{"id":"https://openalex.org/W4417508704","doi":"https://doi.org/10.1109/tpami.2025.3646483","title":"Complexity Control Facilitates Reasoning-Based Compositional Generalization in Transformers","display_name":"Complexity Control Facilitates Reasoning-Based Compositional Generalization in Transformers","publication_year":2025,"publication_date":"2025-12-19","ids":{"openalex":"https://openalex.org/W4417508704","doi":"https://doi.org/10.1109/tpami.2025.3646483","pmid":"https://pubmed.ncbi.nlm.nih.gov/41418004"},"language":"en","primary_location":{"id":"doi:10.1109/tpami.2025.3646483","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tpami.2025.3646483","pdf_url":null,"source":{"id":"https://openalex.org/S199944782","display_name":"IEEE Transactions on Pattern Analysis and Machine Intelligence","issn_l":"0162-8828","issn":["0162-8828","1939-3539","2160-9292"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320439","host_organization_name":"IEEE Computer Society","host_organization_lineage":["https://openalex.org/P4310320439","https://openalex.org/P4310319808"],"host_organization_lineage_names":["IEEE Computer Society","Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Pattern Analysis and Machine Intelligence","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","pubmed"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5084678300","display_name":"Zhongwang Zhang","orcid":"https://orcid.org/0009-0006-4202-8556"},"institutions":[{"id":"https://openalex.org/I4210158445","display_name":"Institute of Natural Science","ror":"https://ror.org/004tze884","country_code":"KP","type":"education","lineage":["https://openalex.org/I4210158445"]}],"countries":["KP"],"is_corresponding":false,"raw_author_name":"Zhongwang Zhang","raw_affiliation_strings":["Institute of Natural Sciences, School of Mathematical Sciences, MOE-LSC, Shanghai Jiao Tong University, Shanghai, China"],"raw_orcid":"https://orcid.org/0009-0006-4202-8556","affiliations":[{"raw_affiliation_string":"Institute of Natural Sciences, School of Mathematical Sciences, MOE-LSC, Shanghai Jiao Tong University, Shanghai, China","institution_ids":["https://openalex.org/I4210158445"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101345522","display_name":"Pengxiao Lin","orcid":"https://orcid.org/0009-0003-4926-8577"},"institutions":[{"id":"https://openalex.org/I4210158445","display_name":"Institute of Natural Science","ror":"https://ror.org/004tze884","country_code":"KP","type":"education","lineage":["https://openalex.org/I4210158445"]}],"countries":["KP"],"is_corresponding":false,"raw_author_name":"Pengxiao Lin","raw_affiliation_strings":["Institute of Natural Sciences, School of Mathematical Sciences, MOE-LSC, Shanghai Jiao Tong University, Shanghai, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Natural Sciences, School of Mathematical Sciences, MOE-LSC, Shanghai Jiao Tong University, Shanghai, China","institution_ids":["https://openalex.org/I4210158445"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100449940","display_name":"Zhiwei Wang","orcid":"https://orcid.org/0000-0001-6729-2237"},"institutions":[{"id":"https://openalex.org/I4210158445","display_name":"Institute of Natural Science","ror":"https://ror.org/004tze884","country_code":"KP","type":"education","lineage":["https://openalex.org/I4210158445"]}],"countries":["KP"],"is_corresponding":false,"raw_author_name":"Zhiwei Wang","raw_affiliation_strings":["Institute of Natural Sciences, School of Mathematical Sciences, MOE-LSC, Shanghai Jiao Tong University, Shanghai, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Natural Sciences, School of Mathematical Sciences, MOE-LSC, Shanghai Jiao Tong University, Shanghai, China","institution_ids":["https://openalex.org/I4210158445"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100680347","display_name":"Yaoyu Zhang","orcid":"https://orcid.org/0000-0001-9374-2502"},"institutions":[{"id":"https://openalex.org/I4210158445","display_name":"Institute of Natural Science","ror":"https://ror.org/004tze884","country_code":"KP","type":"education","lineage":["https://openalex.org/I4210158445"]}],"countries":["KP"],"is_corresponding":false,"raw_author_name":"Yaoyu Zhang","raw_affiliation_strings":["Institute of Natural Sciences, School of Mathematical Sciences, MOE-LSC, Shanghai Jiao Tong University, Shanghai, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Natural Sciences, School of Mathematical Sciences, MOE-LSC, Shanghai Jiao Tong University, Shanghai, China","institution_ids":["https://openalex.org/I4210158445"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5002236438","display_name":"Zhi\u2010Qin John Xu","orcid":"https://orcid.org/0000-0003-0627-3520"},"institutions":[{"id":"https://openalex.org/I4210158445","display_name":"Institute of Natural