{"id":"https://openalex.org/W6951111592","doi":"https://doi.org/10.5555/3535850.3535945","title":"Lyapunov exponents for diversity in differentiable games","display_name":"Lyapunov exponents for diversity in differentiable games","publication_year":2022,"publication_date":"2022-01-01","ids":{"openalex":"https://openalex.org/W6951111592","doi":"https://doi.org/10.5555/3535850.3535945"},"language":"en","primary_location":{"id":"pmh:oai:repository.ubn.ru.nl:2066/250998","is_oa":false,"landing_page_url":"https://hdl.handle.net/2066/250998","pdf_url":null,"source":{"id":"https://openalex.org/S4306401067","display_name":"Radboud Repository (Radboud University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I145872427","host_organization_name":"Radboud University Nijmegen","host_organization_lineage":["https://openalex.org/I145872427"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Article in monograph or in proceedings"},"type":"book","indexed_in":[],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Lorraine, J.","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Lorraine, J.","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":null,"display_name":"Vicol, P.","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Vicol, P.","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":null,"display_name":"Parker-Holder, J.","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Parker-Holder, J.","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":null,"display_name":"Kachman, T.","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Kachman, T.","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":null,"display_name":"Metz, L.","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Metz, L.","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":null,"display_name":"Foerster, J.","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Foerster, J.","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.27012346,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":true,"primary_topic":{"id":"https://openalex.org/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.3422999978065491,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.3422999978065491,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/T11252","display_name":"Evolutionary Game Theory and Cooperation","score":0.10750000178813934,"subfield":{"id":"https://openalex.org/subfields/3312","display_name":"Sociology and Political Science"},"field":{"id":"https://openalex.org/fields/33","display_name":"Social Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T11031","display_name":"Game Theory and Applications","score":0.09870000183582306,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/hessian-matrix","display_name":"Hessian matrix","score":0.6169999837875366},{"id":"https://openalex.org/keywords/differentiable-function","display_name":"Differentiable function","score":0.5241000056266785},{"id":"https://openalex.org/keywords/bifurcation","display_name":"Bifurcation","score":0.49630001187324524},{"id":"https://openalex.org/keywords/dynamical-systems-theory","display_name":"Dynamical systems theory","score":0.4404999911785126},{"id":"https://openalex.org/keywords/field","display_name":"Field (mathematics)","score":0.4300999939441681},{"id":"https://openalex.org/keywords/ridge","display_name":"Ridge","score":0.41350001096725464},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.39730000495910645},{"id":"https://openalex.org/keywords/construct","display_name":"Construct (python library)","score":0.3885999917984009}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6202999949455261},{"id":"https://openalex.org/C203616005","wikidata":"https://www.wikidata.org/wiki/Q620495","display_name":"Hessian matrix","level":2,"score":0.6169999837875366},{"id":"https://openalex.org/C202615002","wikidata":"https://www.wikidata.org/wiki/Q783507","display_name":"Differentiable function","level":2,"score":0.5241000056266785},{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.49630001187324524},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.4404999911785126},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.4300999939441681},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.42010000348091125},{"id":"https://openalex.org/C32277403","wikidata":"https://www.wikidata.org/wiki/Q740445","display_name":"Ridge","level":2,"score":0.41350001096725464},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.39730000495910645},{"id":"https://openalex.org/C2780801425","wikidata":"https://www.wikidata.org/wiki/Q5164392","display_name":"Construct (python