle=A+Survey+of+Memristive+Threshold+Logic+Circuits&rft.volume=PP&rft.issue=99&rft.pages=%3Cspan+class%3D%22nowrap%22%3E1734-%3C%2Fspan%3E1746&rft.date=2016-01-01&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A1798273%23id-name%3DS2CID&rft_id=info%3Abibcode%2F2016arXiv160407121M&rft_id=info%3Aarxiv%2F1604.07121&rft.issn=2162-237X&rft_id=info%3Adoi%2F10.1109%2FTNNLS.2016.2547842&rft_id=info%3Apmid%2F27164608&rft.aulast=Maan&rft.aufirst=A.+K.&rft.au=Jayadevi%2C+D.+A.&rft.au=James%2C+A.+P.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AArtificial+neuron" class="Z3988"></span></span> </li> <li id="cite_note-3"><span class="mw-cite-backlink"><b><a href="#cite_ref-3">^</a></b></span> <span class="reference-text"> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFF._C._Hoppensteadt_and_E._M._Izhikevich1997" class="citation book cs1">F. C. Hoppensteadt and E. M. Izhikevich (1997). <i>Weakly connected neural networks</i>. Springer. p. 4. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-387-94948-2" title="Special:BookSources/978-0-387-94948-2"><bdi>978-0-387-94948-2</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Weakly+connected+neural+networks&rft.pages=4&rft.pub=Springer&rft.date=1997&rft.isbn=978-0-387-94948-2&rft.au=F.+C.+Hoppensteadt+and+E.+M.+Izhikevich&rfr_id=info%3Asid%2Fen.wikipedia.org%3AArtificial+neuron" class="Z3988"></span></span> </li> <li id="cite_note-:0-4"><span class="mw-cite-backlink"><b><a href="#cite_ref-:0_4-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFMinsky1967" class="citation book cs1">Minsky, Marvin Lee (1967-01-01). <i>Computation: Finite and Infinite Machines</i>. Prentice Hall. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-13-165563-8" title="Special:BookSources/978-0-13-165563-8"><bdi>978-0-13-165563-8</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Computation%3A+Finite+and+Infinite+Machines&rft.pub=Prentice+Hall&rft.date=1967-01-01&rft.isbn=978-0-13-165563-8&rft.aulast=Minsky&rft.aufirst=Marvin+Lee&rfr_id=info%3Asid%2Fen.wikipedia.org%3AArtificial+neuron" class="Z3988"></span></span> </li> <li id="cite_note-5"><span class="mw-cite-backlink"><b><a href="#cite_ref-5">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFMcCullochPitts1943" class="citation journal cs1">McCulloch, Warren S.; Pitts, Walter (1943-12-01). <a rel="nofollow" class="external text" href="https://doi.org/10.1007/BF02478259">"A logical calculus of the ideas immanent in nervous activity"</a>. <i>The Bulletin of Mathematical Biophysics</i>. <b>5</b> (4): <span class="nowrap">115–</span>133. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1007%2FBF02478259">10.1007/BF02478259</a>. <a href="/wiki/ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/1522-9602">1522-9602</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=The+Bulletin+of+Mathematical+Biophysics&rft.atitle=A+logical+calculus+of+the+ideas+immanent+in+nervous+activity&rft.volume=5&rft.issue=4&rft.pages=%3Cspan+class%3D%22nowrap%22%3E115-%3C%2Fspan%3E133&rft.date=1943-12-01&rft_id=info%3Adoi%2F10.1007%2FBF02478259&rft.issn=1522-9602&rft.aulast=McCulloch&rft.aufirst=Warren+S.&rft.au=Pitts%2C+Walter&rft_id=https%3A%2F%2Fdoi.org%2F10.1007%2FBF02478259&rfr_id=info%3Asid%2Fen.wikipedia.org%3AArtificial+neuron" class="Z3988"></span></span> </li> <li id="cite_note-6"><span class="mw-cite-backlink"><b><a href="#cite_ref-6">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFGidonZolnikFidzinskiBolduan2020" class="citation journal cs1">Gidon, Albert; Zolnik, Timothy Adam; Fidzinski, Pawel; Bolduan, Felix; Papoutsi, Athanasia; <a href="/wiki/Panayiota_Poirazi" title="Panayiota Poirazi">Poirazi, Panayiota</a>; Holtkamp, Martin; Vida, Imre; Larkum, Matthew Evan (2020-01-03). <a rel="nofollow" class="external text" href="https://doi.org/10.1126%2Fscience.aax6239">"Dendritic action potentials and computation in human layer 2/3 cortical neurons"</a>. <i>Science</i>. <b>367</b> (6473): <span class="nowrap">83–</span>87. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2020Sci...367...83G">2020Sci...367...83G</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.1126%2Fscience.aax6239">10.1126/science.aax6239</a></span>. <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/31896716">31896716</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:209676937">209676937</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Science&rft.atitle=Dendritic+action+potentials+and+computation+in+human+layer+2%2F3+cortical+neurons&rft.volume=367&rft.issue=6473&rft.pages=%3Cspan+class%3D%22nowrap%22%3E83-%3C%2Fspan%3E87&rft.date=2020-01-03&rft_id=info%3Adoi%2F10.1126%2Fscience.aax6239&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A209676937%23id-name%3DS2CID&rft_id=info%3Apmid%2F31896716&rft_id=info%3Abibcode%2F2020Sci...367...83G&rft.aulast=Gidon&rft.aufirst=Albert&rft.au=Zolnik%2C+Timothy+Adam&rft.au=Fidzinski%2C+Pawel&rft.au=Bolduan%2C+Felix&rft.au=Papoutsi%2C+Athanasia&rft.au=Poirazi%2C+Panayiota&rft.au=Holtkamp%2C+Martin&rft.au=Vida%2C+Imre&rft.au=Larkum%2C+Matthew+Evan&rft_id=https%3A%2F%2Fdoi.org%2F10.1126%252Fscience.aax6239&rfr_id=info%3Asid%2Fen.wikipedia.org%3AArtificial+neuron" class="Z3988"></span></span> </li> <li