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MuZero - Wikipedia
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a{color:var(--color-progressive)!important}}@media print{body.ns-0 .mw-parser-output .sidebar{display:none!important}}</style><table class="sidebar sidebar-collapse nomobile nowraplinks"><tbody><tr><td class="sidebar-pretitle">This article is part of the series on</td></tr><tr><th class="sidebar-title-with-pretitle"><a href="/wiki/Computer_chess" title="Computer chess">Chess programming</a></th></tr><tr><td class="sidebar-image"><span typeof="mw:File"><a href="/wiki/File:Chess_Programming.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/5/52/Chess_Programming.svg/150px-Chess_Programming.svg.png" decoding="async" width="150" height="150" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/52/Chess_Programming.svg/225px-Chess_Programming.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/52/Chess_Programming.svg/300px-Chess_Programming.svg.png 2x" data-file-width="64" data-file-height="64" /></a></span></td></tr><tr><td class="sidebar-content plainlist" style="text-align:left"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="color: var(--color-base)"><a href="/wiki/Board_representation_(computer_chess)" title="Board representation (computer chess)">Board representations</a></div><div class="sidebar-list-content mw-collapsible-content" style="text-align:center"> <ul><li><a href="/wiki/0x88" title="0x88">0x88</a></li> <li><a href="/wiki/Chess_bitboard" class="mw-redirect" title="Chess bitboard">Bitboards</a></li></ul></div></div></td> </tr><tr><td class="sidebar-content plainlist" style="text-align:left"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="color: var(--color-base)"><a href="/wiki/Evaluation_function" title="Evaluation function">Evaluation functions</a></div><div class="sidebar-list-content mw-collapsible-content" style="text-align:center"> <ul><li><a href="/wiki/Deep_neural_network" class="mw-redirect" title="Deep neural network">Deep neural networks</a> (<a href="/wiki/Transformer_(deep_learning_architecture)" title="Transformer (deep learning architecture)">Transformers</a>)</li> <li><a href="/wiki/Attention_(machine_learning)" title="Attention (machine learning)">Attention</a></li> <li><a href="/wiki/Efficiently_updatable_neural_network" title="Efficiently updatable neural network">Efficiently updatable neural networks</a></li> <li><a href="/wiki/Evaluation_function#Handcrafted_evaluation_functions" title="Evaluation function">Handcrafted evaluation functions</a></li> <li><a href="/wiki/Piece-square_table" class="mw-redirect" title="Piece-square table">Piece-square tables</a></li> <li><a href="/wiki/Reinforcement_learning" title="Reinforcement learning">Reinforcement learning</a></li> <li><a href="/wiki/Stochastic_gradient_descent" title="Stochastic gradient descent">Stochastic gradient descent</a></li> <li><a href="/wiki/Supervised_learning" title="Supervised learning">Supervised learning</a></li> <li><a href="/w/index.php?title=Texel_tuning&action=edit&redlink=1" class="new" title="Texel tuning (page does not exist)">Texel tuning</a></li> <li><a href="/wiki/Unsupervised_learning" title="Unsupervised learning">Unsupervised learning</a></li></ul></div></div></td> </tr><tr><td class="sidebar-content plainlist" style="text-align:left"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="color: var(--color-base)"><a href="/wiki/Graph_traversal" title="Graph traversal">Graph</a> and <a href="/wiki/Tree_traversal" title="Tree traversal">tree</a> search algorithms</div><div class="sidebar-list-content mw-collapsible-content" style="text-align:center"> <ul><li><a href="/wiki/Minimax" title="Minimax">Minimax</a></li> <li><a href="/wiki/Alpha-beta_pruning" class="mw-redirect" title="Alpha-beta pruning">Alpha-beta pruning</a></li> <li><a href="/wiki/Principal_variation_search" title="Principal variation search">Principal variation search</a></li> <li><a href="/wiki/Quiescence_search" title="Quiescence search">Quiescence search</a></li> <li><a href="/wiki/Monte_Carlo_tree_search" title="Monte Carlo tree search">Monte Carlo tree search</a></li></ul></div></div></td> </tr><tr><td class="sidebar-content plainlist" style="text-align:left"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="color: var(--color-base)"><a href="/wiki/Chess_computer" class="mw-redirect" title="Chess computer">Chess computers</a></div><div class="sidebar-list-content mw-collapsible-content" style="text-align:center"> <ul><li><a href="/wiki/Belle_(chess_machine)" title="Belle (chess machine)">Belle</a></li> <li><a href="/wiki/ChessMachine" title="ChessMachine">ChessMachine</a></li> <li><a href="/wiki/ChipTest" title="ChipTest">ChipTest</a></li> <li><a href="/wiki/Cray_Blitz" title="Cray Blitz">Cray Blitz</a></li> <li><a href="/wiki/Deep_Blue_(chess_computer)" title="Deep Blue (chess computer)">Deep Blue</a></li> <li><a href="/wiki/Deep_Thought_(chess_computer)" title="Deep Thought (chess computer)">Deep Thought</a></li> <li><a href="/wiki/HiTech" title="HiTech">HiTech</a></li> <li><a href="/wiki/Hydra_(chess)" title="Hydra (chess)">Hydra</a></li> <li><a href="/wiki/Mephisto_(chess_computer)" title="Mephisto (chess computer)">Mephisto</a></li> <li><a href="/wiki/Saitek" title="Saitek">Saitek</a></li></ul></div></div></td> </tr><tr><td class="sidebar-content plainlist" style="text-align:left"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="color: var(--color-base)"><a href="/wiki/Chess_engine" title="Chess engine">Chess engines</a></div><div class="sidebar-list-content mw-collapsible-content" style="text-align:center"> <ul><li><a href="/wiki/AlphaZero" title="AlphaZero">AlphaZero</a></li> <li><a href="/wiki/Chess_Tiger" title="Chess Tiger">Chess Tiger</a></li> <li><a href="/wiki/Crafty" title="Crafty">Crafty</a></li> <li><a href="/wiki/CuckooChess" title="CuckooChess">CuckooChess</a></li> <li><a href="/wiki/Deep_Fritz" class="mw-redirect" title="Deep Fritz">Deep Fritz</a></li> <li><a href="/wiki/Dragon_by_Komodo_Chess" class="mw-redirect" title="Dragon by Komodo Chess">Dragon by Komodo Chess</a></li> <li><a href="/wiki/Fairy-Max" class="mw-redirect" title="Fairy-Max">Fairy-Max</a></li> <li><a href="/wiki/Fritz_(chess)" title="Fritz (chess)">Fritz</a></li> <li><a href="/wiki/Fruit_(software)" title="Fruit (software)">Fruit</a></li> <li><a href="/wiki/GNU_Chess" title="GNU Chess">GNU Chess</a></li> <li><a href="/wiki/HIARCS" title="HIARCS">HIARCS</a></li> <li><a href="/wiki/Houdini_(chess)" title="Houdini (chess)">Houdini</a></li> <li><a href="/wiki/Ikarus_(chess)" title="Ikarus (chess)">Ikarus</a></li> <li><a href="/wiki/Junior_(chess_program)" title="Junior (chess program)">Junior</a></li> <li><a href="/wiki/KnightCap" title="KnightCap">KnightCap</a></li> <li><a href="/wiki/Komodo_(chess)" title="Komodo (chess)">Komodo</a></li> <li><a href="/wiki/Leela_Chess_Zero" title="Leela Chess Zero">Leela Chess Zero</a></li> <li><a href="/wiki/MChess_Pro" title="MChess Pro">MChess Pro</a></li> <li><a href="/wiki/Mittens_(chess_engine)" class="mw-redirect" title="Mittens (chess engine)">Mittens</a></li> <li><a class="mw-selflink selflink">MuZero</a></li> <li><a href="/wiki/Naum_(chess)" title="Naum (chess)">Naum</a></li> <li><a href="/wiki/REBEL_(chess)" title="REBEL (chess)">REBEL</a></li> <li><a href="/wiki/Rybka" title="Rybka">Rybka</a></li> <li><a href="/wiki/Shredder_(software)" title="Shredder (software)">Shredder</a></li> <li><a href="/wiki/Sjeng_(chess)" class="mw-redirect" title="Sjeng (chess)">Sjeng</a></li> <li><a href="/wiki/SmarThink" title="SmarThink">SmarThink</a></li> <li><a href="/wiki/Stockfish_(chess)" title="Stockfish (chess)">Stockfish</a></li> <li><a href="/wiki/Torch_(chess_engine)" class="mw-redirect" title="Torch (chess