library)","level":2,"score":0.3885999917984009},{"id":"https://openalex.org/C140479938","wikidata":"https://www.wikidata.org/wiki/Q5254619","display_name":"Iterated function","level":2,"score":0.37049999833106995},{"id":"https://openalex.org/C191544260","wikidata":"https://www.wikidata.org/wiki/Q1238630","display_name":"Lyapunov exponent","level":3,"score":0.3671000003814697},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.34610000252723694},{"id":"https://openalex.org/C60640748","wikidata":"https://www.wikidata.org/wiki/Q2337858","display_name":"Lyapunov function","level":3,"score":0.33489999175071716},{"id":"https://openalex.org/C164380108","wikidata":"https://www.wikidata.org/wiki/Q507187","display_name":"Attractor","level":2,"score":0.32269999384880066},{"id":"https://openalex.org/C186633575","wikidata":"https://www.wikidata.org/wiki/Q845060","display_name":"Maxima and minima","level":2,"score":0.3057999908924103},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.27720001339912415},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.27639999985694885},{"id":"https://openalex.org/C33962884","wikidata":"https://www.wikidata.org/wiki/Q378637","display_name":"Dynamical system (definition)","level":3,"score":0.27309998869895935},{"id":"https://openalex.org/C37736160","wikidata":"https://www.wikidata.org/wiki/Q1801315","display_name":"Adversarial system","level":2,"score":0.26330000162124634},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.2612000107765198},{"id":"https://openalex.org/C2777052490","wikidata":"https://www.wikidata.org/wiki/Q5072826","display_name":"Chaotic","level":2,"score":0.2574000060558319},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.2565000057220459}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:repository.ubn.ru.nl:2066/250998","is_oa":false,"landing_page_url":"https://hdl.handle.net/2066/250998","pdf_url":null,"source":{"id":"https://openalex.org/S4306401067","display_name":"Radboud Repository (Radboud University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I145872427","host_organization_name":"Radboud University Nijmegen","host_organization_lineage":["https://openalex.org/I145872427"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Article in monograph or in proceedings"},{"id":"pmh:ru:oai:repository.ubn.ru.nl:2066/250998","is_oa":false,"landing_page_url":"http://hdl.handle.net/2066/250998","pdf_url":null,"source":{"id":"https://openalex.org/S4306401843","display_name":"Data Archiving and Networked Services (DANS)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1322597698","host_organization_name":"Royal Netherlands Academy of Arts and Sciences","host_organization_lineage":["https://openalex.org/I1322597698"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Proceedings of the 21st International Conference on Autonomous Agents and Multiagent Systems, 842 - 852. Richland, SC : International Foundation for Autonomous Agents and Multiagent Systems","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Ridge":[0,59],"Rider":[1,60],"(RR)":[2],"is":[3,21],"an":[4],"algorithm":[5],"for":[6,23,63,72],"finding":[7,64,110],"diverse":[8,111],"solutions":[9,112],"to":[10,47],"optimization":[11],"problems":[12,88,100,122],"by":[13,52,75,109],"following":[14],"eigenvectors":[15],"of":[16,81,101],"the":[17,79,114],"Hessian":[18],"(\"ridges\").":[19],"RR":[20],"designed":[22],"conservative":[24],"gradient":[25,50],"systems":[26,51],"(i.e.,":[27],"settings":[28],"involving":[29],"a":[30,54],"single":[31],"loss":[32],"function),":[33],"where":[34,89],"it":[35],"branches":[36],"at":[37],"saddles":[38],"-":[39,56,62],"easy-to-find":[40],"bifurcation":[41,66],"points.":[42,67],"We":[43,68,84],"generalize":[44],"this":[45],"idea":[46],"non-conservative,":[48],"multi-agent":[49],"proposing":[53],"method":[55,74,108],"denoted":[57],"Generalized":[58],"(GRR)":[61],"arbitrary":[65],"give":[69],"theoretical":[70],"motivation":[71],"our":[73,107],"leveraging":[76],"machinery":[77],"from":[78],"field":[80],"dynamical":[82],"systems.":[83],"construct":[85],"novel":[86],"toy":[87],"we":[90,104],"can":[91],"visualize":[92],"new":[93],"phenomena":[94],"while":[95],"giving":[96],"insight":[97],"into":[98],"high-dimensional":[99],"interest.":[102],"Finally,":[103],"empirically":[105],"evaluate":[106],"in":[113],"iterated":[115],"prisoners'":[116],"dilemma":[117],"and":[118],"relevant":[119],"machine":[120],"learning":[121],"including":[123],"generative":[124],"adversarial":[125],"networks.":[126]},"counts_by_year":[],"updated_date":"2026-07-14T23:27:15.235271","created_date":"2025-10-10T00:00:00"}