id="cite_note-7"><span class="mw-cite-backlink"><b><a href="#cite_ref-7">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFSquireAlbrightBloomGage2007" class="citation book cs1">Squire, L.; Albright, T.; Bloom, F.; Gage, F.; Spitzer, N., eds. (October 2007). <a rel="nofollow" class="external text" href="https://web.archive.org/web/20150412190625/https://clm.utexas.edu/fietelab/Papers/birdsong_review_topost.pdf"><i>Neural network models of birdsong production, learning, and coding</i></a> <span class="cs1-format">(PDF)</span>. New Encyclopedia of Neuroscience: Elservier. Archived from <a rel="nofollow" class="external text" href="https://clm.utexas.edu/fietelab/Papers/birdsong_review_topost.pdf">the original</a> <span class="cs1-format">(PDF)</span> on 2015-04-12<span class="reference-accessdate">. Retrieved <span class="nowrap">12 April</span> 2015</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Neural+network+models+of+birdsong+production%2C+learning%2C+and+coding&rft.place=New+Encyclopedia+of+Neuroscience&rft.pub=Elservier&rft.date=2007-10&rft_id=https%3A%2F%2Fclm.utexas.edu%2Ffietelab%2FPapers%2Fbirdsong_review_topost.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3AArtificial+neuron" class="Z3988"></span></span> </li> <li id="cite_note-8"><span class="mw-cite-backlink"><b><a href="#cite_ref-8">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFMoore2011" class="citation journal cs1">Moore, J.M.; et al. (2011). <a rel="nofollow" class="external text" href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3182746">"Motor pathway convergence predicts syllable repertoire size in oscine birds"</a>. <i>Proc. Natl. Acad. Sci. USA</i>. <b>108</b> (39): <span class="nowrap">16440–</span>16445. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2011PNAS..10816440M">2011PNAS..10816440M</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.1073%2Fpnas.1102077108">10.1073/pnas.1102077108</a></span>. <a href="/wiki/PMC_(identifier)" class="mw-redirect" title="PMC (identifier)">PMC</a> <span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3182746">3182746</a></span>. <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/21918109">21918109</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Proc.+Natl.+Acad.+Sci.+USA&rft.atitle=Motor+pathway+convergence+predicts+syllable+repertoire+size+in+oscine+birds&rft.volume=108&rft.issue=39&rft.pages=%3Cspan+class%3D%22nowrap%22%3E16440-%3C%2Fspan%3E16445&rft.date=2011&rft_id=https%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fpmc%2Farticles%2FPMC3182746%23id-name%3DPMC&rft_id=info%3Apmid%2F21918109&rft_id=info%3Adoi%2F10.1073%2Fpnas.1102077108&rft_id=info%3Abibcode%2F2011PNAS..10816440M&rft.aulast=Moore&rft.aufirst=J.M.&rft_id=https%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fpmc%2Farticles%2FPMC3182746&rfr_id=info%3Asid%2Fen.wikipedia.org%3AArtificial+neuron" class="Z3988"></span></span> </li> <li id="cite_note-9"><span class="mw-cite-backlink"><b><a href="#cite_ref-9">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFPotluri2014" class="citation arxiv cs1">Potluri, Pushpa Sree (26 November 2014). "Error Correction Capacity of Unary Coding". <a href="/wiki/ArXiv_(identifier)" class="mw-redirect" title="ArXiv (identifier)">arXiv</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://arxiv.org/abs/1411.7406">1411.7406</a></span> [<a rel="nofollow" class="external text" href="https://arxiv.org/archive/cs.IT">cs.IT</a>].</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=preprint&rft.jtitle=arXiv&rft.atitle=Error+Correction+Capacity+of+Unary+Coding&rft.date=2014-11-26&rft_id=info%3Aarxiv%2F1411.7406&rft.aulast=Potluri&rft.aufirst=Pushpa+Sree&rfr_id=info%3Asid%2Fen.wikipedia.org%3AArtificial+neuron" class="Z3988"></span></span> </li> <li id="cite_note-knowablemagazineorganic-10"><span class="mw-cite-backlink"><b><a href="#cite_ref-knowablemagazineorganic_10-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFKleiner2022" class="citation news cs1">Kleiner, Kurt (25 August 2022). <a rel="nofollow" class="external text" href="https://knowablemagazine.org/article/technology/2022/making-computer-chips-act-more-like-brain-cells">"Making computer chips act more like brain cells"</a>. <i>Knowable Magazine</i>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1146%2Fknowable-082422-1">10.1146/knowable-082422-1</a><span class="reference-accessdate">. Retrieved <span class="nowrap">23 September</span> 2022</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Knowable+Magazine&rft.atitle=Making+computer+chips+act+more+like+brain+cells&rft.date=2022-08-25&rft_id=info%3Adoi%2F10.1146%2Fknowable-082422-1&rft.aulast=Kleiner&rft.aufirst=Kurt&rft_id=https%3A%2F%2Fknowablemagazine.org%2Farticle%2Ftechnology%2F2022%2Fmaking-computer-chips-act-more-like-brain-cells&rfr_id=info%3Asid%2Fen.wikipedia.org%3AArtificial+neuron" class="Z3988"></span></span> </li> <li