Science","ror":"https://ror.org/004tze884","country_code":"KP","type":"education","lineage":["https://openalex.org/I4210158445"]}],"countries":["KP"],"is_corresponding":false,"raw_author_name":"Zhi-Qin John Xu","raw_affiliation_strings":["Institute of Natural Sciences, School of Mathematical Sciences, MOE-LSC, Shanghai Jiao Tong University, Shanghai, China"],"raw_orcid":"https://orcid.org/0000-0003-0627-3520","affiliations":[{"raw_affiliation_string":"Institute of Natural Sciences, School of Mathematical Sciences, MOE-LSC, Shanghai Jiao Tong University, Shanghai, China","institution_ids":["https://openalex.org/I4210158445"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":5,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.35795938,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"48","issue":"4","first_page":"4336","last_page":"4349"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12808","display_name":"Ferroelectric and Negative Capacitance Devices","score":0.5609999895095825,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12808","display_name":"Ferroelectric and Negative Capacitance Devices","score":0.5609999895095825,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12090","display_name":"Language and cultural evolution","score":0.03799999877810478,"subfield":{"id":"https://openalex.org/subfields/3316","display_name":"Cultural Studies"},"field":{"id":"https://openalex.org/fields/33","display_name":"Social Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T10656","display_name":"Child and Animal Learning Development","score":0.03420000150799751,"subfield":{"id":"https://openalex.org/subfields/3204","display_name":"Developmental and Educational Psychology"},"field":{"id":"https://openalex.org/fields/32","display_name":"Psychology"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/initialization","display_name":"Initialization","score":0.73089998960495},{"id":"https://openalex.org/keywords/computational-complexity-theory","display_name":"Computational complexity theory","score":0.4722000062465668},{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.4162999987602234},{"id":"https://openalex.org/keywords/transformer","display_name":"Transformer","score":0.40450000762939453},{"id":"https://openalex.org/keywords/robustness","display_name":"Robustness (evolution)","score":0.3580000102519989},{"id":"https://openalex.org/keywords/pattern-recognition","display_name":"Pattern recognition (psychology)","score":0.29829999804496765}],"concepts":[{"id":"https://openalex.org/C114466953","wikidata":"https://www.wikidata.org/wiki/Q6034165","display_name":"Initialization","level":2,"score":0.73089998960495},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.7143999934196472},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.5327000021934509},{"id":"https://openalex.org/C179799912","wikidata":"https://www.wikidata.org/wiki/Q205084","display_name":"Computational complexity theory","level":2,"score":0.4722000062465668},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.4162999987602234},{"id":"https://openalex.org/C66322947","wikidata":"https://www.wikidata.org/wiki/Q11658","display_name":"Transformer","level":3,"score":0.40450000762939453},{"id":"https://openalex.org/C63479239","wikidata":"https://www.wikidata.org/wiki/Q7353546","display_name":"Robustness (evolution)","level":3,"score":0.3580000102519989},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.34369999170303345},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.34119999408721924},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.3407000005245209},{"id":"https://openalex.org/C153180895","wikidata":"https://www.wikidata.org/wiki/Q7148389","display_name":"Pattern recognition (psychology)","level":2,"score":0.29829999804496765},{"id":"https://openalex.org/C26517878","wikidata":"https://www.wikidata.org/wiki/Q228039","display_name":"Key (lock)","level":2,"score":0.29339998960494995},{"id":"https://openalex.org/C87868495","wikidata":"https://www.wikidata.org/wiki/Q750843","display_name":"Information processing","level":2,"score":0.2827000021934509},{"id":"https://openalex.org/C2777402240","wikidata":"https://www.wikidata.org/wiki/Q6783436","display_name":"Masking (illustration)","level":2,"score":0.27160000801086426},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.2578999996185303},{"id":"https://openalex.org/C17500928","wikidata":"https://www.wikidata.org/wiki/Q959968","display_name":"Control system","level":2,"score":0.25429999828338623}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/tpami.2025.3646483","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tpami.2025.3646483","pdf_url":null,"source":{"id":"https://openalex.org/S199944782","display_name":"IEEE Transactions on Pattern Analysis and Machine Intelligence","issn_l":"0162-8828","issn":["0162-8828","1939-3539","2160-9292"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320439","host_organization_name":"IEEE