{"id":"https://openalex.org/W3013559175","doi":"https://doi.org/10.1088/2632-2153/abbd2d","title":"Detecting symmetries with neural networks","display_name":"Detecting symmetries with neural networks","publication_year":2020,"publication_date":"2020-09-30","ids":{"openalex":"https://openalex.org/W3013559175","doi":"https://doi.org/10.1088/2632-2153/abbd2d","mag":"3013559175"},"language":"en","primary_location":{"id":"doi:10.1088/2632-2153/abbd2d","is_oa":true,"landing_page_url":"https://doi.org/10.1088/2632-2153/abbd2d","pdf_url":"https://iopscience.iop.org/article/10.1088/2632-2153/abbd2d/pdf","source":{"id":"https://openalex.org/S4210200687","display_name":"Machine Learning Science and Technology","issn_l":"2632-2153","issn":["2632-2153"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310320083","host_organization_name":"IOP Publishing","host_organization_lineage":["https://openalex.org/P4310320083","https://openalex.org/P4310311669"],"host_organization_lineage_names":["IOP Publishing","Institute of Physics"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Machine Learning: Science and Technology","raw_type":"journal-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://iopscience.iop.org/article/10.1088/2632-2153/abbd2d/pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5049470751","display_name":"Sven Krippendorf","orcid":"https://orcid.org/0000-0001-6374-6828"},"institutions":[{"id":"https://openalex.org/I8204097","display_name":"Ludwig-Maximilians-Universit\u00e4t M\u00fcnchen","ror":"https://ror.org/05591te55","country_code":"DE","type":"education","lineage":["https://openalex.org/I8204097"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Sven Krippendorf","raw_affiliation_strings":["Arnold Sommerfeld Center for Theoretical Physics, Ludwig-Maximilians-Universit\u00e4t, Theresienstra\u00df e 37, 80333 M\u00fcnchen, Germany"],"raw_orcid":"https://orcid.org/0000-0001-6374-6828","affiliations":[{"raw_affiliation_string":"Arnold Sommerfeld Center for Theoretical Physics, Ludwig-Maximilians-Universit\u00e4t, Theresienstra\u00df e 37, 80333 M\u00fcnchen, Germany","institution_ids":["https://openalex.org/I8204097"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5079065127","display_name":"Marc Syvaeri","orcid":null},"institutions":[{"id":"https://openalex.org/I4210089019","display_name":"Max Planck Institute for Physics","ror":"https://ror.org/0079jjr10","country_code":"DE","type":"facility","lineage":["https://openalex.org/I149899117","https://openalex.org/I4210089019"]},{"id":"https://openalex.org/I8204097","display_name":"Ludwig-Maximilians-Universit\u00e4t M\u00fcnchen","ror":"https://ror.org/05591te55","country_code":"DE","type":"education","lineage":["https://openalex.org/I8204097"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Marc Syvaeri","raw_affiliation_strings":["Arnold Sommerfeld Center for Theoretical Physics, Ludwig-Maximilians-Universit\u00e4t, Theresienstra\u00df e 37, 80333 M\u00fcnchen, Germany","Max-Planck-Institut f\u00fcr Physik, F\u00f6hringer Ring 6, 80805 M\u00fcnchen, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Arnold Sommerfeld Center for Theoretical Physics, Ludwig-Maximilians-Universit\u00e4t, Theresienstra\u00df e 37, 80333 M\u00fcnchen, Germany","institution_ids":["https://openalex.org/I8204097"]},{"raw_affiliation_string":"Max-Planck-Institut f\u00fcr Physik, F\u00f6hringer Ring 6, 80805 M\u00fcnchen, Germany","institution_ids":["https://openalex.org/I4210089019"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5049470751"],"corresponding_institution_ids":["https://openalex.org/I8204097"],"apc_list":{"value":1600,"currency":"GBP","value_usd":1962},"apc_paid":{"value":1600,"currency":"GBP","value_usd":1962},"fwci":1.5897,"has_fulltext":false,"cited_by_count":12,"citation_normalized_percentile":{"value":0.86902902,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"2","issue":"1","first_page":"015010","last_page":"015010"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12536","display_name":"Topological and Geometric Data Analysis","score":0.9458000063896179,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12536","display_name":"Topological and Geometric Data Analysis","score":0.9458000063896179,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11304","display_name":"Advanced Neuroimaging Techniques and Applications","score":0.9434999823570251,"subfield":{"id":"https://openalex.org/subfields/2741","display_name":"Radiology, Nuclear Medicine and Imaging"},"field":{"id":"https://openalex.org/fields/27","display_name":"Medicine"},"domain":{"id":"https://openalex.org/domains/4","display_name":"Health