{"id":"https://openalex.org/W7161180266","doi":"https://doi.org/10.48550/arxiv.2605.12671","title":"All Circuits Lead to Rome: Rethinking Functional Anisotropy in Circuit and Sheaf Discovery for LLMs","display_name":"All Circuits Lead to Rome: Rethinking Functional Anisotropy in Circuit and Sheaf Discovery for LLMs","publication_year":2026,"publication_date":"2026-05-12","ids":{"openalex":"https://openalex.org/W7161180266","doi":"https://doi.org/10.48550/arxiv.2605.12671"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2605.12671","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.12671","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":"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.2605.12671","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5136133797","display_name":"Xi Chen","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Chen, Xi","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5136169342","display_name":"Mingyu Jin","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Jin, Mingyu","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5047674908","display_name":"Jingcheng Niu","orcid":"https://orcid.org/0000-0002-2358-9466"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Niu, Jingcheng","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5128189394","display_name":"Yutong Yin","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Yin, Yutong","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5136175239","display_name":"Jinman Zhao","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Zhao, Jinman","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5001757884","display_name":"Bangwei Guo","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Guo, Bangwei","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5136138858","display_name":"Dimitris N. Metaxas","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Metaxas, Dimitris N.","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5136123794","display_name":"Zhaoran Wang","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Wang, Zhaoran","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5136091662","display_name":"Yutao Yue","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Yue, Yutao","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5136159487","display_name":"Gerald Penn","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Penn, Gerald","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/T11948","display_name":"Machine Learning in Materials Science","score":0.22349999845027924,"subfield":{"id":"https://openalex.org/subfields/2505","display_name":"Materials Chemistry"},"field":{"id":"https://openalex.org/fields/25","display_name":"Materials Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11948","display_name":"Machine Learning in Materials Science","score":0.22349999845027924,"subfield":{"id":"https://openalex.org/subfields/2505","display_name":"Materials Chemistry"},"field":{"id":"https://openalex.org/fields/25","display_name":"Materials Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10028","display_name":"Topic Modeling","score":0.21739999949932098,"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/T11273","display_name":"Advanced Graph Neural Networks","score":0.14650000631809235,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/sheaf","display_name":"Sheaf","score":0.7886999845504761},{"id":"https://openalex.org/keywords/superposition-principle","display_name":"Superposition principle","score":0.5569000244140625},{"id":"https://openalex.org/keywords/task","display_name":"Task (project management)","score":0.5515999794006348},{"id":"https://openalex.org/keywords/electronic-circuit","display_name":"Electronic circuit","score":0.43230000138282776},{"id":"https://openalex.org/keywords/morphism","display_name":"Morphism","score":0.37610000371932983},{"id":"https://openalex.org/keywords/distributive-property","display_name":"Distributive property","score":0.37529999017715454},{"id":"https://openalex.org/keywords/term","display_name":"Term (time)","score":0.36239999532699585}],"concepts":[{"id":"https://openalex.org/C4017995","wikidata":"https://www.wikidata.org/wiki/Q595298","display_name":"Sheaf","level":2,"score":0.7886999845504761},{"id":"https://openalex.org/C27753989","wikidata":"https://www.wikidata.org/wiki/Q284885","display_name":"Superposition principle","level":2,"score":0.5569000244140625},{"id":"https://openalex.org/C2780451532","wikidata":"https://www.wikidata.org/wiki/Q759676","display_name":"Task (project management)","level":2,"score":0.5515999794006348},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4810999929904938},{"id":"https://openalex.org/C134146338","wikidata":"https://www.wikidata.org/wiki/Q1815901","display_name":"Electronic circuit","level":2,"score":0.43230000138282776},{"id":"https://openalex.org/C137212723","wikidata":"https://www.wikidata.org/wiki/Q1948412","display_name":"Morphism","level":2,"score":0.37610000371932983},{"id":"https://openalex.org/C11821877","wikidata":"https://www.wikidata.org/wiki/Q187959","display_name":"Distributive