{"id":"https://openalex.org/W7161936091","doi":"https://doi.org/10.48550/arxiv.2605.21488","title":"Equilibrium Reasoners: Learning Attractors Enables Scalable Reasoning","display_name":"Equilibrium Reasoners: Learning Attractors Enables Scalable Reasoning","publication_year":2026,"publication_date":"2026-05-20","ids":{"openalex":"https://openalex.org/W7161936091","doi":"https://doi.org/10.48550/arxiv.2605.21488"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2605.21488","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.21488","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2605.21488","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5136698427","display_name":"Benhao Huang","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Huang, Benhao","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5102893697","display_name":"Zhengyang Geng","orcid":"https://orcid.org/0009-0006-9903-2716"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Geng, Zhengyang","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5075035644","display_name":"J. Zico Kolter","orcid":"https://orcid.org/0000-0002-8106-5759"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Kolter, Zico","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":null,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10462","display_name":"Reinforcement Learning in Robotics","score":0.15700000524520874,"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/T10462","display_name":"Reinforcement Learning in Robotics","score":0.15700000524520874,"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/T12611","display_name":"Neural Networks and Reservoir Computing","score":0.11240000277757645,"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/T10653","display_name":"Robot Manipulation and Learning","score":0.08720000088214874,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/scalability","display_name":"Scalability","score":0.6254000067710876},{"id":"https://openalex.org/keywords/attractor","display_name":"Attractor","score":0.5795999765396118},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5497999787330627},{"id":"https://openalex.org/keywords/scaling","display_name":"Scaling","score":0.5285000205039978},{"id":"https://openalex.org/keywords/perspective","display_name":"Perspective (graphical)","score":0.5095999836921692},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.46950000524520874},{"id":"https://openalex.org/keywords/task","display_name":"Task (project management)","score":0.4560999870300293},{"id":"https://openalex.org/keywords/process","display_name":"Process (computing)","score":0.42149999737739563}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6740999817848206},{"id":"https://openalex.org/C48044578","wikidata":"https://www.wikidata.org/wiki/Q727490","display_name":"Scalability","level":2,"score":0.6254000067710876},{"id":"https://openalex.org/C164380108","wikidata":"https://www.wikidata.org/wiki/Q507187","display_name":"Attractor","level":2,"score":0.5795999765396118},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5497999787330627},{"id":"https://openalex.org/C99844830","wikidata":"https://www.wikidata.org/wiki/Q102441924","display_name":"Scaling","level":2,"score":0.5285000205039978},{"id":"https://openalex.org/C12713177","wikidata":"https://www.wikidata.org/wiki/Q1900281","display_name":"Perspective (graphical)","level":2,"score":0.5095999836921692},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.5015000104904175},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.46950000524520874},{"id":"https://openalex.org/C2780451532","wikidata":"https://www.wikidata.org/wiki/Q759676","display_name":"Task (project management)","level":2,"score":0.4560999870300293},{"id":"https://openalex.org/C98045186","wikidata":"https://www.wikidata.org/wiki/Q205663","display_name":"Process (computing)","level":2,"score":0.42149999737739563},{"id":"https://openalex.org/C185798385","wikidata":"https://www.wikidata.org/wiki/Q1161707","display_name":"Benchmark (surveying)","level":2,"score":0.3926999866962433},{"id":"https://openalex.org/C143587482","wikidata":"https://www.wikidata.org/wiki/Q1543216","display_name":"Iterative and incremental development","level":2,"score":0.38029998540878296},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.3617999851703644},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.34380000829696655},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.3303999900817871},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.3122999966144562},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.2833000123500824},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2808000147342682},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.2711000144481659},{"id":"https://openalex.org/C61445026","wikidata":"https://www.wikidata.org/wiki/Q217608","display_name":"Fixed point","level":2,"score":0.2669999897480011},{"id":"https://openalex.org/C117619785","wikidata":"https://www.wikidata.org/wiki/Q6094414","display_name":"Iterative learning control","level":3,"score":0.2644999921321869},{"id":"https://openalex.org/C28427503","wikidata":"https://www.wikidata.org/wiki/Q13580300","display_name":"Internal model","level":3,"score":0.251800000667572}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2605.21488","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.21488","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2605.21488","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.21488","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Scaling":[0],"test-time":[1,64,96,116,137],"compute":[2,117],"by":[3,80,86],"iteratively":[4],"updating":[5],"a":[6,12,171],"latent":[7,43,149,181],"state":[8],"has":[9],"emerged":[10],"as":[11],"powerful":[13],"paradigm":[14],"for":[15,155,175],"reasoning.":[16],"Yet":[17],"the":[18,143],"internal":[19,74],"mechanisms":[20],"that":[21,35,166],"enable":[22,63],"these":[23],"iterative":[24,180],"models":[25,157],"to":[26,51,113,128,142,158],"generalize":[27],"beyond":[28],"memorized":[29],"patterns":[30],"remain":[31],"unclear.":[32],"We":[33,54],"hypothesize":[34],"generalizable":[36],"reasoning":[37,150,178],"arises":[38],"from":[39,90,95,135,153],"learning":[40],"task-conditioned":[41],"attractors:":[42],"dynamical":[44],"systems":[45],"whose":[46],"stable":[47],"fixed":[48],"points":[49],"correspond":[50],"valid":[52],"solutions.":[53],"formalize":[55],"this":[56],"process":[57],"through":[58],"Equilibrium":[59],"Reasoners":[60],"(EqR),":[61],"which":[62],"scaling":[65,97],"without":[66],"external":[67],"verifiers":[68],"or":[69],"task-specific":[70],"priors.":[71],"EqR":[72],"scales":[73],"dynamics":[75],"along":[76],"two":[77],"axes:":[78],"depth,":[79],"running":[81],"more":[82],"iterations,":[83],"and":[84],"breadth,":[85],"aggregating":[87],"stochastic":[88],"trajectories":[89],"multiple":[91],"initializations.":[92],"Empirically,":[93],"gains":[94],"are":[98],"tightly":[99],"coupled":[100],"with":[101],"stronger":[102],"convergence":[103],"toward":[104],"solution-aligned":[105],"attractors.":[106],"This":[107],"attractor":[108,168],"perspective":[109],"allows":[110],"neural":[111],"networks":[112],"adaptively":[114],"allocate":[115],"based":[118],"on":[119,161],"task":[120],"difficulty.":[121],"While":[122],"simple":[123],"cases":[124,133],"converge":[125],"within":[126],"1":[127],"5":[129],"iteration":[130],"steps,":[131],"harder":[132],"benefit":[134],"massive":[136],"scaling.":[138],"By":[139],"unrolling":[140],"up":[141],"equivalent":[144],"of":[145],"40,000":[146],"layers,":[147],"scalable":[148,177],"boosts":[151],"accuracy":[152],"2.6%":[154],"feedforward":[156],"over":[159],"99%":[160],"Sudoku-Extreme.":[162],"These":[163],"results":[164],"suggest":[165],"learned":[167],"landscapes":[169],"provide":[170],"useful":[172],"mechanistic":[173],"lens":[174],"understanding":[176],"in":[179],"models.":[182]},"counts_by_year":[],"updated_date":"2026-07-28T07:46:37.118299","created_date":"2026-05-22T00:00:00"}