Sciences"}},{"id":"https://openalex.org/T12351","display_name":"Geometry and complex manifolds","score":0.9291999936103821,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/homogeneous-space","display_name":"Homogeneous space","score":0.7737284898757935},{"id":"https://openalex.org/keywords/invariant","display_name":"Invariant (physics)","score":0.6165936589241028},{"id":"https://openalex.org/keywords/embedding","display_name":"Embedding","score":0.6091100573539734},{"id":"https://openalex.org/keywords/symmetry","display_name":"Symmetry (geometry)","score":0.595323920249939},{"id":"https://openalex.org/keywords/unitary-state","display_name":"Unitary state","score":0.5433230996131897},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.5360370874404907},{"id":"https://openalex.org/keywords/group","display_name":"Group (periodic table)","score":0.523745059967041},{"id":"https://openalex.org/keywords/symmetry-group","display_name":"Symmetry group","score":0.5061447024345398},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4730845093727112},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.41498661041259766},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.35358840227127075},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3377833366394043},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.3281615972518921},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.2830260396003723},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.2089928388595581},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.18733498454093933},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.12999141216278076},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.10531830787658691},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.07941895723342896}],"concepts":[{"id":"https://openalex.org/C96469262","wikidata":"https://www.wikidata.org/wiki/Q1324364","display_name":"Homogeneous space","level":2,"score":0.7737284898757935},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.6165936589241028},{"id":"https://openalex.org/C41608201","wikidata":"https://www.wikidata.org/wiki/Q980509","display_name":"Embedding","level":2,"score":0.6091100573539734},{"id":"https://openalex.org/C2779886137","wikidata":"https://www.wikidata.org/wiki/Q21030012","display_name":"Symmetry (geometry)","level":2,"score":0.595323920249939},{"id":"https://openalex.org/C67820243","wikidata":"https://www.wikidata.org/wiki/Q179164","display_name":"Unitary state","level":2,"score":0.5433230996131897},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.5360370874404907},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.523745059967041},{"id":"https://openalex.org/C44306375","wikidata":"https://www.wikidata.org/wiki/Q902019","display_name":"Symmetry group","level":2,"score":0.5061447024345398},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4730845093727112},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.41498661041259766},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.35358840227127075},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3377833366394043},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.3281615972518921},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.2830260396003723},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.2089928388595581},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.18733498454093933},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.12999141216278076},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.10531830787658691},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.07941895723342896},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1088/2632-2153/abbd2d","is_oa":true,"landing_page_url":"https://doi.org/10.1088/2632-2153/abbd2d","pdf_url":"https://iopscience.iop.org/article/10.1088/2632-2153/abbd2d/pdf","source":{"id":"https://openalex.org/S4210200687","display_name":"Machine Learning Science and Technology","issn_l":"2632-2153","issn":["2632-2153"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310320083","host_organization_name":"IOP Publishing","host_organization_lineage":["https://openalex.org/P4310320083","https://openalex.org/P4310311669"],"host_organization_lineage_names":["IOP Publishing","Institute of Physics"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Machine Learning: Science and