engine)">Torch</a></li> <li><a href="/wiki/Turochamp" title="Turochamp">Turochamp</a></li> <li><a href="/wiki/Zappa_(chess)" title="Zappa (chess)">Zappa</a></li></ul></div></div></td> </tr><tr><td class="sidebar-navbar"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374" /><style data-mw-deduplicate="TemplateStyles:r1239400231">.mw-parser-output .navbar{display:inline;font-size:88%;font-weight:normal}.mw-parser-output .navbar-collapse{float:left;text-align:left}.mw-parser-output .navbar-boxtext{word-spacing:0}.mw-parser-output .navbar ul{display:inline-block;white-space:nowrap;line-height:inherit}.mw-parser-output .navbar-brackets::before{margin-right:-0.125em;content:"[ "}.mw-parser-output .navbar-brackets::after{margin-left:-0.125em;content:" ]"}.mw-parser-output .navbar li{word-spacing:-0.125em}.mw-parser-output .navbar a>span,.mw-parser-output .navbar a>abbr{text-decoration:inherit}.mw-parser-output .navbar-mini abbr{font-variant:small-caps;border-bottom:none;text-decoration:none;cursor:inherit}.mw-parser-output .navbar-ct-full{font-size:114%;margin:0 7em}.mw-parser-output .navbar-ct-mini{font-size:114%;margin:0 4em}html.skin-theme-clientpref-night .mw-parser-output .navbar li a abbr{color:var(--color-base)!important}@media(prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .navbar li a abbr{color:var(--color-base)!important}}@media print{.mw-parser-output .navbar{display:none!important}}</style><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Chess_programming_series" title="Template:Chess programming series"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Chess_programming_series" title="Template talk:Chess programming series"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Chess_programming_series" title="Special:EditPage/Template:Chess programming series"><abbr title="Edit this template">e</abbr></a></li></ul></div></td></tr></tbody></table> <p><b>MuZero</b> is a <a href="/wiki/Computer_program" title="Computer program">computer program</a> developed by <a href="/wiki/Artificial_intelligence" title="Artificial intelligence">artificial intelligence</a> research company <a href="/wiki/DeepMind" class="mw-redirect" title="DeepMind">DeepMind</a> to master games without knowing their rules.<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><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><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> Its release in 2019 included benchmarks of its performance in <a href="/wiki/Go_(game)" title="Go (game)">go</a>, <a href="/wiki/Chess" title="Chess">chess</a>, <a href="/wiki/Shogi" title="Shogi">shogi</a>, and a standard suite of <a href="/wiki/Atari" title="Atari">Atari</a> games. The <a href="/wiki/Algorithm" title="Algorithm">algorithm</a> uses an approach similar to <a href="/wiki/AlphaZero" title="AlphaZero">AlphaZero</a>. It matched AlphaZero's performance in chess and shogi, improved on its performance in <a href="/wiki/Go_(game)" title="Go (game)">Go</a> (setting a new world record), and improved on the state of the art in mastering a suite of 57 Atari games (the Arcade Learning Environment), a visually-complex domain. </p><p>MuZero was trained via <a href="/wiki/Self-play_(reinforcement_learning_technique)" class="mw-redirect" title="Self-play (reinforcement learning technique)">self-play</a>, with no access to rules, opening books, or endgame tablebases. The trained algorithm used the same convolutional and residual architecture as AlphaZero, but with 20 percent fewer computation steps per node in the search tree.<sup id="cite_ref-4" class="reference"><a href="#cite_note-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> </p><p>MuZero’s capacity to plan and learn effectively without explicit rules makes it a groundbreaking achievement in <a href="/wiki/Reinforcement_learning" title="Reinforcement learning">reinforcement learning</a> and <a href="/wiki/Artificial_intelligence" title="Artificial intelligence">AI</a>, pushing the boundaries of what is possible in <a href="/wiki/Artificial_intelligence" title="Artificial intelligence">artificial intelligence</a>. </p> <style data-mw-deduplicate="TemplateStyles:r886046785">.mw-parser-output .toclimit-2 .toclevel-1 ul,.mw-parser-output .toclimit-3 .toclevel-2 ul,.mw-parser-output .toclimit-4 .toclevel-3 ul,.mw-parser-output .toclimit-5 .toclevel-4 ul,.mw-parser-output .toclimit-6 .toclevel-5 ul,.mw-parser-output .toclimit-7 .toclevel-6 ul{display:none}</style><div class="toclimit-3"><meta property="mw:PageProp/toc" /></div> <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=MuZero&action=edit&section=1" title="Edit section: History"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1244412712">.mw-parser-output .templatequote{overflow:hidden;margin:1em 0;padding:0 32px}.mw-parser-output .templatequotecite{line-height:1.5em;text-align:left;margin-top:0}@media(min-width:500px){.mw-parser-output .templatequotecite{padding-left:1.6em}}</style><blockquote class="templatequote"><p>MuZero really is discovering for itself how to build a model and understand it just from first principles.</p><div class="templatequotecite">— <cite>David Silver, DeepMind, <i>Wired</i><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></cite></div></blockquote> <p>On November 19, 2019, the DeepMind team released a <a href="/wiki/Preprint" title="Preprint">preprint</a> introducing MuZero. </p> <div class="mw-heading mw-heading3"><h3 id="Derivation_from_AlphaZero">Derivation from AlphaZero</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=MuZero&action=edit&section=2" title="Edit section: Derivation from AlphaZero"><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">Further information: <a href="/wiki/AlphaZero" title="AlphaZero">AlphaZero</a></div><p>MuZero (MZ) is a combination of the high-performance planning of the AlphaZero (AZ) <a href="/wiki/Algorithm" title="Algorithm">algorithm</a> with approaches to model-free reinforcement learning. The combination allows for more efficient training in classical planning regimes, such as Go, while also handling domains with much more complex inputs at each stage, such as visual video games. </p><p>MuZero was derived directly from AZ code, sharing its rules for setting <a href="/wiki/Hyperparameter_(machine_learning)" title="Hyperparameter (machine learning)">hyperparameters</a>. Differences between the approaches include:<sup id="cite_ref-preprint_6-0" class="reference"><a href="#cite_note-preprint-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> </p> <ul><li>AZ's planning process uses a <a href="/wiki/Simulator" class="mw-redirect" title="Simulator">simulator</a>. The simulator knows the rules of the game. It has to be explicitly programmed. A <a href="/wiki/Neural_network" title="Neural network">neural network</a> then predicts the policy and value of a future position. Perfect knowledge of game rules is used in modeling state transitions in the search tree, actions available at each node, and termination of a branch of the tree. MZ does not have access to the rules, and instead learns one with neural networks.</li> <li>AZ has a single model for the game (from board state to predictions); MZ has separate models for <i>representation</i> of the current state (from board state into its internal embedding), <i>dynamics</i> of states (how actions change representations of board states), and <i>prediction</i> of policy and value of a future position (given a state's representation).</li> <li>MZ's hidden model may be complex, and it may turn out it can host computation; exploring the details of the hidden model in a trained instance of MZ is a topic for future exploration.