id="cite_note-11"><span class="mw-cite-backlink"><b><a href="#cite_ref-11">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFKeeneLubranoKazemzadehMelianas2020" class="citation journal cs1">Keene, Scott T.; Lubrano, Claudia; Kazemzadeh, Setareh; Melianas, Armantas; Tuchman, Yaakov; Polino, Giuseppina; Scognamiglio, Paola; Cinà, Lucio; Salleo, Alberto; van de Burgt, Yoeri; Santoro, Francesca (September 2020). <a rel="nofollow" class="external text" href="https://research.tue.nl/nl/publications/ad3d2f99-23e6-4072-934d-2b058d800e42">"A biohybrid synapse with neurotransmitter-mediated plasticity"</a>. <i>Nature Materials</i>. <b>19</b> (9): <span class="nowrap">969–</span>973. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2020NatMa..19..969K">2020NatMa..19..969K</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1038%2Fs41563-020-0703-y">10.1038/s41563-020-0703-y</a>. <a href="/wiki/ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/1476-4660">1476-4660</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/32541935">32541935</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:219691307">219691307</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Nature+Materials&rft.atitle=A+biohybrid+synapse+with+neurotransmitter-mediated+plasticity&rft.volume=19&rft.issue=9&rft.pages=%3Cspan+class%3D%22nowrap%22%3E969-%3C%2Fspan%3E973&rft.date=2020-09&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A219691307%23id-name%3DS2CID&rft_id=info%3Abibcode%2F2020NatMa..19..969K&rft.issn=1476-4660&rft_id=info%3Adoi%2F10.1038%2Fs41563-020-0703-y&rft_id=info%3Apmid%2F32541935&rft.aulast=Keene&rft.aufirst=Scott+T.&rft.au=Lubrano%2C+Claudia&rft.au=Kazemzadeh%2C+Setareh&rft.au=Melianas%2C+Armantas&rft.au=Tuchman%2C+Yaakov&rft.au=Polino%2C+Giuseppina&rft.au=Scognamiglio%2C+Paola&rft.au=Cin%C3%A0%2C+Lucio&rft.au=Salleo%2C+Alberto&rft.au=van+de+Burgt%2C+Yoeri&rft.au=Santoro%2C+Francesca&rft_id=https%3A%2F%2Fresearch.tue.nl%2Fnl%2Fpublications%2Fad3d2f99-23e6-4072-934d-2b058d800e42&rfr_id=info%3Asid%2Fen.wikipedia.org%3AArtificial+neuron" class="Z3988"></span> <ul><li>University press release: <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite class="citation news cs1"><a rel="nofollow" class="external text" href="https://medicalxpress.com/news/2020-06-artificial-synapse-cells.html">"Researchers develop artificial synapse that works with living cells"</a>. <i>Stanford University via medicalxpress.com</i><span class="reference-accessdate">. Retrieved <span class="nowrap">23 September</span> 2022</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Stanford+University+via+medicalxpress.com&rft.atitle=Researchers+develop+artificial+synapse+that+works+with+living+cells&rft_id=https%3A%2F%2Fmedicalxpress.com%2Fnews%2F2020-06-artificial-synapse-cells.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3AArtificial+neuron" class="Z3988"></span></li></ul> </span></li> <li id="cite_note-12"><span class="mw-cite-backlink"><b><a href="#cite_ref-12">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite class="citation news cs1"><a rel="nofollow" class="external text" href="https://www.newscientist.com/article/2332554-artificial-neuron-swaps-dopamine-with-rat-brain-cells-like-a-real-one/">"Artificial neuron swaps dopamine with rat brain cells like a real one"</a>. <i>New Scientist</i><span class="reference-accessdate">. Retrieved <span class="nowrap">16 September</span> 2022</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=New+Scientist&rft.atitle=Artificial+neuron+swaps+dopamine+with+rat+brain+cells+like+a+real+one&rft_id=https%3A%2F%2Fwww.newscientist.com%2Farticle%2F2332554-artificial-neuron-swaps-dopamine-with-rat-brain-cells-like-a-real-one%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3AArtificial+neuron" class="Z3988"></span></span> </li> <li id="cite_note-13"><span class="mw-cite-backlink"><b><a href="#cite_ref-13">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFWangWangWangYang2022" class="citation journal cs1">Wang, Ting; Wang, Ming; Wang, Jianwu; Yang, Le; Ren, Xueyang; Song, Gang; Chen, Shisheng; Yuan, Yuehui; Liu, Ruiqing; Pan, Liang; Li, Zheng; Leow, Wan Ru; Luo, Yifei; Ji, Shaobo; Cui, Zequn; He, Ke; Zhang, Feilong; Lv, Fengting; Tian, Yuanyuan; Cai, Kaiyu; Yang, Bowen; Niu, Jingyi; Zou, Haochen; Liu, Songrui; Xu, Guoliang; Fan, Xing; Hu, Benhui; Loh, Xian Jun; Wang, Lianhui; Chen, Xiaodong (8 August 2022). <span class="id-lock-subscription" title="Paid subscription required"><a rel="nofollow" class="external text" href="https://www.researchgate.net/publication/362561968">"A chemically mediated artificial neuron"</a></span>. <i>Nature Electronics</i>. <b>5</b> (9): <span class="nowrap">586–</span>595. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1038%2Fs41928-022-00803-0">10.1038/s41928-022-00803-0</a>. <a href="/wiki/Hdl_(identifier)" class="mw-redirect" title="Hdl (identifier)">hdl</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://hdl.handle.net/10356%2F163240">10356/163240</a></span>. <a href="/wiki/ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/2520-1131">2520-1131</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:251464760">251464760</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Nature+Electronics&rft.atitle=A+chemically+mediated+artificial+neuron&rft.volume=5&rft.issue=9&rft.pages=%3Cspan+class%3D%22nowrap%22%3E586-%3C%2Fspan%3E595&rft.date=2022-08-08&rft_id=info%3Ahdl%2F10356%2F163240&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A251464760%23id-name%3DS2CID&rft.issn=2520-1131&rft_id=info%3Adoi%2F10.1038%2Fs41928-022-00803-0&rft.aulast=Wang&rft.aufirst=Ting&rft.au=Wang%2C+Ming&rft.au=Wang%2C+Jianwu&rft.au=Yang%2C+Le&rft.au=Ren%2C+Xueyang&rft.au=Song%2C+Gang&rft.au=Chen%2C+Shisheng&rft.au=Yuan%2C+Yuehui&rft.au=Liu%2C+Ruiqing&rft.au=Pan%2C+Liang&rft.au=Li%2C+Zheng&rft.au=Leow%2C+Wan+Ru&rft.au=Luo%2C+Yifei&rft.au=Ji%2C+Shaobo&rft.au=Cui%2C+Zequn&rft.au=He%2C+Ke&rft.au=Zhang%2C+Feilong&rft.au=Lv%2C+Fengting&rft.au=Tian%2C+Yuanyuan&rft.au=Cai%2C+Kaiyu&rft.au=Yang%2C+Bowen&rft.au=Niu%2C+Jingyi&rft.au=Zou%2C+Haochen&rft.au=Liu%2C+Songrui&rft.au=Xu%2C+Guoliang&rft.au=Fan%2C+Xing&rft.au=Hu%2C+Benhui&rft.au=Loh%2C+Xian+Jun&rft.au=Wang%2C+Lianhui&rft.au=Chen%2C+Xiaodong&rft_id=https%3A%2F%2Fwww.researchgate.net%2Fpublication%2F362561968&rfr_id=info%3Asid%2Fen.wikipedia.org%3AArtificial+neuron" class="Z3988"></span></span> </li> <li id="cite_note-14"><span class="mw-cite-backlink"><b><a href="#cite_ref-14">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite class="citation news cs1"><a rel="nofollow" class="external text" href="https://www.independent.co.uk/life-style/gadgets-and-tech/news/brain-computing-memory-artificial-synapse-memristor-a9473671.html">"Scientists create tiny devices that work like the human brain"</a>. <i>The Independent</i>. April 20, 2020. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20200424110621/https://www.independent.co.uk/life-style/gadgets-and-tech/news/brain-computing-memory-artificial-synapse-memristor-a9473671.html">Archived</a> from the original on April 24, 2020<span class="reference-accessdate">. Retrieved <span class="nowrap">May 17,</span> 2020</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=The+Independent&rft.atitle=Scientists+create+tiny+devices+that+work+like+the+human+brain&rft.date=2020-04-20&rft_id=https%3A%2F%2Fwww.independent.co.uk%2Flife-style%2Fgadgets-and-tech%2Fnews%2Fbrain-computing-memory-artificial-synapse-memristor-a9473671.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3AArtificial+neuron" class="Z3988"></span></span> </li> <li id="cite_note-15"><span class="mw-cite-backlink"><b><a href="#cite_ref-15">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite class="citation news cs1"><a rel="nofollow" class="external text" href="https://phys.org/news/2020-04-unveil-electronics-mimic-human-brain.html">"Researchers unveil electronics that mimic the human brain in efficient learning"</a>. <i>phys.org</i>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20200528112833/https://phys.org/news/2020-04-unveil-electronics-mimic-human-brain.html">Archived</a> from the original on May 28, 2020<span class="reference-accessdate">. Retrieved <span class="nowrap">May 17,</span> 2020</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=phys.org&rft.atitle=Researchers+unveil+electronics+that+mimic+the+human+brain+in+efficient+learning&rft_id=https%3A%2F%2Fphys.org%2Fnews%2F2020-04-unveil-electronics-mimic-human-brain.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3AArtificial+neuron" class="Z3988"></span></span> </li> <li id="cite_note-16"><span class="mw-cite-backlink"><b><a href="#cite_ref-16">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFFuLiuGaoWard2020" class="citation journal cs1">Fu, Tianda; Liu, Xiaomeng; Gao, Hongyan; Ward, Joy E.; Liu, Xiaorong; Yin, Bing; Wang, Zhongrui; Zhuo, Ye; Walker, David J. F.; Joshua Yang, J.; Chen, Jianhan; Lovley, Derek R.; Yao, Jun (April 20, 2020). <a rel="nofollow" class="external text" href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7171104">"Bioinspired bio-voltage memristors"</a>. <i>Nature Communications</i>. <b>11</b> (1): 1861. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2020NatCo..11.1861F">2020NatCo..11.1861F</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.1038%2Fs41467-020-15759-y">10.1038/s41467-020-15759-y</a></span>. <a href="/wiki/PMC_(identifier)" class="mw-redirect" title="PMC (identifier)">PMC</a> <span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7171104">7171104</a></span>. <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/32313096">32313096</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Nature+Communications&rft.atitle=Bioinspired+bio-voltage+memristors&rft.volume=11&rft.issue=1&rft.pages=1861&rft.date=2020-04-20&rft_id=https%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fpmc%2Farticles%2FPMC7171104%23id-name%3DPMC&rft_id=info%3Apmid%2F32313096&rft_id=info%3Adoi%2F10.1038%2Fs41467-020-15759-y&rft_id=info%3Abibcode%2F2020NatCo..11.1861F&rft.aulast=Fu&rft.aufirst=Tianda&rft.au=Liu%2C+Xiaomeng&rft.au=Gao%2C+Hongyan&rft.au=Ward%2C+Joy+E.