Technology","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2003.13679","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2003.13679","pdf_url":"https://arxiv.org/pdf/2003.13679","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},{"id":"mag:3013559175","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/2003.13679","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"doi:10.48550/arxiv.2003.13679","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2003.13679","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"doi:10.1088/2632-2153/abbd2d","is_oa":true,"landing_page_url":"https://doi.org/10.1088/2632-2153/abbd2d","pdf_url":"https://iopscience.iop.org/article/10.1088/2632-2153/abbd2d/pdf","source":{"id":"https://openalex.org/S4210200687","display_name":"Machine Learning Science and Technology","issn_l":"2632-2153","issn":["2632-2153"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310320083","host_organization_name":"IOP Publishing","host_organization_lineage":["https://openalex.org/P4310320083","https://openalex.org/P4310311669"],"host_organization_lineage_names":["IOP Publishing","Institute of Physics"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Machine Learning: Science and Technology","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3013559175.pdf","grobid_xml":"https://content.openalex.org/works/W3013559175.grobid-xml"},"referenced_works_count":30,"referenced_works":["https://openalex.org/W1508021176","https://openalex.org/W1973565526","https://openalex.org/W1987760861","https://openalex.org/W1996379477","https://openalex.org/W1996475841","https://openalex.org/W1997683411","https://openalex.org/W2035026703","https://openalex.org/W2065762817","https://openalex.org/W2107346888","https://openalex.org/W2279221249","https://openalex.org/W2290847742","https://openalex.org/W2639368885","https://openalex.org/W2766409877","https://openalex.org/W2806878911","https://openalex.org/W2810731239","https://openalex.org/W2891834385","https://openalex.org/W2901947642","https://openalex.org/W2949671925","https://openalex.org/W2950577311","https://openalex.org/W2960999379","https://openalex.org/W2997692532","https://openalex.org/W3008165446","https://openalex.org/W3009084733","https://openalex.org/W3011698838","https://openalex.org/W3100056294","https://openalex.org/W3100170200","https://openalex.org/W3105927042","https://openalex.org/W6636510571","https://openalex.org/W6675354045","https://openalex.org/W6694954494"],"related_works":["https://openalex.org/W3089384272","https://openalex.org/W3100056294","https://openalex.org/W2997692532","https://openalex.org/W2806878911","https://openalex.org/W3105570377","https://openalex.org/W2991376628","https://openalex.org/W2960999379","https://openalex.org/W2891834385","https://openalex.org/W2766409877","https://openalex.org/W2625973082","https://openalex.org/W2519061191","https://openalex.org/W2886960264","https://openalex.org/W2021779185","https://openalex.org/W3103282954","https://openalex.org/W2940343590","https://openalex.org/W2925283579","https://openalex.org/W2626828082","https://openalex.org/W162069620","https://openalex.org/W3125333547","https://openalex.org/W2963003392"],"abstract_inverted_index":{"Abstract":[0],"Identifying":[1],"symmetries":[2,126],"in":[3,40,65,83,140],"data":[4,17,138],"sets":[5],"is":[6,13,56,76,109,121],"generally":[7],"difficult,":[8],"but":[9],"knowledge":[10],"about":[11],"them":[12],"crucial":[14,122],"for":[15,111],"efficient":[16],"handling.":[18],"Here":[19],"we":[20,78,104,134],"present":[21,57,77,87,135],"a":[22,54,136],"method":[23,108],"how":[24],"neural":[25,46],"networks":[26],"can":[27],"be":[28],"used":[29],"to":[30,51,59,123],"identify":[31,52,60,124],"symmetries.":[32],"We":[33,86],"make":[34],"extensive":[35],"use":[36],"of":[37,44,62,114,142],"the":[38,41,45,63,66,80,84,98,112,128],"structure":[39],"embedding":[42],"layer":[43],"network":[47],"which":[48,70],"allows":[49],"us":[50],"whether":[53],"symmetry":[55,64,74],"and":[58,97],"orbits":[61,82],"input.":[67,85],"To":[68],"determine":[69],"continuous":[71],"or":[72],"discrete":[73,125],"group":[75,100],"analyse":[79],"invariant":[81],"examples":[88],"based":[89],"on":[90,127],"rotation":[91],"groups":[92],"SO":[93],"(":[94],"n":[95],")":[96],"unitary":[99],"SU":[101],"(2).":[102],"Further":[103],"find":[105],"that":[106],"this":[107,132],"useful":[110],"classification":[113],"complete":[115],"intersection":[116],"Calabi-Yau":[117],"manifolds":[118],"where":[119],"it":[120],"input":[129],"space.":[130],"For":[131],"example":[133],"novel":[137],"representation":[139],"terms":[141],"graphs.":[143]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":6},{"year":2018,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}