{"id":"https://openalex.org/W7131383102","doi":"https://doi.org/10.48550/arxiv.2602.20433","title":"Disentangling Geometry, Performance, and Training in Language Models","display_name":"Disentangling Geometry, Performance, and Training in Language Models","publication_year":2026,"publication_date":"2026-02-24","ids":{"openalex":"https://openalex.org/W7131383102","doi":"https://doi.org/10.48550/arxiv.2602.20433"},"language":null,"primary_location":{"id":"pmh:doi:10.48550/arxiv.2602.20433","is_oa":true,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4406922384","display_name":"Open MIND","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","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":null,"any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5126836822","display_name":"Atharva Kulkarni","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Kulkarni, Atharva","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5035773495","display_name":"Jacob M. Springer","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Springer, Jacob Mitchell","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5126835725","display_name":"Arjun Subramonian","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Subramonian, Arjun","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5126791358","display_name":"Swabha Swayamdipta","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Swayamdipta, Swabha","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5126836822"],"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/T12026","display_name":"Explainable Artificial Intelligence (XAI)","score":0.6919000148773193,"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/T12026","display_name":"Explainable Artificial Intelligence (XAI)","score":0.6919000148773193,"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/T10028","display_name":"Topic Modeling","score":0.07000000029802322,"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/T11689","display_name":"Adversarial Robustness in Machine Learning","score":0.05460000038146973,"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/interpretability","display_name":"Interpretability","score":0.8457000255584717},{"id":"https://openalex.org/keywords/language-model","display_name":"Language model","score":0.5940999984741211},{"id":"https://openalex.org/keywords/rank","display_name":"Rank (graph theory)","score":0.4758000075817108},{"id":"https://openalex.org/keywords/suite","display_name":"Suite","score":0.4345000088214874},{"id":"https://openalex.org/keywords/key","display_name":"Key (lock)","score":0.4237000048160553},{"id":"https://openalex.org/keywords/transformer","display_name":"Transformer","score":0.39259999990463257},{"id":"https://openalex.org/keywords/adversarial-system","display_name":"Adversarial system","score":0.38019999861717224}],"concepts":[{"id":"https://openalex.org/C2781067378","wikidata":"https://www.wikidata.org/wiki/Q17027399","display_name":"Interpretability","level":2,"score":0.8457000255584717},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6510999798774719},{"id":"https://openalex.org/C137293760","wikidata":"https://www.wikidata.org/wiki/Q3621696","display_name":"Language model","level":2,"score":0.5940999984741211},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.5408999919891357},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.5149000287055969},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.4758000075817108},{"id":"https://openalex.org/C79581498","wikidata":"https://www.wikidata.org/wiki/Q1367530","display_name":"Suite","level":2,"score":0.4345000088214874},{"id":"https://openalex.org/C26517878","wikidata":"https://www.wikidata.org/wiki/Q228039","display_name":"Key (lock)","level":2,"score":0.4237000048160553},{"id":"https://openalex.org/C66322947","wikidata":"https://www.wikidata.org/wiki/Q11658","display_name":"Transformer","level":3,"score":0.39259999990463257},{"id":"https://openalex.org/C204321447","wikidata":"https://www.wikidata.org/wiki/Q30642","display_name":"Natural language processing","level":1,"score":0.3831000030040741},{"id":"https://openalex.org/C37736160","wikidata":"https://www.wikidata.org/wiki/Q1801315","display_name":"Adversarial