</li> <li>MZ does not expect a two-player game where winners take all. It works with standard reinforcement-learning scenarios, including single-agent environments with continuous intermediate rewards, possibly of arbitrary magnitude and with time discounting. AZ was designed for two-player games that could be won, drawn, or lost.</li></ul> <div class="mw-heading mw-heading3"><h3 id="Comparison_with_R2D2">Comparison with R2D2</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=MuZero&action=edit&section=3" title="Edit section: Comparison with R2D2"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The previous state of the art technique for learning to play the suite of Atari games was R2D2, the Recurrent Replay Distributed DQN.<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> </p><p>MuZero surpassed both R2D2's mean and median performance across the suite of games, though it did not do better in every game. </p> <div class="mw-heading mw-heading2"><h2 id="Training_and_results">Training and results</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=MuZero&action=edit&section=4" title="Edit section: Training and results"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>MuZero used 16 third-generation <a href="/wiki/Tensor_processing_unit" class="mw-redirect" title="Tensor processing unit">tensor processing units</a> (TPUs) for training, and 1000 TPUs for selfplay for board games, with 800 simulations per step and 8 TPUs for training and 32 TPUs for selfplay for Atari games, with 50 simulations per step. </p><p>AlphaZero used 64 second-generation TPUs for training, and 5000 first-generation TPUs for selfplay. As TPU design has improved (third-generation chips are 2x as powerful individually as second-generation chips, with further advances in bandwidth and networking across chips in a pod), these are comparable training setups. </p><p>R2D2 was trained for 5 days through 2M training steps. </p> <div class="mw-heading mw-heading3"><h3 id="Initial_results">Initial results</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=MuZero&action=edit&section=5" title="Edit section: Initial results"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>MuZero matched AlphaZero's performance in chess and Shogi after roughly 1 million training steps. It matched AZ's performance in Go after 500,000 training steps and surpassed it by 1 million steps. It matched R2D2's mean and median performance across the Atari game suite after 500 thousand training steps and surpassed it by 1 million steps, though it never performed well on 6 games in the suite. </p> <div class="mw-heading mw-heading2"><h2 id="Reactions_and_related_work">Reactions and related work</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=MuZero&action=edit&section=6" title="Edit section: Reactions and related work"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>MuZero was viewed as a significant advancement over AlphaZero, and a generalizable step forward in unsupervised learning techniques.<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><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> The work was seen as advancing understanding of how to compose systems from smaller components, a systems-level development more than a pure machine-learning development.<sup id="cite_ref-10" class="reference"><a href="#cite_note-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup> </p><p>While only pseudocode was released by the development team, Werner Duvaud produced an open source implementation based on that.<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> </p><p>MuZero has been used as a reference implementation in other work, for instance as a way to generate model-based behavior.<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> </p><p>In late 2021, a more efficient variant of MuZero was proposed, named EfficientZero. It "achieves 194.3 percent mean human performance and 109.0 percent median performance on the Atari 100k benchmark with only two hours of real-time game experience".<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>In early 2022, a variant of MuZero was proposed to play stochastic games (for example <a href="/wiki/2048_(video_game)" title="2048 (video game)">2048</a>, <a href="/wiki/Backgammon" title="Backgammon">backgammon</a>), called Stochastic MuZero, which uses afterstate dynamics and chance codes to account for the stochastic nature of the environment when training the dynamics network.<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> </p> <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=MuZero&action=edit&section=7" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/General_game_playing" title="General game playing">General game playing</a></li> <li><a href="/wiki/Unsupervised_learning" title="Unsupervised learning">Unsupervised learning</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=MuZero&action=edit&section=8" 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 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.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="CITEREFWiggers2019" class="citation web cs1">Wiggers, Kyle (20 November 2019). <a rel="nofollow" class="external text" href="https://venturebeat.com/2019/11/20/deepminds-muzero-teaches-itself-how-to-win-at-atari-chess-shogi-and-go/">"DeepMind's MuZero teaches itself how to win at Atari, chess, shogi, and Go"</a>. VentureBeat<span class="reference-accessdate">. Retrieved <span class="nowrap">22 July</span> 2020</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=DeepMind%27s+MuZero+teaches+itself+how+to+win+at+Atari%2C+chess%2C+shogi%2C+and+Go&rft.pub=VentureBeat&rft.date=2019-11-20&rft.aulast=Wiggers&rft.aufirst=Kyle&rft_id=https%3A%2F%2Fventurebeat.com%2F2019%2F11%2F20%2Fdeepminds-muzero-teaches-itself-how-to-win-at-atari-chess-shogi-and-go%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMuZero" 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="CITEREFFriedel" class="citation news cs1">Friedel, Frederic. <a rel="nofollow" class="external text" href="https://en.chessbase.com/post/muzero-figures-out-chess-rules-and-all">"MuZero figures out chess, rules and all"</a>. ChessBase GmbH<span class="reference-accessdate">. Retrieved <span class="nowrap">22 July</span> 2020</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=MuZero+figures+out+chess%2C+rules+and+all&rft.aulast=Friedel&rft.aufirst=Frederic&rft_id=https%3A%2F%2Fen.chessbase.com%2Fpost%2Fmuzero-figures-out-chess-rules-and-all&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMuZero" 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="CITEREFRodriguez" class="citation news cs1">Rodriguez, Jesus. <a rel="nofollow" class="external text" href="https://www.kdnuggets.com/2019/12/deepmind-unveils-muzero-agent-chess-shogi-atari-go.html">"DeepMind Unveils MuZero, a New Agent that Mastered Chess, Shogi, Atari and Go Without Knowing the Rules"</a>. <i>KDnuggets</i><span class="reference-accessdate">. Retrieved <span class="nowrap">22 July</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=KDnuggets&rft.atitle=DeepMind+Unveils+MuZero%2C+a+New+Agent+that+Mastered+Chess%2C+Shogi%2C+Atari+and+Go+Without+Knowing+the+Rules&rft.aulast=Rodriguez&rft.aufirst=Jesus&rft_id=https%3A%2F%2Fwww.kdnuggets.com%2F2019%2F12%2Fdeepmind-unveils-muzero-agent-chess-shogi-atari-go.