{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,26]],"date-time":"2026-06-26T07:39:15Z","timestamp":1782459555535,"version":"3.54.5"},"reference-count":53,"publisher":"IOP Publishing","issue":"2","license":[{"start":{"date-parts":[[2021,4,21]],"date-time":"2021-04-21T00:00:00Z","timestamp":1618963200000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2021,4,21]],"date-time":"2021-04-21T00:00:00Z","timestamp":1618963200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/iopscience.iop.org\/info\/page\/text-and-data-mining"}],"funder":[{"DOI":"10.13039\/501100001870","name":"Foundation for Polish Science","doi-asserted-by":"crossref","award":["(POIR.04.04.00-00-5C55\/17-00"],"award-info":[{"award-number":["(POIR.04.04.00-00-5C55\/17-00"]}],"id":[{"id":"10.13039\/501100001870","id-type":"DOI","asserted-by":"crossref"}]},{"name":"DOE","award":["DE-SC0011632"],"award-info":[{"award-number":["DE-SC0011632"]}]},{"name":"NSF","award":["PHY-1848089"],"award-info":[{"award-number":["PHY-1848089"]}]}],"content-domain":{"domain":["iopscience.iop.org"],"crossmark-restriction":false},"short-container-title":["Mach. 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We find that the Reformer and shared-QK Transformer network architectures outperform fully-connected networks, though all perform at <jats:inline-formula>\n                     <jats:tex-math\/>\n                     <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" overflow=\"scroll\">\n                        <mml:mo>\u2273<\/mml:mo>\n                     <\/mml:math>\n                     <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"mlstabe91fieqn1.gif\" xlink:type=\"simple\"\/>\n                  <\/jats:inline-formula>95% accuracy. Perhaps surprisingly, we find that accuracy increases with the length of the braid word, and that the networks learn a direct correlation between the confidence of their predictions and the degree of the Jones polynomial. Finally, we utilize reinforcement learning (RL) to find sequences of Markov moves and braid relations that simplify knots and can identify unknots by explicitly giving the sequence of unknotting actions. Trust region policy optimization (TRPO) performs consistently well, reducing <jats:inline-formula>\n                     <jats:tex-math\/>\n                     <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" overflow=\"scroll\">\n                        <mml:mo>\u2273<\/mml:mo>\n                     <\/mml:math>\n                     <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"mlstabe91fieqn2.gif\" xlink:type=\"simple\"\/>\n                  <\/jats:inline-formula>80% of the unknots with up to 96 crossings we tested to the empty braid word, and thoroughly outperformed other RL algorithms and random walkers. Studying these actions, we find that braid relations are more useful in simplifying to the unknot than one of the Markov moves.<\/jats:p>","DOI":"10.1088\/2632-2153\/abe91f","type":"journal-article","created":{"date-parts":[[2021,2,23]],"date-time":"2021-02-23T22:35:13Z","timestamp":1614119713000},"page":"025035","update-policy":"https:\/\/doi.org\/10.1088\/crossmark-policy","source":"Crossref","is-referenced-by-count":38,"title":["Learning to unknot"],"prefix":"10.1088","volume":"2","author":[{"given":"Sergei","family":"Gukov","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0535-2622","authenticated-orcid":false,"given":"James","family":"Halverson","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Fabian","family":"Ruehle","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Piotr","family":"Su\u0142kowski","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"266","published-online":{"date-parts":[[2021,4,21]]},"reference":[{"key":"mlstabe91fbib1","author":"Silver"},{"key":"mlstabe91fbib2","doi-asserted-by":"publisher","first-page":"484","DOI":"10.1038\/nature16961","article-title":"Mastering the game of Go with deep neural networks and tree search","volume":"529","author":"Silver","year":"2016","journal-title":"Nature"},{"key":"mlstabe91fbib3","doi-asserted-by":"publisher","first-page":"354","DOI":"10.1038\/nature24270","article-title":"Mastering the game of go without human knowledge","volume":"550","author":"Silver","year":"2017","journal-title":"Nature"},{"key":"mlstabe91fbib4","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.96.121902","article-title":"BPS states, knots and quivers","volume":"96","author":"Kucharski","year":"2017","journal-title":"Phys. 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