{"id":"https://openalex.org/W7162506741","doi":"https://doi.org/10.48550/arxiv.2605.26484","title":"Extra-Merge: Tracing the Rank-1 Subspace of Model Merging in Language Model Pre-Training","display_name":"Extra-Merge: Tracing the Rank-1 Subspace of Model Merging in Language Model Pre-Training","publication_year":2026,"publication_date":"2026-05-26","ids":{"openalex":"https://openalex.org/W7162506741","doi":"https://doi.org/10.48550/arxiv.2605.26484"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2605.26484","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.26484","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.2605.26484","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5137118211","display_name":"Wenjie Zhou","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Zhou, Wenjie","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5137109490","display_name":"Bohan Wang","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Wang, Bohan","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5137118639","display_name":"Hongtao Zhang","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Zhang, Hongtao","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5137087589","display_name":"Chenxi Jia","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Jia, Chenxi","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5137133228","display_name":"Wei Chen","orcid":"https://orcid.org/0000-0002-3277-7629"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Chen, Wei","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5137162336","display_name":"Xueqi Cheng","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Cheng, Xueqi","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/T10028","display_name":"Topic Modeling","score":0.17669999599456787,"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/T10028","display_name":"Topic Modeling","score":0.17669999599456787,"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/T11636","display_name":"Artificial Intelligence in Healthcare and Education","score":0.1378999948501587,"subfield":{"id":"https://openalex.org/subfields/2718","display_name":"Health Informatics"},"field":{"id":"https://openalex.org/fields/27","display_name":"Medicine"},"domain":{"id":"https://openalex.org/domains/4","display_name":"Health Sciences"}},{"id":"https://openalex.org/T12535","display_name":"Machine Learning and Data Classification","score":0.09210000187158585,"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/subspace-topology","display_name":"Subspace topology","score":0.7807000279426575},{"id":"https://openalex.org/keywords/noise","display_name":"Noise (video)","score":0.598800003528595},{"id":"https://openalex.org/keywords/filter","display_name":"Filter (signal processing)","score":0.5339999794960022},{"id":"https://openalex.org/keywords/language-model","display_name":"Language model","score":0.5164999961853027},{"id":"https://openalex.org/keywords/tracing","display_name":"Tracing","score":0.4666999876499176},{"id":"https://openalex.org/keywords/gradient-descent","display_name":"Gradient descent","score":0.44179999828338623},{"id":"https://openalex.org/keywords/linear-model","display_name":"Linear model","score":0.3677999973297119}],"concepts":[{"id":"https://openalex.org/C32834561","wikidata":"https://www.wikidata.org/wiki/Q660730","display_name":"Subspace topology","level":2,"score":0.7807000279426575},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6294000148773193},{"id":"https://openalex.org/C99498987","wikidata":"https://www.wikidata.org/wiki/Q2210247","display_name":"Noise (video)","level":3,"score":0.598800003528595},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5598000288009644},{"id":"https://openalex.org/C106131492","wikidata":"https://www.wikidata.org/wiki/Q3072260","display_name":"Filter (signal processing)","level":2,"score":0.5339999794960022},{"id":"https://openalex.org/C137293760","wikidata":"https://www.wikidata.org/wiki/Q3621696","display_name":"Language model","level":2,"score":0.5164999961853027},{"id":"https://openalex.org/C138673069","wikidata":"https://www.wikidata.org/wiki/Q322229","display_name":"Tracing","level":2,"score":0.4666999876499176},{"id":"https://openalex.org/C153258448","wikidata":"https://www.wikidata.org/wiki/Q1199743","display_name":"Gradient descent","level":3,"score":0.44179999828338623},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.37940001487731934},{"id":"https://openalex.org/C163175372","wikidata":"https://www.wikidata.org/wiki/Q3339222","display_name":"Linear model","level":2,"score":0.3677999973297119},{"id":"https://openalex.org/C114289077","wikidata":"https://www.wikidata.org/wiki/Q3284399","display_name":"Statistical model","level":2,"score":0.3228999972343445},{"id":"https://openalex.org/C13662910","wikidata":"https://www.wikidata.org/wiki/Q193139","display_name":"Trajectory","level":2,"score":0.319599986076355},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.30730000138282776},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.28200000524520874},{"id":"https://openalex.org/C2776207758","wikidata":"https://www.wikidata.org/wiki/Q5303302","display_name":"Downstream (manufacturing)","level":2,"score":0.2784000039100647},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.27720001339912415},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.25870001316070557},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.25589999556541443},{"id":"https://openalex.org/C206688291","wikidata":"https://www.wikidata.org/wiki/Q7617819","display_name":"Stochastic gradient descent","level":3,"score":0.25540000200271606},{"id":"https://openalex.org/C26517878","wikidata":"https://www.wikidata.org/wiki/Q228039","display_name":"Key (lock)","level":2,"score":0.25360000133514404}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2605.26484","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.26484","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.2605.26484","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.26484","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":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Model":[0],"merging":[1,117],"has":[2],"emerged":[3],"as":[4,64],"a":[5,31,46,58,65,86],"lightweight":[6],"paradigm":[7],"for":[8],"enhancing":[9],"Large":[10],"Language":[11],"Models":[12],"(LLMs),":[13],"yet":[14],"its":[15],"underlying":[16],"mechanisms":[17],"remain":[18],"poorly":[19],"understood.":[20],"In":[21],"this":[22,55,81,92],"work,":[23],"we":[24,83],"analyze":[25],"late-stage":[26],"pre-training":[27],"trajectories":[28],"and":[29,105,130],"uncover":[30],"\\textbf{Rank-1":[32],"Subspace}":[33],"phenomenon:":[34],"while":[35],"raw":[36],"optimization":[37],"steps":[38],"oscillate":[39],"violently,":[40],"consecutive":[41],"\\emph{merged}":[42],"checkpoints":[43],"collapse":[44],"onto":[45],"stable,":[47],"approximately":[48],"one-dimensional":[49],"linear":[50],"manifold.":[51],"We":[52],"theoretically":[53],"ground":[54],"observation":[56],"in":[57],"\\emph{river-valley}":[59],"landscape":[60],"analysis:":[61],"averaging":[62],"acts":[63],"geometric":[66],"low-pass":[67],"filter":[68],"that":[69,89,112],"dampens":[70],"high-curvature":[71],"noise":[72],"to":[73,94,109,133],"reveal":[74],"the":[75,134],"optimal":[76],"descent":[77],"direction.":[78],"Capitalizing":[79],"on":[80,126],"insight,":[82],"propose":[84],"\\textbf{Extra-Merge},":[85],"training-free":[87],"strategy":[88],"extrapolates":[90],"along":[91],"subspace":[93],"minimize":[95],"loss":[96],"without":[97],"additional":[98],"gradient":[99],"updates.":[100],"Extensive":[101],"experiments":[102],"across":[103],"GPT-2":[104],"LLaMA":[106],"families":[107],"(124M":[108],"2B)":[110],"demonstrate":[111],"Extra-Merge":[113],"consistently":[114],"outperforms":[115],"standard":[116],"baselines.":[118],"Notably,":[119],"it":[120],"yields":[121],"consistent":[122],"zero-shot":[123],"accuracy":[124],"gains":[125],"Pythia-12B":[127],"downstream":[128],"tasks":[129],"generalizes":[131],"effectively":[132],"Muon":[135],"optimizer":[136],"\\citep{jordan2024muon}.":[137]},"counts_by_year":[],"updated_date":"2026-07-28T07:46:37.118299","created_date":"2026-05-28T00:00:00"}