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMuZero" class="Z3988"></span></span> </li> <li id="cite_note-4"><span class="mw-cite-backlink"><b><a href="#cite_ref-4">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFSchrittwieserAntonoglouHubertSimonyan2020" class="citation journal cs1">Schrittwieser, Julian; Antonoglou, Ioannis; Hubert, Thomas; Simonyan, Karen; Sifre, Laurent; Schmitt, Simon; Guez, Arthur; Lockhart, Edward; Hassabis, Demis; Graepel, Thore; Lillicrap, Timothy (2020). "Mastering Atari, Go, chess and shogi by planning with a learned model". <i>Nature</i>. <b>588</b> (7839): <span class="nowrap">604–</span>609. <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/1911.08265">1911.08265</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/2020Natur.588..604S">2020Natur.588..604S</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%2Fs41586-020-03051-4">10.1038/s41586-020-03051-4</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/33361790">33361790</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:208158225">208158225</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=Mastering+Atari%2C+Go%2C+chess+and+shogi+by+planning+with+a+learned+model&rft.volume=588&rft.issue=7839&rft.pages=%3Cspan+class%3D%22nowrap%22%3E604-%3C%2Fspan%3E609&rft.date=2020&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A208158225%23id-name%3DS2CID&rft_id=info%3Abibcode%2F2020Natur.588..604S&rft_id=info%3Aarxiv%2F1911.08265&rft_id=info%3Apmid%2F33361790&rft_id=info%3Adoi%2F10.1038%2Fs41586-020-03051-4&rft.aulast=Schrittwieser&rft.aufirst=Julian&rft.au=Antonoglou%2C+Ioannis&rft.au=Hubert%2C+Thomas&rft.au=Simonyan%2C+Karen&rft.au=Sifre%2C+Laurent&rft.au=Schmitt%2C+Simon&rft.au=Guez%2C+Arthur&rft.au=Lockhart%2C+Edward&rft.au=Hassabis%2C+Demis&rft.au=Graepel%2C+Thore&rft.au=Lillicrap%2C+Timothy&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMuZero" 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 class="citation magazine cs1"><a rel="nofollow" class="external text" href="https://www.wired.com/story/what-alphago-teach-how-people-learn/">"What AlphaGo Can Teach Us About How People Learn"</a>. <i>Wired</i>. <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/1059-1028">1059-1028</a><span class="reference-accessdate">. Retrieved <span class="nowrap">2020-12-25</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Wired&rft.atitle=What+AlphaGo+Can+Teach+Us+About+How+People+Learn&rft.issn=1059-1028&rft_id=https%3A%2F%2Fwww.wired.com%2Fstory%2Fwhat-alphago-teach-how-people-learn%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMuZero" class="Z3988"></span></span> </li> <li id="cite_note-preprint-6"><span class="mw-cite-backlink"><b><a href="#cite_ref-preprint_6-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFSilverHubertSchrittwieserAntonoglou2017" class="citation arxiv cs1"><a href="/wiki/David_Silver_(programmer)" class="mw-redirect" title="David Silver (programmer)">Silver, David</a>; Hubert, Thomas; Schrittwieser, Julian; Antonoglou, Ioannis; Lai, Matthew; Guez, Arthur; Lanctot, Marc; Sifre, Laurent; <a href="/wiki/Dharshan_Kumaran" title="Dharshan Kumaran">Kumaran, Dharshan</a>; Graepel, Thore; Lillicrap, Timothy; Simonyan, Karen; <a href="/wiki/Demis_Hassabis" title="Demis Hassabis">Hassabis, Demis</a> (5 December 2017). "Mastering Chess and Shogi by Self-Play with a General Reinforcement Learning Algorithm". <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/1712.01815">1712.01815</a></span> [<a rel="nofollow" class="external text" href="https://arxiv.org/archive/cs.AI">cs.AI</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=Mastering+Chess+and+Shogi+by+Self-Play+with+a+General+Reinforcement+Learning+Algorithm&rft.date=2017-12-05&rft_id=info%3Aarxiv%2F1712.01815&rft.aulast=Silver&rft.aufirst=David&rft.au=Hubert%2C+Thomas&rft.au=Schrittwieser%2C+Julian&rft.au=Antonoglou%2C+Ioannis&rft.au=Lai%2C+Matthew&rft.au=Guez%2C+Arthur&rft.au=Lanctot%2C+Marc&rft.au=Sifre%2C+Laurent&rft.au=Kumaran%2C+Dharshan&rft.au=Graepel%2C+Thore&rft.au=Lillicrap%2C+Timothy&rft.au=Simonyan%2C+Karen&rft.au=Hassabis%2C+Demis&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMuZero" 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="CITEREFKapturowskiOstrovskiQuanMunos" class="citation conference cs1">Kapturowski, Steven; Ostrovski, Georg; Quan, John; Munos, Remi; Dabney, Will. <a rel="nofollow" class="external text" href="https://openreview.net/pdf?id=r1lyTjAqYX"><i>RECURRENT EXPERIENCE REPLAY IN DISTRIBUTED REINFORCEMENT LEARNING</i></a>. ICLR 2019 – via Open Review.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=conference&rft.btitle=RECURRENT+EXPERIENCE+REPLAY+IN+DISTRIBUTED+REINFORCEMENT+LEARNING&rft.aulast=Kapturowski&rft.aufirst=Steven&rft.au=Ostrovski%2C+Georg&rft.au=Quan%2C+John&rft.au=Munos%2C+Remi&rft.au=Dabney%2C+Will&rft_id=https%3A%2F%2Fopenreview.net%2Fpdf%3Fid%3Dr1lyTjAqYX&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMuZero" 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="CITEREFShah2019" class="citation journal cs1">Shah, Rohin (27 November 2019). <a rel="nofollow" class="external text" href="https://www.lesswrong.com/posts/NSCBF7MTLF2HdhEnD/an-75-solving-atari-and-go-with-learned-game-models-and">"[AN #75]: Solving Atari and Go with learned game models, and thoughts from a MIRI employee - LessWrong 2.0"</a>. <i>www.lesswrong.com</i><span class="reference-accessdate">. Retrieved <span class="nowrap">2020-06-07</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=www.lesswrong.com&rft.atitle=%5BAN+%2375%5D%3A+Solving+Atari+and+Go+with+learned+game+models%2C+and+thoughts+from+a+MIRI+employee+-+LessWrong+2.0&rft.date=2019-11-27&rft.aulast=Shah&rft.aufirst=Rohin&rft_id=https%3A%2F%2Fwww.lesswrong.com%2Fposts%2FNSCBF7MTLF2HdhEnD%2Fan-75-solving-atari-and-go-with-learned-game-models-and&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMuZero" 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="CITEREFWu" class="citation web cs1">Wu, Jun. <a rel="nofollow" class="external text" href="https://www.forbes.com/sites/cognitiveworld/2019/12/10/reinforcement-learning-deep-learnings-partner/">"Reinforcement Learning, Deep Learning's Partner"</a>. <i>Forbes</i><span class="reference-accessdate">. Retrieved <span class="nowrap">2020-07-15</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=Forbes&rft.atitle=Reinforcement+Learning%2C+Deep+Learning%27s+Partner&rft.aulast=Wu&rft.aufirst=Jun&rft_id=https%3A%2F%2Fwww.forbes.com%2Fsites%2Fcognitiveworld%2F2019%2F12%2F10%2Freinforcement-learning-deep-learnings-partner%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMuZero" class="Z3988"></span></span> </li> <li id="cite_note-10"><span class="mw-cite-backlink"><b><a href="#cite_ref-10">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite class="citation web cs1"><a rel="nofollow" class="external text" href="http://cachestocaches.com/2019/12/my-state-of-the-field/">"Machine Learning & Robotics: My (biased) 2019 State of the Field"</a>. <i>cachestocaches.com</i><span class="reference-accessdate">. Retrieved <span class="nowrap">2020-07-15</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=cachestocaches.com&rft.atitle=Machine+Learning+%26+Robotics%3A+My+%28biased%29+2019+State+of+the+Field&rft_id=http%3A%2F%2Fcachestocaches.com%2F2019%2F12%2Fmy-state-of-the-field%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMuZero" 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="CITEREFDuvaud2020" class="citation cs2">Duvaud, Werner (2020-07-15), <a rel="nofollow" class="external text" href="https://github.com/werner-duvaud/muzero-general"><i>werner-duvaud/muzero-general</i></a><span class="reference-accessdate">, retrieved <span class="nowrap">2020-07-15</span></span></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=werner-duvaud%2Fmuzero-general&rft.date=2020-07-15&rft.aulast=Duvaud&rft.aufirst=Werner&rft_id=https%3A%2F%2Fgithub.com%2Fwerner-duvaud%2Fmuzero-general&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMuZero" class="Z3988"></span></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 id="CITEREFvan_SeijenNekoeiRacahChandar2020" class="citation arxiv cs1">van Seijen, Harm; Nekoei, Hadi; Racah, Evan; Chandar, Sarath (2020-07-06). "The LoCA Regret: A Consistent Metric to Evaluate Model-Based Behavior in Reinforcement Learning". <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/2007.03158">2007.03158</a></span> [<a