{"id":"https://openalex.org/W7160544910","doi":"https://doi.org/10.48550/arxiv.2605.05115","title":"Manifold Steering Reveals the Shared Geometry of Neural Network Representation and Behavior","display_name":"Manifold Steering Reveals the Shared Geometry of Neural Network Representation and Behavior","publication_year":2026,"publication_date":"2026-05-06","ids":{"openalex":"https://openalex.org/W7160544910","doi":"https://doi.org/10.48550/arxiv.2605.05115"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2605.05115","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.05115","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":false,"raw_source_name":null,"raw_type":"article"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2605.05115","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5135632897","display_name":"Daniel Wurgaft","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Wurgaft, Daniel","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5063383301","display_name":"Can Rager","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Rager, Can","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5120318092","display_name":"Matthew Kowal","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Kowal, Matthew","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5135594592","display_name":"Vasudev Shyam","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Shyam, Vasudev","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5063601771","display_name":"Sheridan Feucht","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Feucht, Sheridan","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5077350902","display_name":"Usha Bhalla","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Bhalla, Usha","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5092671619","display_name":"Tal Haklay","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Haklay, Tal","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5135567323","display_name":"Eric Bigelow","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Bigelow, Eric","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5082174299","display_name":"Rapha\u00ebl Sarfati","orcid":"https://orcid.org/0000-0003-4944-0632"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Sarfati, Raphael","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5135583142","display_name":"Thomas McGrath","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"McGrath, Thomas","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5135575501","display_name":"Owen Lewis","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Lewis, Owen","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5062612448","display_name":"Jack Merullo","orcid":"https://orcid.org/0009-0005-9673-6809"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Merullo, Jack","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5127823961","display_name":"Noah Goodman","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Goodman, Noah","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5135606853","display_name":"Thomas Fel","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Fel, Thomas","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5002577142","display_name":"Atticus Geiger","orcid":"https://orcid.org/0000-0002-9170-506X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Geiger, Atticus","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5069090559","display_name":"Ekdeep Singh Lubana","orcid":"https://orcid.org/0000-0002-7200-9341"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Lubana, Ekdeep Singh","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":16,"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/T11431","display_name":"Action Observation and Synchronization","score":0.18000000715255737,"subfield":{"id":"https://openalex.org/subfields/3207","display_name":"Social Psychology"},"field":{"id":"https://openalex.org/fields/32","display_name":"Psychology"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},"topics":[{"id":"https://openalex.org/T11431","display_name":"Action Observation and Synchronization","score":0.18000000715255737,"subfield":{"id":"https://openalex.org/subfields/3207","display_name":"Social Psychology"},"field":{"id":"https://openalex.org/fields/32","display_name":"Psychology"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T11273","display_name":"Advanced Graph Neural Networks","score":0.11259999871253967,"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/T11094","display_name":"Face Recognition and Perception","score":0.07270000129938126,"subfield":{"id":"https://openalex.org/subfields/2805","display_name":"Cognitive Neuroscience"},"field":{"id":"https://openalex.org/fields/28","display_name":"Neuroscience"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/manifold","display_name":"Manifold (fluid mechanics)","score":0.6017000079154968},{"id":"https://openalex.org/keywords/representation","display_name":"Representation (politics)","score":0.5385000109672546},{"id":"https://openalex.org/keywords/curvature","display_name":"Curvature","score":0.5109000205993652},{"id":"https://openalex.org/keywords/euclidean-space","display_name":"Euclidean space","score":0.5015000104904175},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.38609999418258667},{"id":"https://openalex.org/keywords/differential-geometry","display_name":"Differential geometry","score":0.37439998984336853},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.3634999990463257},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.3603000044822693}],"concepts":[{"id":"https://openalex.org/C529865628","wikidata":"https://www.wikidata.org/wiki/Q1790740","display_name":"Manifold (fluid