property","level":2,"score":0.37529999017715454},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.3637999892234802},{"id":"https://openalex.org/C61797465","wikidata":"https://www.wikidata.org/wiki/Q1188986","display_name":"Term (time)","level":2,"score":0.36239999532699585},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3499999940395355},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.33889999985694885},{"id":"https://openalex.org/C198942812","wikidata":"https://www.wikidata.org/wiki/Q496618","display_name":"Semantic property","level":2,"score":0.3359000086784363},{"id":"https://openalex.org/C50335755","wikidata":"https://www.wikidata.org/wiki/Q483247","display_name":"Phenomenon","level":2,"score":0.3346000015735626},{"id":"https://openalex.org/C2776036281","wikidata":"https://www.wikidata.org/wiki/Q48769818","display_name":"Constraint (computer-aided design)","level":2,"score":0.296999990940094},{"id":"https://openalex.org/C33332235","wikidata":"https://www.wikidata.org/wiki/Q18362","display_name":"Theoretical physics","level":1,"score":0.2791999876499176},{"id":"https://openalex.org/C165064840","wikidata":"https://www.wikidata.org/wiki/Q1321061","display_name":"Matching (statistics)","level":2,"score":0.2728999853134155},{"id":"https://openalex.org/C21847791","wikidata":"https://www.wikidata.org/wiki/Q191081","display_name":"Logical conjunction","level":2,"score":0.2655999958515167},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2596000134944916},{"id":"https://openalex.org/C189950617","wikidata":"https://www.wikidata.org/wiki/Q937228","display_name":"Property (philosophy)","level":2,"score":0.25220000743865967}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2605.12671","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.12671","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":"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.2605.12671","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.12671","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":"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":[{"score":0.6585409641265869,"display_name":"Peace, Justice and strong institutions","id":"https://metadata.un.org/sdg/16"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"In":[0],"this":[1,126],"paper,":[2],"we":[3,23,78,175],"present":[4],"empirical":[5],"and":[6,18,70,138,152,182,213,225],"theoretical":[7,185],"evidence":[8],"against":[9],"a":[10,41,50,83,117,177,184,216],"central":[11],"but":[12,112],"largely":[13],"implicit":[14],"assumption":[15],"in":[16,33,208],"circuit":[17,191],"sheaf":[19,151],"discovery":[20,99,103],"(CSD),":[21],"which":[22],"term":[24],"the":[25,29,87,102,132],"Functional":[26],"Anisotropy":[27],"Hypothesis:":[28],"idea":[30],"that":[31,49,65,85,125,154,188,205],"functions":[32],"large":[34],"language":[35],"models":[36],"(LLMs)":[37],"are":[38,66,210],"localised":[39],"to":[40],"unique":[42],"or":[43,63,106,168],"near-unique":[44],"internal":[45],"mechanism.":[46],"We":[47,123,145],"show":[48,153],"single":[51],"LLM":[52],"task":[53,110],"can":[54],"instead":[55],"be":[56,223],"supported":[57],"by":[58],"multiple,":[59],"structurally":[60],"distinct":[61],"circuits":[62,105],"sheaves":[64,107,136],"simultaneously":[67],"faithful,":[68],"sparse,":[69],"complete.":[71],"To":[72,171],"systematically":[73],"uncover":[74],"such":[75],"competing":[76],"mechanisms,":[77],"introduce":[79],"Overlap-Aware":[80],"Sheaf":[81],"Repulsion,":[82],"method":[84],"augments":[86],"CSD":[88,121,143,220],"objective":[89],"with":[90,108],"an":[91,148],"explicit":[92],"penalty":[93],"on":[94],"structural":[95],"overlap":[96],"across":[97,116,141],"multiple":[98],"runs,":[100],"enabling":[101],"of":[104,119,134,156,166,218],"strong":[109],"performance":[111],"minimal":[113],"shared":[114],"structure":[115],"plethora":[118],"common":[120],"benchmarks.":[122],"find":[124],"phenomenon":[127],"becomes":[128],"increasingly":[129],"pronounced":[130],"as":[131],"number":[133],"discovered":[135],"grows":[137],"persists":[139],"robustly":[140],"major":[142],"methods.":[144],"further":[146],"identify":[147],"ultra-sparse":[149],"three-edge":[150],"none":[155],"its":[157],"edges":[158],"is":[159],"individually":[160],"indispensable,":[161],"undermining":[162],"even":[163],"weakened":[164],"notions":[165],"canonical":[167],"essential":[169],"components.":[170],"explain":[172],"these":[173],"findings,":[174],"propose":[176],"Distributive":[178],"Dense":[179],"Circuit":[180],"Hypothesis":[181],"provide":[183],"analysis":[186],"demonstrating":[187],"non-unique,":[189],"low-overlap":[190],"explanations":[192,207],"arise":[193],"naturally":[194],"from":[195],"high-dimensional":[196],"superposition":[197],"under":[198],"mild":[199],"assumptions.":[200],"Together,":[201],"our":[202],"results":[203,221],"suggest":[204],"mechanistic":[206],"LLMs":[209],"inherently":[211],"non-canonical":[212],"call":[214],"for":[215],"rethinking":[217],"how":[219],"should":[222],"interpreted":[224],"evaluated.":[226]},"counts_by_year":[],"updated_date":"2026-07-01T06:00:48.157686","created_date":"2026-05-15T00:00:00"}