rel="nofollow" class="external text" href="https://arxiv.org/archive/cs.stat">cs.stat</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=The+LoCA+Regret%3A+A+Consistent+Metric+to+Evaluate+Model-Based+Behavior+in+Reinforcement+Learning&rft.date=2020-07-06&rft_id=info%3Aarxiv%2F2007.03158&rft.aulast=van+Seijen&rft.aufirst=Harm&rft.au=Nekoei%2C+Hadi&rft.au=Racah%2C+Evan&rft.au=Chandar%2C+Sarath&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMuZero" 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="CITEREFYeLiuKurutachAbbeel2021" class="citation arxiv cs1">Ye, Weirui; Liu, Shaohuai; Kurutach, Thanard; Abbeel, Pieter; Gao, Yang (2021-12-11). "Mastering Atari Games with Limited Data". <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/2111.00210">2111.00210</a></span> [<a rel="nofollow" class="external text" href="https://arxiv.org/archive/cs.LG">cs.LG</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=Mastering+Atari+Games+with+Limited+Data&rft.date=2021-12-11&rft_id=info%3Aarxiv%2F2111.00210&rft.aulast=Ye&rft.aufirst=Weirui&rft.au=Liu%2C+Shaohuai&rft.au=Kurutach%2C+Thanard&rft.au=Abbeel%2C+Pieter&rft.au=Gao%2C+Yang&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMuZero" 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 id="CITEREFAntonoglouSchrittwieserOzairHubert2022" class="citation web cs1">Antonoglou, Ioannis; Schrittwieser, Julian; Ozair, Serjil; Hubert, Thomas; Silver, David (2022-01-28). <a rel="nofollow" class="external text" href="https://openreview.net/forum?id=X6D9bAHhBQ1">"Planning in Stochastic Environments with a Learned Model"</a><span class="reference-accessdate">. Retrieved <span class="nowrap">2023-12-12</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Planning+in+Stochastic+Environments+with+a+Learned+Model&rft.date=2022-01-28&rft.aulast=Antonoglou&rft.aufirst=Ioannis&rft.au=Schrittwieser%2C+Julian&rft.au=Ozair%2C+Serjil&rft.au=Hubert%2C+Thomas&rft.au=Silver%2C+David&rft_id=https%3A%2F%2Fopenreview.net%2Fforum%3Fid%3DX6D9bAHhBQ1&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMuZero" class="Z3988"></span></span> </li> </ol></div></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=MuZero&action=edit&section=9" title="Edit section: External links"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li>Initial <a rel="nofollow" class="external text" href="https://arxiv.org/pdf/1911.08265.pdf">MuZero preprint</a></li> <li><a rel="nofollow" class="external text" href="http://www.furidamu.org/blog/2020/05/02/opensource-muzero-implementations/">Open source implementations</a></li></ul> <div class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374" /><style data-mw-deduplicate="TemplateStyles:r1236075235">.mw-parser-output .navbox{box-sizing:border-box;border:1px solid #a2a9b1;width:100%;clear:both;font-size:88%;text-align:center;padding:1px;margin:1em auto 0}.mw-parser-output .navbox .navbox{margin-top:0}.mw-parser-output .navbox+.navbox,.mw-parser-output .navbox+.navbox-styles+.navbox{margin-top:-1px}.mw-parser-output .navbox-inner,.mw-parser-output .navbox-subgroup{width:100%}.mw-parser-output .navbox-group,.mw-parser-output .navbox-title,.mw-parser-output .navbox-abovebelow{padding:0.25em 1em;line-height:1.5em;text-align:center}.mw-parser-output .navbox-group{white-space:nowrap;text-align:right}.mw-parser-output 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title="Template:Google AI"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Google_AI" title="Template talk:Google AI"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Google_AI" title="Special:EditPage/Template:Google AI"><abbr title="Edit this template">e</abbr></a></li></ul></div><div id="Google_AI352" style="font-size:114%;margin:0 4em"><a href="/wiki/Google_AI" title="Google AI">Google AI</a></div></th></tr><tr><td class="navbox-abovebelow" colspan="2"><div> <ul><li><a href="/wiki/Google" title="Google">Google</a></li> <li><a href="/wiki/Google_Brain" title="Google Brain">Google Brain</a></li> <li><a href="/wiki/Google_DeepMind" title="Google DeepMind">Google DeepMind</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Computer programs</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:1%">AlphaGo</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:1%">Versions</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/AlphaGo" title="AlphaGo">AlphaGo</a> (2015)</li> <li><a href="/wiki/Master_(software)" title="Master (software)">Master</a> (2016)</li> <li><a href="/wiki/AlphaGo_Zero" title="AlphaGo Zero">AlphaGo Zero</a> (2017)</li> <li><a href="/wiki/AlphaZero" title="AlphaZero">AlphaZero</a> (2017)</li> <li><a class="mw-selflink selflink">MuZero</a> (2019)</li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Competitions</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/AlphaGo_versus_Fan_Hui" title="AlphaGo versus Fan Hui">Fan Hui</a> (2015)</li> <li><a href="/wiki/AlphaGo_versus_Lee_Sedol" title="AlphaGo versus Lee Sedol">Lee Sedol</a> (2016)</li> <li><a href="/wiki/AlphaGo_versus_Ke_Jie" title="AlphaGo versus Ke Jie">Ke Jie</a> (2017)</li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">In popular culture</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><i><a href="/wiki/AlphaGo_(film)" title="AlphaGo (film)">AlphaGo</a></i> (2017)</li> <li><i><a href="/wiki/The_MANIAC" title="The MANIAC">The MANIAC</a></i> (2023)</li></ul> </div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Other</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/AlphaFold" title="AlphaFold">AlphaFold</a> (2018)</li> <li><a href="/wiki/AlphaStar_(software)" title="AlphaStar (software)">AlphaStar</a> (2019)</li> <li><a href="/wiki/AlphaDev" title="AlphaDev">AlphaDev</a> (2023)</li> <li><a href="/wiki/AlphaGeometry" title="AlphaGeometry">AlphaGeometry</a> (2024)</li></ul> </div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Machine learning</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:1%">Neural networks</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Inception_(deep_learning_architecture)" title="Inception (deep learning architecture)">Inception</a> (2014)</li> <li><a href="/wiki/WaveNet" title="WaveNet">WaveNet</a> (2016)</li> <li><a href="/wiki/MobileNet" title="MobileNet">MobileNet</a> (2017)</li> <li><a href="/wiki/Transformer_(deep_learning_architecture)" title="Transformer (deep learning architecture)">Transformer</a> (2017)</li> <li><a href="/wiki/EfficientNet" title="EfficientNet">EfficientNet</a> (2019)</li> <li><a href="/wiki/Gato_(DeepMind)" title="Gato (DeepMind)">Gato</a> (2022)</li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Other</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Quantum_Artificial_Intelligence_Lab" title="Quantum Artificial Intelligence Lab">Quantum Artificial Intelligence Lab</a></li> <li><a href="/wiki/TensorFlow" title="TensorFlow">TensorFlow</a></li> <li><a href="/wiki/Tensor_Processing_Unit" title="Tensor Processing Unit">Tensor Processing Unit</a></li></ul> </div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Generative AI</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:1%">Chatbots</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Google_Assistant" title="Google Assistant">Assistant</a> (2016)</li> <li><a href="/wiki/Sparrow_(chatbot)" title="Sparrow (chatbot)">Sparrow</a> (2022)</li> <li><a href="/wiki/Gemini_(chatbot)" title="Gemini (chatbot)">Gemini</a> (2023)</li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Language models</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/BERT_(language_model)" title="BERT (language model)">BERT</a> (2018)</li> <li><a href="/wiki/XLNet" title="XLNet">XLNet</a> (2019)</li> <li><a href="/wiki/T5_(language_model)" title="T5 (language