mechanics)","level":2,"score":0.6017000079154968},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.5385000109672546},{"id":"https://openalex.org/C195065555","wikidata":"https://www.wikidata.org/wiki/Q214881","display_name":"Curvature","level":2,"score":0.5109000205993652},{"id":"https://openalex.org/C186450821","wikidata":"https://www.wikidata.org/wiki/Q17295","display_name":"Euclidean space","level":2,"score":0.5015000104904175},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.45080000162124634},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.42879998683929443},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3910999894142151},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.38609999418258667},{"id":"https://openalex.org/C192939610","wikidata":"https://www.wikidata.org/wiki/Q188444","display_name":"Differential geometry","level":2,"score":0.37439998984336853},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.3634999990463257},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.3603000044822693},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.3596000075340271},{"id":"https://openalex.org/C13662910","wikidata":"https://www.wikidata.org/wiki/Q193139","display_name":"Trajectory","level":2,"score":0.34940001368522644},{"id":"https://openalex.org/C129782007","wikidata":"https://www.wikidata.org/wiki/Q162886","display_name":"Euclidean geometry","level":2,"score":0.32749998569488525},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.3140999972820282},{"id":"https://openalex.org/C2780451532","wikidata":"https://www.wikidata.org/wiki/Q759676","display_name":"Task (project management)","level":2,"score":0.304500013589859},{"id":"https://openalex.org/C7305733","wikidata":"https://www.wikidata.org/wiki/Q207961","display_name":"Geometric shape","level":2,"score":0.290800005197525},{"id":"https://openalex.org/C2781238097","wikidata":"https://www.wikidata.org/wiki/Q175026","display_name":"Object (grammar)","level":2,"score":0.2858000099658966},{"id":"https://openalex.org/C109546454","wikidata":"https://www.wikidata.org/wiki/Q3798604","display_name":"Information geometry","level":4,"score":0.28119999170303345},{"id":"https://openalex.org/C64876066","wikidata":"https://www.wikidata.org/wiki/Q5141226","display_name":"Cognitive neuroscience of visual object recognition","level":3,"score":0.27799999713897705},{"id":"https://openalex.org/C74544821","wikidata":"https://www.wikidata.org/wiki/Q1783105","display_name":"Contact geometry","level":2,"score":0.26190000772476196},{"id":"https://openalex.org/C75291252","wikidata":"https://www.wikidata.org/wiki/Q1315756","display_name":"TRACE (psycholinguistics)","level":2,"score":0.25}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2605.05115","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.05115","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:10.48550/arxiv.2605.05115","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.05115","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":false,"raw_source_name":null,"raw_type":"article"},"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":{"Neural":[0],"representations":[1,67],"carry":[2],"rich":[3],"geometric":[4],"structure;":[5],"but":[6,210],"does":[7],"that":[8,41,89,101,137,201],"structure":[9],"causally":[10],"shape":[11],"behavior?":[12],"To":[13],"address":[14],"this":[15,145],"question,":[16],"we":[17,37,59,87,94,162,187],"intervene":[18],"along":[19,91,132],"paths":[20,131],"through":[21,115],"activation":[22,46,63,127,135],"space":[23,47,128],"defined":[24],"by":[25],"different":[26],"geometries,":[27],"and":[28,68,118,153,157,168],"measure":[29],"the":[30,43,54,80,139,149,214,227,234,239],"behavioral":[31,99],"trajectories":[32,100,136],"they":[33],"induce.":[34],"In":[35,159,182],"particular,":[36],"test":[38,79],"whether":[39],"interventions":[40,125],"respect":[42],"geometry":[44,112,150,192,202],"of":[45,141,151,230],"will":[48],"yield":[49],"behaviors":[50],"close":[51],"to":[52,66,73,129,194,237],"those":[53],"model":[55],"exhibits":[56],"naturally.":[57],"Concretely,":[58],"first":[60],"fit":[61],"an":[62],"manifold":[64,71,96],"$M_h$":[65],"a":[69,110,183,189],"behavior":[70,154],"$M_y$":[72,133],"output":[74],"probability":[75],"distributions.":[76],"We":[77,143],"then":[78],"link":[81],"$M_h":[82],"\\leftrightarrow":[83],"M_y$":[84],"via":[85,221],"interventions:":[86],"find":[88],"steering":[90,106,231],"$M_h$,":[92],"which":[93,108],"term":[95],"steering,":[97],"yields":[98],"follow":[102],"$M_y$,":[103],"while":[104],"linear":[105],"--":[107,113],"assumes":[109],"Euclidean":[111],"cuts":[114],"off-manifold":[116],"regions":[117],"hence":[119],"produces":[120],"unnatural":[121],"outputs.":[122],"Moreover,":[123],"optimizing":[124],"in":[126,203,212],"produce":[130],"recovers":[134],"trace":[138],"curvature":[140],"$M_h$.":[142],"demonstrate":[144],"bidirectional":[146],"relationship":[147],"between":[148],"representation":[152,205],"across":[155],"tasks":[156,165,176],"modalities.":[158],"language":[160],"models,":[161],"use":[163,188],"reasoning":[164],"with":[166,177,191],"cyclic":[167],"sequential":[169],"geometries":[170],"as":[171,173],"well":[172],"in-context":[174],"learning":[175],"more":[178],"complex":[179],"graph":[180],"geometries.":[181],"video":[184],"world":[185],"model,":[186],"task":[190],"corresponding":[193],"physical":[195],"dynamics.":[196],"Overall,":[197],"our":[198],"work":[199],"shows":[200],"neural":[204],"is":[206,211],"not":[207],"merely":[208],"incidental,":[209],"fact":[213],"proper":[215],"object":[216],"for":[217],"enabling":[218],"principled":[219],"control":[220],"intervention":[222],"on":[223],"internals.":[224],"This":[225],"recasts":[226],"core":[228],"problem":[229],"from":[232],"finding":[233,238],"right":[235,240],"direction":[236],"geometry.":[241]},"counts_by_year":[],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2026-05-08T00:00:00"}