system","level":2,"score":0.38019999861717224},{"id":"https://openalex.org/C2776207758","wikidata":"https://www.wikidata.org/wiki/Q5303302","display_name":"Downstream (manufacturing)","level":2,"score":0.3675000071525574},{"id":"https://openalex.org/C51632099","wikidata":"https://www.wikidata.org/wiki/Q3985153","display_name":"Training set","level":2,"score":0.3596000075340271},{"id":"https://openalex.org/C2777211547","wikidata":"https://www.wikidata.org/wiki/Q17141490","display_name":"Training (meteorology)","level":2,"score":0.3481999933719635},{"id":"https://openalex.org/C2776035688","wikidata":"https://www.wikidata.org/wiki/Q1606558","display_name":"Affect (linguistics)","level":2,"score":0.30809998512268066},{"id":"https://openalex.org/C63479239","wikidata":"https://www.wikidata.org/wiki/Q7353546","display_name":"Robustness (evolution)","level":3,"score":0.29580000042915344},{"id":"https://openalex.org/C132010649","wikidata":"https://www.wikidata.org/wiki/Q189222","display_name":"Intuition","level":2,"score":0.2770000100135803},{"id":"https://openalex.org/C189430467","wikidata":"https://www.wikidata.org/wiki/Q7293293","display_name":"Ranking (information retrieval)","level":2,"score":0.27549999952316284}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:doi:10.48550/arxiv.2602.20433","is_oa":true,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4406922384","display_name":"Open MIND","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Article"},{"id":"doi:10.48550/arxiv.2602.20433","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2602.20433","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":"article"}],"best_oa_location":{"id":"pmh:doi:10.48550/arxiv.2602.20433","is_oa":true,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4406922384","display_name":"Open MIND","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","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":{"Geometric":[0],"properties":[1],"of":[2,52],"Transformer":[3],"weights,":[4],"particularly":[5,43],"the":[6,33,39,66,142,176],"unembedding":[7,40],"matrix,":[8],"have":[9],"been":[10],"widely":[11],"useful":[12],"in":[13,101],"language":[14,55],"model":[15,36],"interpretability":[16],"research.":[17],"Yet,":[18],"their":[19],"utility":[20],"for":[21],"estimating":[22],"downstream":[23,169],"performance":[24,37,99],"remains":[25],"unclear.":[26],"In":[27],"this":[28,75],"work,":[29,88],"we":[30,89,109,121,156],"systematically":[31],"investigate":[32],"relationship":[34],"between":[35],"and":[38,82,136,153],"matrix":[41],"geometry,":[42,178],"its":[44],"effective":[45,73,93,124],"rank.":[46],"Our":[47],"experiments,":[48],"involving":[49],"a":[50,71],"suite":[51],"108":[53],"OLMo-style":[54],"models":[56,68,115],"trained":[57],"under":[58],"controlled":[59],"variation,":[60],"reveal":[61],"several":[62],"key":[63],"findings.":[64],"While":[65],"best-performing":[67],"often":[69],"exhibit":[70,118],"high":[72],"rank,":[74],"trend":[76],"is":[77,126],"not":[78,96,117],"universal":[79],"across":[80],"tasks":[81],"training":[83,186],"setups.":[84],"Contrary":[85],"to":[86,149],"prior":[87],"find":[90,110,157],"that":[91,123,158,175],"low":[92],"rank":[94,125],"does":[95],"cause":[97],"late-stage":[98],"degradation":[100],"small":[102],"models,":[103],"but":[104,164],"instead":[105],"co-occurs":[106],"with":[107],"it;":[108],"adversarial":[111],"cases":[112],"where":[113],"low-rank":[114],"do":[116],"saturation.":[119],"Moreover,":[120],"show":[122],"strongly":[127],"influenced":[128],"by":[129,181],"pre-training":[130],"hyperparameters,":[131],"such":[132],"as":[133,179],"batch":[134],"size":[135],"weight":[137],"decay,":[138],"which":[139],"in-turn":[140],"affect":[141],"model's":[143,177],"performance.":[144,170,190],"Lastly,":[145],"extending":[146],"our":[147,172],"analysis":[148],"other":[150],"geometric":[151],"metrics":[152,160],"final-layer":[154],"representation,":[155],"these":[159],"are":[161],"largely":[162],"aligned,":[163],"none":[165],"can":[166],"reliably":[167],"predict":[168],"Overall,":[171],"findings":[173],"suggest":[174],"captured":[180],"existing":[182],"metrics,":[183],"primarily":[184],"reflects":[185],"choices":[187],"rather":[188],"than":[189]},"counts_by_year":[],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2026-02-26T00:00:00"}