model)">T5</a> (2019)</li> <li><a href="/wiki/LaMDA" title="LaMDA">LaMDA</a> (2021)</li> <li><a href="/wiki/Chinchilla_(language_model)" title="Chinchilla (language model)">Chinchilla</a> (2022)</li> <li><a href="/wiki/PaLM" title="PaLM">PaLM</a> (2022)</li> <li><a href="/wiki/Gemini_(language_model)" title="Gemini (language model)">Gemini</a> (2023)</li> <li><a href="/wiki/VideoPoet" title="VideoPoet">VideoPoet</a> (2024)</li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Other</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/DreamBooth" title="DreamBooth">DreamBooth</a> (2022)</li> <li><a href="/wiki/NotebookLM" title="NotebookLM">NotebookLM</a> (2023)</li> <li><a href="/wiki/Google_Vids" title="Google Vids">Vids</a> (2024)</li></ul> </div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">See also</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li>"<a href="/wiki/Attention_Is_All_You_Need" title="Attention Is All You Need">Attention Is All You Need</a>"</li> <li><a href="/wiki/Future_of_Go_Summit" title="Future of Go Summit">Future of Go Summit</a></li> <li><a href="/wiki/Generative_pre-trained_transformer" title="Generative pre-trained transformer">Generative pre-trained transformer</a></li> <li><a href="/wiki/Google_Labs" title="Google Labs">Google Labs</a></li> <li><a href="/wiki/Google_Pixel" title="Google Pixel">Google Pixel</a></li> <li><a href="/wiki/Google_Workspace" title="Google Workspace">Google Workspace</a></li> <li><a href="/wiki/Robot_Constitution" title="Robot Constitution">Robot Constitution</a></li></ul> </div></td></tr><tr><td class="navbox-abovebelow" colspan="2"><div> <ul><li><span class="noviewer" typeof="mw:File"><span title="Category"><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/9/96/Symbol_category_class.svg/16px-Symbol_category_class.svg.png" decoding="async" width="16" height="16" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/9/96/Symbol_category_class.svg/23px-Symbol_category_class.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/9/96/Symbol_category_class.svg/31px-Symbol_category_class.svg.png 2x" data-file-width="180" data-file-height="185" /></span></span> <a href="/wiki/Category:Google_DeepMind" title="Category:Google DeepMind">Category</a></li> <li><span class="noviewer" typeof="mw:File"><span title="Commons page"><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/20px-Commons-logo.svg.png" decoding="async" width="12" height="16" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/40px-Commons-logo.svg.png 2x" data-file-width="1024" data-file-height="1376" /></span></span> <a href="https://commons.wikimedia.org/wiki/Category:DeepMind" class="extiw" title="commons:Category:DeepMind">Commons</a></li></ul> </div></td></tr></tbody></table></div> <div class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374" /><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236075235" /></div><div role="navigation" class="navbox" aria-labelledby="Artificial_intelligence_(AI)752" style="padding:3px"><table class="nowraplinks hlist mw-collapsible autocollapse navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374" /><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239400231" /><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Artificial_intelligence_navbox" title="Template:Artificial intelligence navbox"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Artificial_intelligence_navbox" title="Template talk:Artificial intelligence navbox"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Artificial_intelligence_navbox" title="Special:EditPage/Template:Artificial intelligence navbox"><abbr title="Edit this template">e</abbr></a></li></ul></div><div id="Artificial_intelligence_(AI)752" style="font-size:114%;margin:0 4em"><a href="/wiki/Artificial_intelligence" title="Artificial intelligence">Artificial intelligence</a> (AI)</div></th></tr><tr><td class="navbox-abovebelow" colspan="2"><div><a href="/wiki/History_of_artificial_intelligence" title="History of artificial intelligence">History</a> (<a href="/wiki/Timeline_of_artificial_intelligence" title="Timeline of artificial intelligence">timeline</a>)</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Concepts</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Parameter" title="Parameter">Parameter</a> <ul><li><a href="/wiki/Hyperparameter_(machine_learning)" title="Hyperparameter (machine learning)">Hyperparameter</a></li></ul></li> <li><a href="/wiki/Loss_functions_for_classification" title="Loss functions for classification">Loss functions</a></li> <li><a href="/wiki/Regression_analysis" title="Regression analysis">Regression</a> <ul><li><a href="/wiki/Bias%E2%80%93variance_tradeoff" title="Bias–variance tradeoff">Bias–variance tradeoff</a></li> <li><a href="/wiki/Double_descent" title="Double descent">Double descent</a></li> <li><a href="/wiki/Overfitting" title="Overfitting">Overfitting</a></li></ul></li> <li><a href="/wiki/Cluster_analysis" title="Cluster analysis">Clustering</a></li> <li><a href="/wiki/Gradient_descent" title="Gradient descent">Gradient descent</a> <ul><li><a href="/wiki/Stochastic_gradient_descent" title="Stochastic gradient descent">SGD</a></li> <li><a href="/wiki/Quasi-Newton_method" title="Quasi-Newton method">Quasi-Newton method</a></li> <li><a href="/wiki/Conjugate_gradient_method" title="Conjugate gradient method">Conjugate gradient method</a></li></ul></li> <li><a href="/wiki/Backpropagation" title="Backpropagation">Backpropagation</a></li> <li><a href="/wiki/Attention_(machine_learning)" title="Attention (machine learning)">Attention</a></li> <li><a href="/wiki/Convolution" title="Convolution">Convolution</a></li> <li><a href="/wiki/Normalization_(machine_learning)" title="Normalization (machine learning)">Normalization</a> <ul><li><a href="/wiki/Batch_normalization" title="Batch normalization">Batchnorm</a></li></ul></li> <li><a href="/wiki/Activation_function" title="Activation function">Activation</a> <ul><li><a href="/wiki/Softmax_function" title="Softmax function">Softmax</a></li> <li><a href="/wiki/Sigmoid_function" title="Sigmoid function">Sigmoid</a></li> <li><a href="/wiki/Rectifier_(neural_networks)" title="Rectifier (neural networks)">Rectifier</a></li></ul></li> <li><a href="/wiki/Gating_mechanism" title="Gating mechanism">Gating</a></li> <li><a href="/wiki/Weight_initialization" title="Weight initialization">Weight initialization</a></li> <li><a href="/wiki/Regularization_(mathematics)" title="Regularization (mathematics)">Regularization</a></li> <li><a href="/wiki/Training,_validation,_and_test_data_sets" title="Training, validation, and test data sets">Datasets</a> <ul><li><a href="/wiki/Data_augmentation" title="Data augmentation">Augmentation</a></li></ul></li> <li><a href="/wiki/Prompt_engineering" title="Prompt engineering">Prompt engineering</a></li> <li><a href="/wiki/Reinforcement_learning" title="Reinforcement learning">Reinforcement learning</a> <ul><li><a href="/wiki/Q-learning" title="Q-learning">Q-learning</a></li> <li><a href="/wiki/State%E2%80%93action%E2%80%93reward%E2%80%93state%E2%80%93action" title="State–action–reward–state–action">SARSA</a></li> <li><a href="/wiki/Imitation_learning" title="Imitation learning">Imitation</a></li> <li><a href="/wiki/Policy_gradient_method" title="Policy gradient method">Policy gradient</a></li></ul></li> <li><a href="/wiki/Diffusion_process" title="Diffusion process">Diffusion</a></li> <li><a href="/wiki/Latent_diffusion_model" title="Latent diffusion model">Latent diffusion model</a></li> <li><a href="/wiki/Autoregressive_model" title="Autoregressive model">Autoregression</a></li> <li><a href="/wiki/Adversarial_machine_learning" title="Adversarial machine learning">Adversary</a></li> <li><a href="/wiki/Retrieval-augmented_generation" title="Retrieval-augmented