{"id":"https://openalex.org/W7134918364","doi":"https://doi.org/10.48550/arxiv.2603.09221","title":"Beyond Test-Time Memory: State-Space Optimal Control for LLM Reasoning","display_name":"Beyond Test-Time Memory: State-Space Optimal Control for LLM Reasoning","publication_year":2026,"publication_date":"2026-03-10","ids":{"openalex":"https://openalex.org/W7134918364","doi":"https://doi.org/10.48550/arxiv.2603.09221"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2603.09221","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.09221","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":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.2603.09221","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5128772994","display_name":"Peihao Wang","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Wang, Peihao","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5128714362","display_name":"Shan Yang","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Yang, Shan","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100709594","display_name":"Xijun Wang","orcid":"https://orcid.org/0000-0001-9375-8280"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Wang, Xijun","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5032057441","display_name":"Tesi Xiao","orcid":"https://orcid.org/0009-0001-6519-493X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Xiao, Tesi","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5128713761","display_name":"Xin Liu","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Liu, Xin","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5128690858","display_name":"Changlong Yu","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Yu, Changlong","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100937834","display_name":"Yu Lou","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Lou, Yu","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5128735849","display_name":"Pan Li","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Li, Pan","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5128773501","display_name":"Zhangyang Wang","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Wang, Zhangyang","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5128748129","display_name":"Ming Lin","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Lin, Ming","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5128709198","display_name":"Ren\u00e9 Vidal","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Vidal, Ren\u00e9","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/T10462","display_name":"Reinforcement Learning in Robotics","score":0.43320000171661377,"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/T10462","display_name":"Reinforcement Learning in Robotics","score":0.43320000171661377,"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/T10906","display_name":"AI-based Problem Solving and Planning","score":0.17499999701976776,"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/T11714","display_name":"Multimodal Machine Learning Applications","score":0.06109999865293503,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"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/reinforcement-learning","display_name":"Reinforcement learning","score":0.6255999803543091},{"id":"https://openalex.org/keywords/optimal-control","display_name":"Optimal control","score":0.5482000112533569},{"id":"https://openalex.org/keywords/scalability","display_name":"Scalability","score":0.5133000016212463},{"id":"https://openalex.org/keywords/solver","display_name":"Solver","score":0.49380001425743103},{"id":"https://openalex.org/keywords/embedding","display_name":"Embedding","score":0.48919999599456787},{"id":"https://openalex.org/keywords/inference","display_name":"Inference","score":0.47780001163482666},{"id":"https://openalex.org/keywords/component","display_name":"Component (thermodynamics)","score":0.44620001316070557},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.41909998655319214}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.7009999752044678},{"id":"https://openalex.org/C97541855","wikidata":"https://www.wikidata.org/wiki/Q830687","display_name":"Reinforcement learning","level":2,"score":0.6255999803543091},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.5482000112533569},{"id":"https://openalex.org/C48044578","wikidata":"https://www.wikidata.org/wiki/Q727490","display_name":"Scalability","level":2,"score":0.5133000016212463},{"id":"https://openalex.org/C2778770139","wikidata":"https://www.wikidata.org/wiki/Q1966904","display_name":"Solver","level":2,"score":0.49380001425743103},{"id":"https://openalex.org/C41608201","wikidata":"https://www.wikidata.org/wiki/Q980509","display_name":"Embedding","level":2,"score":0.48919999599456787},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.48010000586509705},{"id":"https://openalex.org/C2776214188","wikidata":"https://www.wikidata.org/wiki/Q408386","display_name":"Inference","level":2,"score":0.47780001163482666},{"id":"https://openalex.org/C168167062","wikidata":"https://www.wikidata.org/wiki/Q1117970","display_name":"Component (thermodynamics)","level":2,"score":0.44620001316070557},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.41909998655319214},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.39309999346733093},{"id":"https://openalex.org/C14646407","wikidata":"https://www.wikidata.org/wiki/Q1430750","display_name":"Bellman equation","level":2,"score":0.3919999897480011},{"id":"https://openalex.org/C125411270","wikidata":"https://www.wikidata.org/wiki/Q18653","display_name":"Encoding (memory)","level":2,"score":0.3564000129699707},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.35339999198913574},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.3116999864578247},{"id":"https://openalex.org/C166088908","wikidata":"https://www.wikidata.org/wiki/Q308495","display_name":"Abductive reasoning","level":2,"score":0.3012000024318695},{"id":"https://openalex.org/C2779231336","wikidata":"https://www.wikidata.org/wiki/Q7534724","display_name":"Sketch","level":2,"score":0.2930000126361847},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.2773999869823456},{"id":"https://openalex.org/C106189395","wikidata":"https://www.wikidata.org/wiki/Q176789","display_name":"Markov decision process","level":3,"score":0.27090001106262207},{"id":"https://openalex.org/C159423971","wikidata":"https://www.wikidata.org/wiki/Q177251","display_name":"Associative property","level":2,"score":0.27059999108314514},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.2596000134944916},{"id":"https://openalex.org/C2779182362","wikidata":"https://www.wikidata.org/wiki/Q17126187","display_name":"Session (web analytics)","level":2,"score":0.2574000060558319},{"id":"https://openalex.org/C177284502","wikidata":"https://www.wikidata.org/wiki/Q1005390","display_name":"Adapter (computing)","level":2,"score":0.25040000677108765}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2603.09221","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.09221","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":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.2603.09221","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.09221","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":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":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Associative":[0],"memory":[1],"has":[2],"long":[3],"underpinned":[4],"the":[5,48,59,86],"design":[6],"of":[7],"sequential":[8],"models.":[9],"Beyond":[10],"recall,":[11],"humans":[12],"reason":[13],"by":[14,135],"projecting":[15],"future":[16],"states":[17,71],"and":[18,57,82,108,141,147,161],"selecting":[19],"goal-directed":[20],"actions,":[21],"a":[22,76,99,105,112],"capability":[23],"that":[24,150],"modern":[25],"language":[26],"models":[27],"increasingly":[28],"require":[29],"but":[30],"do":[31],"not":[32],"natively":[33],"encode.":[34],"While":[35],"prior":[36],"work":[37],"uses":[38],"reinforcement":[39],"learning":[40],"or":[41],"test-time":[42,167],"training,":[43],"planning":[44,68,91],"remains":[45],"external":[46],"to":[47,89,137],"model":[49],"architecture.":[50],"We":[51],"formulate":[52],"reasoning":[53,133,165],"as":[54,85,111,123,154],"optimal":[55,152],"control":[56,153],"introduce":[58],"Test-Time":[60],"Control":[61],"(TTC)":[62],"layer,":[63],"which":[64],"performs":[65],"finite-horizon":[66],"LQR":[67,101],"over":[69],"latent":[70],"at":[72],"inference":[73],"time,":[74],"represents":[75],"value":[77],"function":[78],"within":[79],"neural":[80],"architectures,":[81],"leverages":[83],"it":[84,110],"nested":[87],"objective":[88],"enable":[90],"before":[92],"prediction.":[93],"To":[94],"ensure":[95],"scalability,":[96],"we":[97],"derive":[98],"hardware-efficient":[100],"solver":[102],"based":[103],"on":[104,139,145],"symplectic":[106],"formulation":[107],"implement":[109],"fused":[113],"CUDA":[114],"kernel,":[115],"enabling":[116],"parallel":[117],"execution":[118],"with":[119],"minimal":[120],"overhead.":[121],"Integrated":[122],"an":[124,155,159],"adapter":[125],"into":[126],"pretrained":[127],"LLMs,":[128],"TTC":[129],"layers":[130],"improve":[131],"mathematical":[132],"performance":[134],"up":[136],"+27.8%":[138],"MATH-500":[140],"2-3x":[142],"Pass@8":[143],"improvements":[144],"AMC":[146],"AIME,":[148],"demonstrating":[149],"embedding":[151],"architectural":[156],"component":[157],"provides":[158],"effective":[160],"scalable":[162],"mechanism":[163],"for":[164],"beyond":[166],"training.":[168]},"counts_by_year":[],"updated_date":"2026-07-01T06:00:48.157686","created_date":"2026-03-12T00:00:00"}