Computer Society","host_organization_lineage":["https://openalex.org/P4310320439","https://openalex.org/P4310319808"],"host_organization_lineage_names":["IEEE Computer Society","Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Pattern Analysis and Machine Intelligence","raw_type":"journal-article"},{"id":"pmid:41418004","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/41418004","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE transactions on pattern analysis and machine intelligence","raw_type":null}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1339871232","display_name":null,"funder_award_id":"92270001","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G377228980","display_name":null,"funder_award_id":"12371511","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G6034297041","display_name":null,"funder_award_id":"12571567","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G6076456921","display_name":null,"funder_award_id":"12422119","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G7202909770","display_name":null,"funder_award_id":"025ZR1402280","funder_id":"https://openalex.org/F4320309612","funder_display_name":"Natural Science Foundation of Shanghai"}],"funders":[{"id":"https://openalex.org/F4320309612","display_name":"Natural Science Foundation of Shanghai","ror":null},{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320321885","display_name":"Science and Technology Commission of Shanghai Municipality","ror":"https://ror.org/03kt66j61"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":32,"referenced_works":["https://openalex.org/W1998058722","https://openalex.org/W2118373646","https://openalex.org/W2914483840","https://openalex.org/W2938647293","https://openalex.org/W2963095610","https://openalex.org/W2963791871","https://openalex.org/W2970290486","https://openalex.org/W2994720379","https://openalex.org/W3017374003","https://openalex.org/W3100475986","https://openalex.org/W3103334733","https://openalex.org/W3104739822","https://openalex.org/W4206039841","https://openalex.org/W4225974998","https://openalex.org/W4229005331","https://openalex.org/W4235344441","https://openalex.org/W4250954493","https://openalex.org/W4312824283","https://openalex.org/W4320009668","https://openalex.org/W4360980513","https://openalex.org/W4385245566","https://openalex.org/W4385573838","https://openalex.org/W4385893535","https://openalex.org/W4389520103","https://openalex.org/W4389520373","https://openalex.org/W4391128820","https://openalex.org/W4394698525","https://openalex.org/W4412945379","https://openalex.org/W4416034111","https://openalex.org/W7133224126","https://openalex.org/W7133224150","https://openalex.org/W7134065365"],"related_works":[],"abstract_inverted_index":{"Transformers":[0],"have":[1],"demonstrated":[2],"impressive":[3],"capabilities":[4],"across":[5,134],"various":[6],"tasks,":[7,145],"yet":[8],"their":[9],"performance":[10],"on":[11,63],"compositional":[12,31],"problems":[13],"remains":[14],"a":[15,100],"subject":[16],"of":[17,41,150],"debate.":[18],"In":[19],"this":[20],"study,":[21],"we":[22,82],"investigate":[23],"the":[24,39,50,73,107,120,147],"internal":[25,85],"mechanisms":[26,87],"underlying":[27],"Transformers'":[28],"behavior":[29],"in":[30],"tasks.":[32],"We":[33,130],"find":[34],"that":[35,55,96],"complexity":[36,80,102,114],"control":[37],"strategies-particularly":[38],"choice":[40],"parameter":[42],"initialization":[43],"scale":[44],"and":[45,77,141],"weight":[46],"decay-significantly":[47],"influence":[48],"whether":[49],"model":[51],"learns":[52],"primitive-level":[53],"rules":[54],"generalize":[56],"out-of-distribution":[57],"(reasoning-based":[58],"solutions)":[59],"or":[60],"relies":[61],"solely":[62],"memorized":[64],"mappings":[65],"(memory-based":[66],"solutions).":[67],"By":[68],"applying":[69],"masking":[70],"strategies":[71],"to":[72,118,126],"model's":[74],"information":[75],"circuits":[76],"employing":[78],"multiple":[79,135],"metrics,":[81],"reveal":[83],"distinct":[84],"working":[86],"associated":[88],"with":[89,106],"different":[90],"solution":[91],"types.":[92],"Further":[93],"analysis":[94],"reveals":[95],"reasoning-based":[97],"solutions":[98,125],"exhibit":[99],"lower":[101,113],"bias,":[103],"which":[104],"aligns":[105],"well-studied":[108],"neuron":[109],"condensation":[110],"phenomenon.":[111],"This":[112],"bias":[115],"is":[116],"hypothesized":[117],"be":[119],"key":[121],"factor":[122],"enabling":[123],"these":[124,132],"learn":[127],"reasoning":[128],"rules.":[129],"validate":[131],"conclusions":[133],"real-world":[136],"datasets,":[137],"including":[138],"image":[139],"generation":[140],"natural":[142],"language":[143],"processing":[144],"confirming":[146],"broad":[148],"applicability":[149],"our":[151],"findings.":[152]},"counts_by_year":[],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-12-19T00:00:00"}