generation">RAG</a></li> <li><a href="/wiki/Uncanny_valley" title="Uncanny valley">Uncanny valley</a></li> <li><a href="/wiki/Reinforcement_learning_from_human_feedback" title="Reinforcement learning from human feedback">RLHF</a></li> <li><a href="/wiki/Self-supervised_learning" title="Self-supervised learning">Self-supervised learning</a></li> <li><a href="/wiki/Recursive_self-improvement" title="Recursive self-improvement">Recursive self-improvement</a></li> <li><a href="/wiki/Word_embedding" title="Word embedding">Word embedding</a></li> <li><a href="/wiki/Hallucination_(artificial_intelligence)" title="Hallucination (artificial intelligence)">Hallucination</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Applications</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Machine_learning" title="Machine learning">Machine learning</a> <ul><li><a href="/wiki/Prompt_engineering#In-context_learning" title="Prompt engineering">In-context learning</a></li></ul></li> <li><a href="/wiki/Neural_network_(machine_learning)" title="Neural network (machine learning)">Artificial neural network</a> <ul><li><a href="/wiki/Deep_learning" title="Deep learning">Deep learning</a></li></ul></li> <li><a href="/wiki/Language_model" title="Language model">Language model</a> <ul><li><a href="/wiki/Large_language_model" title="Large language model">Large language model</a></li> <li><a href="/wiki/Neural_machine_translation" title="Neural machine translation">NMT</a></li></ul></li> <li><a href="/wiki/Artificial_general_intelligence" title="Artificial general intelligence">Artificial general intelligence</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Implementations</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:1%">Audio–visual</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/AlexNet" title="AlexNet">AlexNet</a></li> <li><a href="/wiki/WaveNet" title="WaveNet">WaveNet</a></li> <li><a href="/wiki/Human_image_synthesis" title="Human image synthesis">Human image synthesis</a></li> <li><a href="/wiki/Handwriting_recognition" title="Handwriting recognition">HWR</a></li> <li><a href="/wiki/Optical_character_recognition" title="Optical character recognition">OCR</a></li> <li><a href="/wiki/Deep_learning_speech_synthesis" title="Deep learning speech synthesis">Speech synthesis</a> <ul><li><a href="/wiki/15.ai" title="15.ai">15.ai</a></li> <li><a href="/wiki/ElevenLabs" title="ElevenLabs">ElevenLabs</a></li></ul></li> <li><a href="/wiki/Speech_recognition" title="Speech recognition">Speech recognition</a> <ul><li><a href="/wiki/Whisper_(speech_recognition_system)" title="Whisper (speech recognition system)">Whisper</a></li></ul></li> <li><a href="/wiki/Facial_recognition_system" title="Facial recognition system">Facial recognition</a></li> <li><a href="/wiki/AlphaFold" title="AlphaFold">AlphaFold</a></li> <li><a href="/wiki/Text-to-image_model" title="Text-to-image model">Text-to-image models</a> <ul><li><a href="/wiki/Aurora_(text-to-image_model)" class="mw-redirect" title="Aurora (text-to-image model)">Aurora</a></li> <li><a href="/wiki/DALL-E" title="DALL-E">DALL-E</a></li> <li><a href="/wiki/Adobe_Firefly" title="Adobe Firefly">Firefly</a></li> <li><a href="/wiki/Flux_(text-to-image_model)" title="Flux (text-to-image model)">Flux</a></li> <li><a href="/wiki/Ideogram_(text-to-image_model)" title="Ideogram (text-to-image model)">Ideogram</a></li> <li><a href="/wiki/Imagen_(text-to-image_model)" title="Imagen (text-to-image model)">Imagen</a></li> <li><a href="/wiki/Midjourney" title="Midjourney">Midjourney</a></li> <li><a href="/wiki/Stable_Diffusion" title="Stable Diffusion">Stable Diffusion</a></li></ul></li> <li><a href="/wiki/Text-to-video_model" title="Text-to-video model">Text-to-video models</a> <ul><li><a href="/wiki/Dream_Machine_(text-to-video_model)" title="Dream Machine (text-to-video model)">Dream Machine</a></li> <li><a href="/wiki/Runway_(company)#Gen-3_Alpha" title="Runway (company)">Gen-3 Alpha</a></li> <li><a href="/wiki/MiniMax_(company)#Hailuo_AI" title="MiniMax (company)">Hailuo AI</a></li> <li><a href="/wiki/Kling_(text-to-video_model)" class="mw-redirect" title="Kling (text-to-video model)">Kling</a></li> <li><a href="/wiki/Sora_(text-to-video_model)" title="Sora (text-to-video model)">Sora</a></li> <li><a href="/wiki/Google_DeepMind#Video_model" title="Google DeepMind">Veo</a></li></ul></li> <li><a href="/wiki/Music_and_artificial_intelligence" title="Music and artificial intelligence">Music generation</a> <ul><li><a href="/wiki/Suno_AI" title="Suno AI">Suno AI</a></li> <li><a href="/wiki/Udio" title="Udio">Udio</a></li></ul></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Text</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Word2vec" title="Word2vec">Word2vec</a></li> <li><a href="/wiki/Seq2seq" title="Seq2seq">Seq2seq</a></li> <li><a href="/wiki/GloVe" title="GloVe">GloVe</a></li> <li><a href="/wiki/BERT_(language_model)" title="BERT (language model)">BERT</a></li> <li><a href="/wiki/T5_(language_model)" title="T5 (language model)">T5</a></li> <li><a href="/wiki/Llama_(language_model)" title="Llama (language model)">Llama</a></li> <li><a href="/wiki/Chinchilla_(language_model)" title="Chinchilla (language model)">Chinchilla AI</a></li> <li><a href="/wiki/PaLM" title="PaLM">PaLM</a></li> <li><a href="/wiki/Generative_pre-trained_transformer" title="Generative pre-trained transformer">GPT</a> <ul><li><a href="/wiki/GPT-1" title="GPT-1">1</a></li> <li><a href="/wiki/GPT-2" title="GPT-2">2</a></li> <li><a href="/wiki/GPT-3" title="GPT-3">3</a></li> <li><a href="/wiki/GPT-J" title="GPT-J">J</a></li> <li><a href="/wiki/ChatGPT" title="ChatGPT">ChatGPT</a></li> <li><a href="/wiki/GPT-4" title="GPT-4">4</a></li> <li><a href="/wiki/GPT-4o" title="GPT-4o">4o</a></li> <li><a href="/wiki/GPT-4.5" title="GPT-4.5">4.5</a></li> <li><a href="/wiki/OpenAI_o1" title="OpenAI o1">o1</a></li> <li><a href="/wiki/OpenAI_o3" title="OpenAI o3">o3</a></li></ul></li> <li><a href="/wiki/Claude_(language_model)" title="Claude (language model)">Claude</a></li> <li><a href="/wiki/Gemini_(language_model)" title="Gemini (language model)">Gemini</a> <ul><li><a href="/wiki/Gemini_(chatbot)" title="Gemini (chatbot)">chatbot</a></li></ul></li> <li><a href="/wiki/Grok_(chatbot)" title="Grok (chatbot)">Grok</a></li> <li><a href="/wiki/LaMDA" title="LaMDA">LaMDA</a></li> <li><a href="/wiki/BLOOM_(language_model)" title="BLOOM (language model)">BLOOM</a></li> <li><a href="/wiki/Project_Debater" title="Project Debater">Project Debater</a></li> <li><a href="/wiki/IBM_Watson" title="IBM Watson">IBM Watson</a></li> <li><a href="/wiki/IBM_Watsonx" title="IBM Watsonx">IBM Watsonx</a></li> <li><a href="/wiki/IBM_Granite" title="IBM Granite">Granite</a></li> <li><a href="/wiki/Huawei_PanGu" title="Huawei PanGu">PanGu-Σ</a></li> <li><a href="/wiki/DeepSeek_(chatbot)" title="DeepSeek (chatbot)">DeepSeek</a></li> <li><a href="/wiki/Qwen" title="Qwen">Qwen</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Decisional</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/AlphaGo" title="AlphaGo">AlphaGo</a></li> <li><a href="/wiki/AlphaZero" title="AlphaZero">AlphaZero</a></li> <li><a href="/wiki/OpenAI_Five" title="OpenAI Five">OpenAI Five</a></li> <li><a href="/wiki/Self-driving_car" title="Self-driving car">Self-driving car</a></li> <li><a class="mw-selflink selflink">MuZero</a></li> <li><a href="/wiki/Action_selection" title="Action selection">Action selection</a> <ul><li><a href="/wiki/AutoGPT" title="AutoGPT">AutoGPT</a></li></ul></li> <li><a href="/wiki/Robot_control" title="Robot control">Robot control</a></li></ul> </div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">People</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Alan_Turing" title="Alan Turing">Alan