&rft.au=Liu%2C+Xiaorong&rft.au=Yin%2C+Bing&rft.au=Wang%2C+Zhongrui&rft.au=Zhuo%2C+Ye&rft.au=Walker%2C+David+J.+F.&rft.au=Joshua+Yang%2C+J.&rft.au=Chen%2C+Jianhan&rft.au=Lovley%2C+Derek+R.&rft.au=Yao%2C+Jun&rft_id=https%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fpmc%2Farticles%2FPMC7171104&rfr_id=info%3Asid%2Fen.wikipedia.org%3AArtificial+neuron" class="Z3988"></span></span> </li> <li id="cite_note-sciame-17"><span class="mw-cite-backlink"><b><a href="#cite_ref-sciame_17-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFBolakhe" class="citation news cs1">Bolakhe, Saugat. <a rel="nofollow" class="external text" href="https://www.scientificamerican.com/article/lego-robot-with-an-organic-brain-learns-to-navigate-a-maze/">"Lego Robot with an Organic 'Brain' Learns to Navigate a Maze"</a>. <i>Scientific American</i><span class="reference-accessdate">. Retrieved <span class="nowrap">1 February</span> 2022</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Scientific+American&rft.atitle=Lego+Robot+with+an+Organic+%27Brain%27+Learns+to+Navigate+a+Maze&rft.aulast=Bolakhe&rft.aufirst=Saugat&rft_id=https%3A%2F%2Fwww.scientificamerican.com%2Farticle%2Flego-robot-with-an-organic-brain-learns-to-navigate-a-maze%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3AArtificial+neuron" class="Z3988"></span></span> </li> <li id="cite_note-18"><span class="mw-cite-backlink"><b><a href="#cite_ref-18">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFKrauhausenKoutsourasMelianasKeene2021" class="citation journal cs1">Krauhausen, Imke; Koutsouras, Dimitrios A.; Melianas, Armantas; Keene, Scott T.; Lieberth, Katharina; Ledanseur, Hadrien; Sheelamanthula, Rajendar; Giovannitti, Alexander; Torricelli, Fabrizio; Mcculloch, Iain; Blom, Paul W. M.; Salleo, Alberto; Burgt, Yoeri van de; Gkoupidenis, Paschalis (December 2021). <a rel="nofollow" class="external text" href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8664264">"Organic neuromorphic electronics for sensorimotor integration and learning in robotics"</a>. <i>Science Advances</i>. <b>7</b> (50): eabl5068. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2021SciA....7.5068K">2021SciA....7.5068K</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1126%2Fsciadv.abl5068">10.1126/sciadv.abl5068</a>. <a href="/wiki/Hdl_(identifier)" class="mw-redirect" title="Hdl (identifier)">hdl</a>:<a rel="nofollow" class="external text" href="https://hdl.handle.net/10754%2F673986">10754/673986</a>. <a href="/wiki/PMC_(identifier)" class="mw-redirect" title="PMC (identifier)">PMC</a> <span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8664264">8664264</a></span>. <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/34890232">34890232</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:245046482">245046482</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Science+Advances&rft.atitle=Organic+neuromorphic+electronics+for+sensorimotor+integration+and+learning+in+robotics&rft.volume=7&rft.issue=50&rft.pages=eabl5068&rft.date=2021-12&rft_id=https%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fpmc%2Farticles%2FPMC8664264%23id-name%3DPMC&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A245046482%23id-name%3DS2CID&rft_id=info%3Abibcode%2F2021SciA....7.5068K&rft_id=info%3Apmid%2F34890232&rft_id=info%3Adoi%2F10.1126%2Fsciadv.abl5068&rft_id=info%3Ahdl%2F10754%2F673986&rft.aulast=Krauhausen&rft.aufirst=Imke&rft.au=Koutsouras%2C+Dimitrios+A.&rft.au=Melianas%2C+Armantas&rft.au=Keene%2C+Scott+T.&rft.au=Lieberth%2C+Katharina&rft.au=Ledanseur%2C+Hadrien&rft.au=Sheelamanthula%2C+Rajendar&rft.au=Giovannitti%2C+Alexander&rft.au=Torricelli%2C+Fabrizio&rft.au=Mcculloch%2C+Iain&rft.au=Blom%2C+Paul+W.+M.&rft.au=Salleo%2C+Alberto&rft.au=Burgt%2C+Yoeri+van+de&rft.au=Gkoupidenis%2C+Paschalis&rft_id=https%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fpmc%2Farticles%2FPMC8664264&rfr_id=info%3Asid%2Fen.wikipedia.org%3AArtificial+neuron" class="Z3988"></span></span> </li> <li id="cite_note-19"><span class="mw-cite-backlink"><b><a href="#cite_ref-19">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFSarkarLieberthPavlouFrank2022" class="citation journal cs1">Sarkar, Tanmoy; Lieberth, Katharina; Pavlou, Aristea; Frank, Thomas; Mailaender, Volker; McCulloch, Iain; Blom, Paul W. M.; Torriccelli, Fabrizio; Gkoupidenis, Paschalis (7 November 2022). <a rel="nofollow" class="external text" href="https://doi.org/10.1038%2Fs41928-022-00859-y">"An organic artificial spiking neuron for in situ neuromorphic sensing and biointerfacing"</a>. <i>Nature Electronics</i>. <b>5</b> (11): <span class="nowrap">774–</span>783. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.1038%2Fs41928-022-00859-y">10.1038/s41928-022-00859-y</a></span>. <a href="/wiki/Hdl_(identifier)" class="mw-redirect" title="Hdl (identifier)">hdl</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://hdl.handle.net/10754%2F686016">10754/686016</a></span>. <a href="/wiki/ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/2520-1131">2520-1131</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:253413801">253413801</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Nature+Electronics&rft.atitle=An+organic+artificial+spiking+neuron+for+in+situ+neuromorphic+sensing+and+biointerfacing&rft.volume=5&rft.issue=11&rft.pages=%3Cspan+class%3D%22nowrap%22%3E774-%3C%2Fspan%3E783&rft.date=2022-11-07&rft_id=info%3Ahdl%2F10754%2F686016&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A253413801%23id-name%3DS2CID&rft.issn=2520-1131&rft_id=info%3Adoi%2F10.1038%2Fs41928-022-00859-y&rft.aulast=Sarkar&rft.aufirst=Tanmoy&rft.au=Lieberth%2C+Katharina&rft.au=Pavlou%2C+Aristea&rft.au=Frank%2C+Thomas&rft.au=Mailaender%2C+Volker&rft.au=McCulloch%2C+Iain&rft.au=Blom%2C+Paul+W.+M.&rft.au=Torriccelli%2C+Fabrizio&rft.au=Gkoupidenis%2C+Paschalis&rft_id=https%3A%2F%2Fdoi.org%2F10.1038%252Fs41928-022-00859-y&rfr_id=info%3Asid%2Fen.wikipedia.org%3AArtificial+neuron" class="Z3988"></span></span> </li> <li id="cite_note-20"><span class="mw-cite-backlink"><b><a href="#cite_ref-20">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite class="citation journal cs1"><a rel="nofollow" class="external text" href="https://www.nature.com/articles/s41928-022-00862-3">"Artificial neurons emulate biological counterparts to enable synergetic operation"</a>. <i>Nature Electronics</i>. <b>5</b> (11): <span class="nowrap">721–</span>722. 10 November 2022. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1038%2Fs41928-022-00862-3">10.1038/s41928-022-00862-3</a>. <a href="/wiki/ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/2520-1131">2520-1131</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:253469402">253469402</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Nature+Electronics&rft.atitle=Artificial+neurons+emulate+biological+counterparts+to+enable+synergetic+operation&rft.volume=5&rft.issue=11&rft.pages=%3Cspan+class%3D%22nowrap%22%3E721-%3C%2Fspan%3E722&rft.date=2022-11-10&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A253469402%23id-name%3DS2CID&rft.issn=2520-1131&rft_id=info%3Adoi%2F10.1038%2Fs41928-022-00862-3&rft_id=https%3A%2F%2Fwww.nature.com%2Farticles%2Fs41928-022-00862-3&rfr_id=info%3Asid%2Fen.wikipedia.org%3AArtificial+neuron" class="Z3988"></span></span> </li> <li id="cite_note-Anthony2001-21"><span class="mw-cite-backlink"><b><a href="#cite_ref-Anthony2001_21-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFMartin_Anthony2001" class="citation book cs1">Martin Anthony (January 2001). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=qOy4yLBqhFcC&pg=PA3"><i>Discrete Mathematics of Neural Networks: Selected Topics</i></a>. SIAM. pp. 3–. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-89871-480-7" title="Special:BookSources/978-0-89871-480-7"><bdi>978-0-89871-480-7</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Discrete+Mathematics+of+Neural+Networks%3A+Selected+Topics&rft.pages=3-&rft.pub=SIAM&rft.date=2001-01&rft.isbn=978-0-89871-480-7&rft.au=Martin+Anthony&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DqOy4yLBqhFcC%26pg%3DPA3&rfr_id=info%3Asid%2Fen.wikipedia.org%3AArtificial+neuron" class="Z3988"></span></span> </li> <li id="cite_note-Aggarwal2014-22"><span class="mw-cite-backlink"><b><a href="#cite_ref-Aggarwal2014_22-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFCharu_C._Aggarwal2014" class="citation book cs1">Charu C. Aggarwal (25 July 2014). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=gJhBBAAAQBAJ&pg=PA209"><i>Data Classification: Algorithms and Applications</i></a>. CRC Press. pp. 209–. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1-4665-8674-1" title="Special:BookSources/978-1-4665-8674-1"><bdi>978-1-4665-8674-1</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Data+Classification%3A+Algorithms+and+Applications&rft.pages=209-&rft.pub=CRC+Press&rft.date=2014-07-25&rft.isbn=978-1-4665-8674-1&rft.au=Charu+C.+Aggarwal&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DgJhBBAAAQBAJ%26pg%3DPA209&rfr_id=info%3Asid%2Fen.wikipedia.org%3AArtificial+neuron" class="Z3988"></span></span> </li> <li id="cite_note-23"><span class="mw-cite-backlink"><b><a href="#cite_ref-23">^</a></b></span> <span class="reference-text"><a href="/wiki/Paul_Werbos" title="Paul Werbos">Paul Werbos</a>, Beyond Regression: New Tools for Prediction and Analysis in the Behavioral Sciences. PhD thesis, Harvard University, 1974</span> </li> <li id="cite_note-24"><span class="mw-cite-backlink"><b><a href="#cite_ref-24">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFWerbos1990" class="citation journal cs1"><a href="/wiki/Paul_Werbos" title="Paul Werbos">Werbos, P.J.