{"id":"https://openalex.org/W7159579112","doi":"https://doi.org/10.48550/arxiv.2604.27656","title":"When Does Structure Matter in Continual Learning? Dimensionality Controls When Modularity Shapes Representational Geometry","display_name":"When Does Structure Matter in Continual Learning? Dimensionality Controls When Modularity Shapes Representational Geometry","publication_year":2026,"publication_date":"2026-04-30","ids":{"openalex":"https://openalex.org/W7159579112","doi":"https://doi.org/10.48550/arxiv.2604.27656"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2604.27656","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.27656","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":null,"license_id":null,"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.2604.27656","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5120349562","display_name":"Kathrin Korte","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Korte, Kathrin","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5134978020","display_name":"Joachim Winter Pedersen","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Pedersen, Joachim Winter","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5064736397","display_name":"Eleni Nisioti","orcid":"https://orcid.org/0000-0001-7170-7108"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Nisioti, Eleni","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5020511097","display_name":"Sebastian Risi","orcid":"https://orcid.org/0000-0003-3607-8400"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Risi, Sebastian","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/T11307","display_name":"Domain Adaptation and Few-Shot Learning","score":0.7534999847412109,"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/T11307","display_name":"Domain Adaptation and Few-Shot Learning","score":0.7534999847412109,"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/T11804","display_name":"Quantum many-body systems","score":0.021199999377131462,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.01489999983459711,"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/curse-of-dimensionality","display_name":"Curse of dimensionality","score":0.7615000009536743},{"id":"https://openalex.org/keywords/modularity","display_name":"Modularity (biology)","score":0.6881999969482422},{"id":"https://openalex.org/keywords/modular-design","display_name":"Modular design","score":0.6172999739646912},{"id":"https://openalex.org/keywords/task","display_name":"Task (project management)","score":0.5964000225067139},{"id":"https://openalex.org/keywords/salient","display_name":"Salient","score":0.4512999951839447},{"id":"https://openalex.org/keywords/similarity","display_name":"Similarity (geometry)","score":0.43970000743865967},{"id":"https://openalex.org/keywords/feature","display_name":"Feature (linguistics)","score":0.4271000027656555},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.4138000011444092},{"id":"https://openalex.org/keywords/key","display_name":"Key (lock)","score":0.41029998660087585}],"concepts":[{"id":"https://openalex.org/C111030470","wikidata":"https://www.wikidata.org/wiki/Q1430460","display_name":"Curse of dimensionality","level":2,"score":0.7615000009536743},{"id":"https://openalex.org/C2779478453","wikidata":"https://www.wikidata.org/wiki/Q6889748","display_name":"Modularity (biology)","level":2,"score":0.6881999969482422},{"id":"https://openalex.org/C101468663","wikidata":"https://www.wikidata.org/wiki/Q1620158","display_name":"Modular design","level":2,"score":0.6172999739646912},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.6014999747276306},{"id":"https://openalex.org/C2780451532","wikidata":"https://www.wikidata.org/wiki/Q759676","display_name":"Task (project management)","level":2,"score":0.5964000225067139},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.49729999899864197},{"id":"https://openalex.org/C2780719617","wikidata":"https://www.wikidata.org/wiki/Q1030752","display_name":"Salient","level":2,"score":0.4512999951839447},{"id":"https://openalex.org/C103278499","wikidata":"https://www.wikidata.org/wiki/Q254465","display_name":"Similarity (geometry)","level":3,"score":0.43970000743865967},{"id":"https://openalex.org/C2776401178","wikidata":"https://www.wikidata.org/wiki/Q12050496","display_name":"Feature (linguistics)","level":2,"score":0.4271000027656555},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.4138000011444092},{"id":"https://openalex.org/C26517878","wikidata":"https://www.wikidata.org/wiki/Q228039","display_name":"Key (lock)","level":2,"score":0.41029998660087585},{"id":"https://openalex.org/C12362212","wikidata":"https://www.wikidata.org/wiki/Q728435","display_name":"Linear subspace","level":2,"score":0.38199999928474426},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.32679998874664307},{"id":"https://openalex.org/C2778755073","wikidata":"https://www.wikidata.org/wiki/Q10858537","display_name":"Scale (ratio)","level":2,"score":0.32409998774528503},{"id":"https://openalex.org/C47559304","wikidata":"https://www.wikidata.org/wiki/Q1702189","display_name":"Orthogonalization","level":2,"score":0.3160000145435333},{"id":"https://openalex.org/C153180895","wikidata":"https://www.wikidata.org/wiki/Q7148389","display_name":"Pattern recognition (psychology)","level":2,"score":0.3149000108242035},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.3100999891757965},{"id":"https://openalex.org/C70518039","wikidata":"https://www.wikidata.org/wiki/Q16000077","display_name":"Dimensionality reduction","level":2,"score":0.303600013256073},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.2994000017642975},{"id":"https://openalex.org/C59404180","wikidata":"https://www.wikidata.org/wiki/Q17013334","display_name":"Feature learning","level":2,"score":0.2912999987602234},{"id":"https://openalex.org/C150899416","wikidata":"https://www.wikidata.org/wiki/Q1820378","display_name":"Transfer of learning","level":2,"score":0.2883000075817108},{"id":"https://openalex.org/C2781121602","wikidata":"https://www.wikidata.org/wiki/Q3504403","display_name":"Modular neural network","level":4,"score":0.28690001368522644},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.2854999899864197},{"id":"https://openalex.org/C204241405","wikidata":"https://www.wikidata.org/wiki/Q461499","display_name":"Transformation (genetics)","level":3,"score":0.27709999680519104},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.2615000009536743},{"id":"https://openalex.org/C2776061190","wikidata":"https://www.wikidata.org/wiki/Q7451805","display_name":"Separation (statistics)","level":2,"score":0.26089999079704285},{"id":"https://openalex.org/C12713177","wikidata":"https://www.wikidata.org/wiki/Q1900281","display_name":"Perspective (graphical)","level":2,"score":0.26010000705718994},{"id":"https://openalex.org/C108583219","wikidata":"https://www.wikidata.org/wiki/Q197536","display_name":"Deep learning","level":2,"score":0.25870001316070557},{"id":"https://openalex.org/C31170391","wikidata":"https://www.wikidata.org/wiki/Q188619","display_name":"Hierarchy","level":2,"score":0.2554999887943268},{"id":"https://openalex.org/C116834253","wikidata":"https://www.wikidata.org/wiki/Q2039217","display_name":"Identification (biology)","level":2,"score":0.25369998812675476}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2604.27656","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.27656","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":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2604.27656","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.27656","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":null,"license_id":null,"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":{"To":[0],"preserve":[1],"previously":[2],"learned":[3,129],"representations,":[4],"continual":[5,227],"learning":[6,48,79,117,228],"systems":[7],"must":[8],"strike":[9],"a":[10,81,91,97,206,222],"balance":[11],"between":[12],"plasticity,":[13],"the":[14,109,124,128,194],"ability":[15],"to":[16,146],"acquire":[17],"new":[18,47],"knowledge,":[19],"and":[20,57,74,108,182,217],"stability.":[21],"This":[22,188],"stability-plasticity":[23],"dilemma":[24],"affects":[25],"how":[26,69],"representations":[27,142],"can":[28],"be":[29],"reused":[30],"across":[31],"tasks:":[32],"shared":[33],"structure":[34],"enables":[35],"transfer":[36],"when":[37,46,56,211],"tasks":[38,149],"are":[39,143],"similar":[40,174],"but":[41],"may":[42],"also":[43],"induce":[44],"interference":[45],"disrupts":[49],"existing":[50],"representations.":[51,130],"However,":[52],"it":[53],"remains":[54],"unclear":[55],"why":[58],"structural":[59,212],"separation":[60,160,184,213],"influences":[61],"this":[62,65],"trade-off.":[63],"In":[64,153],"study,":[66],"we":[67,120],"examine":[68],"network":[70,95,196],"architecture,":[71],"task":[72,83,103],"similarity,":[73],"representational":[75,202],"dimensionality":[76,126,203],"jointly":[77],"shape":[78],"in":[80,138,155,193],"sequential":[82],"paradigm":[84],"inspired":[85],"by":[86,100],"transfer-interference":[87],"studies.":[88],"We":[89,131],"compare":[90],"task-partitioned":[92],"modular":[93,163],"recurrent":[94],"with":[96,171],"single-module":[98],"baseline":[99],"systematically":[101],"varying":[102],"similarity":[104],"(low,":[105],"medium,":[106],"high)":[107],"scale":[110],"of":[111,127,168],"weight":[112],"initialization,":[113],"which":[114],"induces":[115],"different":[116],"regimes":[118,140],"that":[119,133,201],"empirically":[121],"characterize":[122],"through":[123],"effective":[125],"find":[132],"architecture":[134],"has":[135],"minimal":[136],"impact":[137],"high-dimensional":[139],"where":[141],"sufficiently":[144],"unconstrained":[145],"accommodate":[147],"multiple":[148],"without":[150],"strong":[151],"interference.":[152],"contrast,":[154],"lower-dimensional":[156],"(rich)":[157],"regimes,":[158],"architectural":[159],"is":[161,191],"decisive:":[162],"networks":[164],"exhibit":[165],"graded":[166,189],"alignment":[167],"task-specific":[169],"subspaces":[170],"overlap":[172],"for":[173,178,185,225],"tasks,":[175,181],"partial":[176],"orthogonalization":[177],"moderately":[179],"dissimilar":[180,186],"stronger":[183],"tasks.":[187],"geometry":[190,220],"absent":[192],"single":[195],"baseline.":[197],"Our":[198],"findings":[199],"suggest":[200],"acts":[204],"as":[205,221],"key":[207],"organizing":[208],"variable":[209],"governing":[210],"becomes":[214],"functionally":[215],"relevant,":[216],"highlight":[218],"adaptive":[219],"central":[223],"principle":[224],"designing":[226],"systems.":[229]},"counts_by_year":[],"updated_date":"2026-07-28T07:46:37.118299","created_date":"2026-05-02T00:00:00"}