Turing</a></li> <li><a href="/wiki/Warren_Sturgis_McCulloch" title="Warren Sturgis McCulloch">Warren Sturgis McCulloch</a></li> <li><a href="/wiki/Walter_Pitts" title="Walter Pitts">Walter Pitts</a></li> <li><a href="/wiki/John_von_Neumann" title="John von Neumann">John von Neumann</a></li> <li><a href="/wiki/Claude_Shannon" title="Claude Shannon">Claude Shannon</a></li> <li><a href="/wiki/Marvin_Minsky" title="Marvin Minsky">Marvin Minsky</a></li> <li><a href="/wiki/John_McCarthy_(computer_scientist)" title="John McCarthy (computer scientist)">John McCarthy</a></li> <li><a href="/wiki/Nathaniel_Rochester_(computer_scientist)" title="Nathaniel Rochester (computer scientist)">Nathaniel Rochester</a></li> <li><a href="/wiki/Allen_Newell" title="Allen Newell">Allen Newell</a></li> <li><a href="/wiki/Cliff_Shaw" title="Cliff Shaw">Cliff Shaw</a></li> <li><a href="/wiki/Herbert_A._Simon" title="Herbert A. Simon">Herbert A. Simon</a></li> <li><a href="/wiki/Oliver_Selfridge" title="Oliver Selfridge">Oliver Selfridge</a></li> <li><a href="/wiki/Frank_Rosenblatt" title="Frank Rosenblatt">Frank Rosenblatt</a></li> <li><a href="/wiki/Bernard_Widrow" title="Bernard Widrow">Bernard Widrow</a></li> <li><a href="/wiki/Joseph_Weizenbaum" title="Joseph Weizenbaum">Joseph Weizenbaum</a></li> <li><a href="/wiki/Seymour_Papert" title="Seymour Papert">Seymour Papert</a></li> <li><a href="/wiki/Seppo_Linnainmaa" title="Seppo Linnainmaa">Seppo Linnainmaa</a></li> <li><a href="/wiki/Paul_Werbos" title="Paul Werbos">Paul Werbos</a></li> <li><a href="/wiki/J%C3%BCrgen_Schmidhuber" title="Jürgen Schmidhuber">Jürgen Schmidhuber</a></li> <li><a href="/wiki/Yann_LeCun" title="Yann LeCun">Yann LeCun</a></li> <li><a href="/wiki/Geoffrey_Hinton" title="Geoffrey Hinton">Geoffrey Hinton</a></li> <li><a href="/wiki/John_Hopfield" title="John Hopfield">John Hopfield</a></li> <li><a href="/wiki/Yoshua_Bengio" title="Yoshua Bengio">Yoshua Bengio</a></li> <li><a href="/wiki/Lotfi_A._Zadeh" title="Lotfi A. Zadeh">Lotfi A. Zadeh</a></li> <li><a href="/wiki/Stephen_Grossberg" title="Stephen Grossberg">Stephen Grossberg</a></li> <li><a href="/wiki/Alex_Graves_(computer_scientist)" title="Alex Graves (computer scientist)">Alex Graves</a></li> <li><a href="/wiki/Andrew_Ng" title="Andrew Ng">Andrew Ng</a></li> <li><a href="/wiki/Fei-Fei_Li" title="Fei-Fei Li">Fei-Fei Li</a></li> <li><a href="/wiki/Alex_Krizhevsky" title="Alex Krizhevsky">Alex Krizhevsky</a></li> <li><a href="/wiki/Ilya_Sutskever" title="Ilya Sutskever">Ilya Sutskever</a></li> <li><a href="/wiki/Demis_Hassabis" title="Demis Hassabis">Demis Hassabis</a></li> <li><a href="/wiki/David_Silver_(computer_scientist)" title="David Silver (computer scientist)">David Silver</a></li> <li><a href="/wiki/Ian_Goodfellow" title="Ian Goodfellow">Ian Goodfellow</a></li> <li><a href="/wiki/Andrej_Karpathy" title="Andrej Karpathy">Andrej Karpathy</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Architectures</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Neural_Turing_machine" title="Neural Turing machine">Neural Turing machine</a></li> <li><a href="/wiki/Differentiable_neural_computer" title="Differentiable neural computer">Differentiable neural computer</a></li> <li><a href="/wiki/Transformer_(deep_learning_architecture)" title="Transformer (deep learning architecture)">Transformer</a> <ul><li><a href="/wiki/Vision_transformer" title="Vision transformer">Vision transformer (ViT)</a></li></ul></li> <li><a href="/wiki/Recurrent_neural_network" title="Recurrent neural network">Recurrent neural network (RNN)</a></li> <li><a href="/wiki/Long_short-term_memory" title="Long short-term memory">Long short-term memory (LSTM)</a></li> <li><a href="/wiki/Gated_recurrent_unit" title="Gated recurrent unit">Gated recurrent unit (GRU)</a></li> <li><a href="/wiki/Echo_state_network" title="Echo state network">Echo state network</a></li> <li><a href="/wiki/Multilayer_perceptron" title="Multilayer perceptron">Multilayer perceptron (MLP)</a></li> <li><a href="/wiki/Convolutional_neural_network" title="Convolutional neural network">Convolutional neural network (CNN)</a></li> <li><a href="/wiki/Residual_neural_network" title="Residual neural network">Residual neural network (RNN)</a></li> <li><a href="/wiki/Highway_network" title="Highway network">Highway network</a></li> <li><a href="/wiki/Mamba_(deep_learning_architecture)" title="Mamba (deep learning architecture)">Mamba</a></li> <li><a href="/wiki/Autoencoder" title="Autoencoder">Autoencoder</a></li> <li><a href="/wiki/Variational_autoencoder" title="Variational autoencoder">Variational autoencoder (VAE)</a></li> <li><a href="/wiki/Generative_adversarial_network" title="Generative adversarial network">Generative adversarial network (GAN)</a></li> <li><a href="/wiki/Graph_neural_network" title="Graph neural network">Graph neural network (GNN)</a></li></ul> </div></td></tr><tr><td class="navbox-abovebelow" colspan="2"><div> <ul><li><span class="noviewer" typeof="mw:File"><a href="/wiki/File:Symbol_portal_class.svg" class="mw-file-description" title="Portal"><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/e/e2/Symbol_portal_class.svg/16px-Symbol_portal_class.svg.png" decoding="async" width="16" height="16" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/e/e2/Symbol_portal_class.svg/23px-Symbol_portal_class.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/e/e2/Symbol_portal_class.svg/31px-Symbol_portal_class.svg.png 2x" data-file-width="180" data-file-height="185" /></a></span> Portals <ul><li><a href="/wiki/Portal:Technology" title="Portal:Technology">Technology</a></li></ul></li> <li><span class="noviewer" typeof="mw:File"><span title="Category"><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/9/96/Symbol_category_class.svg/16px-Symbol_category_class.svg.png" decoding="async" width="16" height="16" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/9/96/Symbol_category_class.svg/23px-Symbol_category_class.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/9/96/Symbol_category_class.svg/31px-Symbol_category_class.svg.png 2x" data-file-width="180" data-file-height="185" /></span></span> <a href="/wiki/Category:Artificial_intelligence" title="Category:Artificial intelligence">Category</a> <ul><li><a href="/wiki/Category:Artificial_neural_networks" title="Category:Artificial neural networks">Artificial neural networks</a></li> <li><a href="/wiki/Category:Machine_learning" title="Category:Machine learning">Machine learning</a></li></ul></li> <li><span class="noviewer" typeof="mw:File"><span title="List-Class article"><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/d/db/Symbol_list_class.svg/16px-Symbol_list_class.svg.png" decoding="async" width="16" height="16" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/d/db/Symbol_list_class.svg/23px-Symbol_list_class.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/d/db/Symbol_list_class.svg/31px-Symbol_list_class.svg.png 2x" data-file-width="180" data-file-height="185" /></span></span> List <ul><li><a href="/wiki/List_of_artificial_intelligence_companies" title="List of artificial intelligence companies">Companies</a></li> <li><a href="/wiki/List_of_artificial_intelligence_projects" title="List of artificial intelligence projects">Projects</a></li></ul></li></ul> </div></td></tr></tbody></table></div> <!-- NewPP limit report Parsed by mw‐web.eqiad.main‐8669bc5c8‐pxfwr Cached time: 20250318164303 Cache expiry: 2592000 Reduced expiry: false Complications: [vary‐revision‐sha1, show‐toc] CPU time usage: 0.400 seconds Real time usage: 0.565 seconds Preprocessor visited node count: 1702/1000000 Post‐expand include size: 110801/2097152 bytes Template argument size: 2270/2097152 bytes Highest 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