</a> (1990). <a rel="nofollow" class="external text" href="https://zenodo.org/record/1262035">"Backpropagation through time: what it does and how to do it"</a>. <i>Proceedings of the IEEE</i>. <b>78</b> (10): <span class="nowrap">1550–</span>1560. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1109%2F5.58337">10.1109/5.58337</a>. <a href="/wiki/ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/0018-9219">0018-9219</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:18470994">18470994</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Proceedings+of+the+IEEE&rft.atitle=Backpropagation+through+time%3A+what+it+does+and+how+to+do+it&rft.volume=78&rft.issue=10&rft.pages=%3Cspan+class%3D%22nowrap%22%3E1550-%3C%2Fspan%3E1560&rft.date=1990&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A18470994%23id-name%3DS2CID&rft.issn=0018-9219&rft_id=info%3Adoi%2F10.1109%2F5.58337&rft.aulast=Werbos&rft.aufirst=P.J.&rft_id=https%3A%2F%2Fzenodo.org%2Frecord%2F1262035&rfr_id=info%3Asid%2Fen.wikipedia.org%3AArtificial+neuron" class="Z3988"></span></span> </li> <li id="cite_note-Hahnloser2000-25"><span class="mw-cite-backlink"><b><a href="#cite_ref-Hahnloser2000_25-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFHahnloserSarpeshkarMahowaldDouglas2000" class="citation journal cs1">Hahnloser, Richard H. R.; Sarpeshkar, Rahul; Mahowald, Misha A.; Douglas, Rodney J.; Seung, H. Sebastian (2000). "Digital selection and analogue amplification coexist in a cortex-inspired silicon circuit". <i>Nature</i>. <b>405</b> (6789): <span class="nowrap">947–</span>951. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2000Natur.405..947H">2000Natur.405..947H</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1038%2F35016072">10.1038/35016072</a>. <a href="/wiki/ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/0028-0836">0028-0836</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/10879535">10879535</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:4399014">4399014</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Nature&rft.atitle=Digital+selection+and+analogue+amplification+coexist+in+a+cortex-inspired+silicon+circuit&rft.volume=405&rft.issue=6789&rft.pages=%3Cspan+class%3D%22nowrap%22%3E947-%3C%2Fspan%3E951&rft.date=2000&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A4399014%23id-name%3DS2CID&rft_id=info%3Abibcode%2F2000Natur.405..947H&rft.issn=0028-0836&rft_id=info%3Adoi%2F10.1038%2F35016072&rft_id=info%3Apmid%2F10879535&rft.aulast=Hahnloser&rft.aufirst=Richard+H.+R.&rft.au=Sarpeshkar%2C+Rahul&rft.au=Mahowald%2C+Misha+A.&rft.au=Douglas%2C+Rodney+J.&rft.au=Seung%2C+H.+Sebastian&rfr_id=info%3Asid%2Fen.wikipedia.org%3AArtificial+neuron" class="Z3988"></span></span> </li> <li id="cite_note-Hahnloser2001-26"><span class="mw-cite-backlink"><b><a href="#cite_ref-Hahnloser2001_26-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFR_HahnloserH.S._Seung2001" class="citation conference cs1">R Hahnloser; H.S. Seung (2001). <i>Permitted and Forbidden Sets in Symmetric Threshold-Linear Networks</i>. NIPS 2001.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=conference&rft.btitle=Permitted+and+Forbidden+Sets+in+Symmetric+Threshold-Linear+Networks&rft.date=2001&rft.au=R+Hahnloser&rft.au=H.S.+Seung&rfr_id=info%3Asid%2Fen.wikipedia.org%3AArtificial+neuron" class="Z3988"></span></span> </li> <li id="cite_note-glorot2011-27"><span class="mw-cite-backlink"><b><a href="#cite_ref-glorot2011_27-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFXavier_GlorotAntoine_BordesYoshua_Bengio2011" class="citation conference cs1">Xavier Glorot; Antoine Bordes; <a href="/wiki/Yoshua_Bengio" title="Yoshua Bengio">Yoshua Bengio</a> (2011). <a rel="nofollow" class="external text" href="http://jmlr.org/proceedings/papers/v15/glorot11a/glorot11a.pdf"><i>Deep sparse rectifier neural networks</i></a> <span class="cs1-format">(PDF)</span>. AISTATS.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=conference&rft.btitle=Deep+sparse+rectifier+neural+networks&rft.date=2011&rft.au=Xavier+Glorot&rft.au=Antoine+Bordes&rft.au=Yoshua+Bengio&rft_id=http%3A%2F%2Fjmlr.org%2Fproceedings%2Fpapers%2Fv15%2Fglorot11a%2Fglorot11a.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3AArtificial+neuron" class="Z3988"></span></span> </li> <li id="cite_note-28"><span class="mw-cite-backlink"><b><a href="#cite_ref-28">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFYann_LeCunLeon_BottouGenevieve_B._OrrKlaus-Robert_Müller1998" class="citation encyclopaedia cs1"><a href="/wiki/Yann_LeCun" title="Yann LeCun">Yann LeCun</a>; <a href="/wiki/Leon_Bottou" class="mw-redirect" title="Leon Bottou">Leon Bottou</a>; Genevieve B. Orr; <a href="/wiki/Klaus-Robert_M%C3%BCller" title="Klaus-Robert Müller">Klaus-Robert Müller</a> (1998). <a rel="nofollow" class="external text" href="http://yann.lecun.com/exdb/publis/pdf/lecun-98b.pdf">"Efficient BackProp"</a> <span class="cs1-format">(PDF)</span>. In G. Orr; K. Müller (eds.). <i>Neural Networks: Tricks of the Trade</i>. Springer.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Efficient+BackProp&rft.btitle=Neural+Networks%3A+Tricks+of+the+Trade&rft.pub=Springer&rft.date=1998&rft.au=Yann+LeCun&rft.au=Leon+Bottou&rft.au=Genevieve+B.+Orr&rft.au=Klaus-Robert+M%C3%BCller&rft_id=http%3A%2F%2Fyann.lecun.com%2Fexdb%2Fpublis%2Fpdf%2Flecun-98b.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3AArtificial+neuron" class="Z3988"></span></span> </li> <li id="cite_note-maas2014-29"><span class="mw-cite-backlink"><b><a href="#cite_ref-maas2014_29-0">^</a></b></span> <span class="reference-text">Andrew L. Maas, Awni Y. Hannun, Andrew Y. Ng (2014). <a rel="nofollow" class="external text" href="https://ai.stanford.edu/~amaas/papers/relu_hybrid_icml2013_final.pdf">Rectifier Nonlinearities Improve Neural Network Acoustic Models</a>.</span> </li> </ol></div></div> <div class="mw-heading mw-heading2"><h2 id="Further_reading">Further reading</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Artificial_neuron&action=edit&section=15" title="Edit section: Further reading"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1239549316">.mw-parser-output .refbegin{margin-bottom:0.5em}.mw-parser-output .refbegin-hanging-indents>ul{margin-left:0}.mw-parser-output .refbegin-hanging-indents>ul>li{margin-left:0;padding-left:3.2em;text-indent:-3.2em}.mw-parser-output .refbegin-hanging-indents ul,.mw-parser-output .refbegin-hanging-indents ul li{list-style:none}@media(max-width:720px){.mw-parser-output .refbegin-hanging-indents>ul>li{padding-left:1.6em;text-indent:-1.6em}}.mw-parser-output .refbegin-columns{margin-top:0.3em}.mw-parser-output .refbegin-columns ul{margin-top:0}.mw-parser-output .refbegin-columns li{page-break-inside:avoid;break-inside:avoid-column}@media screen{.mw-parser-output .refbegin{font-size:90%}}</style><div class="refbegin" style=""> <ul><li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFMcCullochPitts1943" class="citation journal cs1"><a href="/wiki/Warren_McCulloch" class="mw-redirect" title="Warren McCulloch">McCulloch, Warren S.</a>; <a href="/wiki/Walter_Pitts" title="Walter Pitts">Pitts, Walter</a> (1943). "A logical calculus of the ideas immanent in nervous activity". <i>Bulletin of Mathematical Biophysics</i>. <b>5</b> (4): <span class="nowrap">115–</span>133. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1007%2Fbf02478259">10.1007/bf02478259</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Bulletin+of+Mathematical+Biophysics&rft.atitle=A+logical+calculus+of+the+ideas+immanent+in+nervous+activity&rft.volume=5&rft.issue=4&rft.pages=%3Cspan+class%3D%22nowrap%22%3E115-%3C%2Fspan%3E133&rft.date=1943&rft_id=info%3Adoi%2F10.1007%2Fbf02478259&rft.aulast=McCulloch&rft.aufirst=Warren+S.&rft.au=Pitts%2C+Walter&rfr_id=info%3Asid%2Fen.wikipedia.org%3AArtificial+neuron" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFSamardakNogaretJansonBalanov2009" class="citation journal cs1">Samardak, A.; Nogaret, A.; Janson, N. B.; Balanov, A. G.; Farrer, I.; Ritchie, D. A. (2009-06-05). <a rel="nofollow" class="external text" href="https://dspace.lboro.ac.uk/2134/12736">"Noise-Controlled Signal Transmission in a Multithread Semiconductor Neuron"</a>. <i>Physical Review Letters</i>. <b>102</b> (22): 226802. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2009PhRvL.102v6802S">2009PhRvL.102v6802S</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1103%2Fphysrevlett.102.226802">10.1103/physrevlett.102.226802</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/19658886">19658886</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:11211062">11211062</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Physical+Review+Letters&rft.atitle=Noise-Controlled+Signal+Transmission+in+a+Multithread+Semiconductor+Neuron&rft.volume=102&rft.issue=22&rft.pages=226802&rft.date=2009-06-05&rft_id=info%3Adoi%2F10.1103%2Fphysrevlett.102.226802&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A11211062%23id-name%3DS2CID&rft_id=info%3Apmid%2F19658886&rft_id=info%3Abibcode%2F2009PhRvL.102v6802S&rft.aulast=Samardak&rft.aufirst=A.&rft.au=Nogaret%2C+A.&rft.au=Janson%2C+N.+B.&rft.au=Balanov%2C+A.+G.&rft.au=Farrer%2C+I.&rft.au=Ritchie%2C+D.+A.&rft_id=https%3A%2F%2Fdspace.lboro.ac.uk%2F2134%2F12736&rfr_id=info%3Asid%2Fen.wikipedia.org%3AArtificial+neuron" class="Z3988"></span></li></ul> </div> <div class="mw-heading mw-heading2"><h2 id="External_links">External links</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Artificial_neuron&action=edit&section=16" title="Edit section: External links"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a rel="nofollow" class="external text" href="https://www.youtube.com/watch?v=NhTZnnJJP64">Artifical [<i>sic</i>] neuron mimicks function of human cells</a></li> <li><a rel="nofollow" class="external text" href="http://www.mind.ilstu.edu/curriculum/modOverview.php?modGUI=212">McCulloch-Pitts Neurons (Overview)</a></li></ul>    </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?useformat=desktop&type=1x1&usesul3=0" alt="" width="1" height="1" style="border: none; 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