{"id":"https://openalex.org/W7139038209","doi":"https://doi.org/10.1609/aaai.v40i40.40697","title":"SCALE: Selective Resource Allocation for Overcoming Performance Bottlenecks in Mathematical Test-time Scaling","display_name":"SCALE: Selective Resource Allocation for Overcoming Performance Bottlenecks in Mathematical Test-time Scaling","publication_year":2026,"publication_date":"2026-03-14","ids":{"openalex":"https://openalex.org/W7139038209","doi":"https://doi.org/10.1609/aaai.v40i40.40697"},"language":null,"primary_location":{"id":"doi:10.1609/aaai.v40i40.40697","is_oa":true,"landing_page_url":"https://doi.org/10.1609/aaai.v40i40.40697","pdf_url":"https://ojs.aaai.org/index.php/AAAI/article/download/40697/44658","source":{"id":"https://openalex.org/S4210191458","display_name":"Proceedings of the AAAI Conference on Artificial Intelligence","issn_l":"2159-5399","issn":["2159-5399","2374-3468"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/P4310320058","host_organization_name":"Association for the Advancement of Artificial Intelligence","host_organization_lineage":["https://openalex.org/P4310320058"],"host_organization_lineage_names":["Association for the Advancement of Artificial Intelligence"],"type":"conference"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the AAAI Conference on Artificial Intelligence","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://ojs.aaai.org/index.php/AAAI/article/download/40697/44658","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5102595552","display_name":"Yang Xiao","orcid":"https://orcid.org/0009-0009-1480-8821"},"institutions":[{"id":"https://openalex.org/I14243506","display_name":"Hong Kong Polytechnic University","ror":"https://ror.org/0030zas98","country_code":"HK","type":"education","lineage":["https://openalex.org/I14243506"]}],"countries":["HK"],"is_corresponding":false,"raw_author_name":"Yang Xiao","raw_affiliation_strings":["The Hong Kong Polytechnic University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"The Hong Kong Polytechnic University","institution_ids":["https://openalex.org/I14243506"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5002321609","display_name":"Chunpu Xu","orcid":null},"institutions":[{"id":"https://openalex.org/I14243506","display_name":"Hong Kong Polytechnic University","ror":"https://ror.org/0030zas98","country_code":"HK","type":"education","lineage":["https://openalex.org/I14243506"]}],"countries":["HK"],"is_corresponding":false,"raw_author_name":"Chunpu Xu","raw_affiliation_strings":["The Hong Kong Polytechnic University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"The Hong Kong Polytechnic University","institution_ids":["https://openalex.org/I14243506"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5129780608","display_name":"Ruifeng Yuan","orcid":null},"institutions":[{"id":"https://openalex.org/I14243506","display_name":"Hong Kong Polytechnic University","ror":"https://ror.org/0030zas98","country_code":"HK","type":"education","lineage":["https://openalex.org/I14243506"]}],"countries":["HK"],"is_corresponding":false,"raw_author_name":"Ruifeng Yuan","raw_affiliation_strings":["The Hong Kong Polytechnic University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"The Hong Kong Polytechnic University","institution_ids":["https://openalex.org/I14243506"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5039894407","display_name":"Jessie Wang","orcid":null},"institutions":[{"id":"https://openalex.org/I14243506","display_name":"Hong Kong Polytechnic University","ror":"https://ror.org/0030zas98","country_code":"HK","type":"education","lineage":["https://openalex.org/I14243506"]}],"countries":["HK"],"is_corresponding":false,"raw_author_name":"Jessie Wang","raw_affiliation_strings":["The Hong Kong Polytechnic University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"The Hong Kong Polytechnic University","institution_ids":["https://openalex.org/I14243506"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5129965877","display_name":"Wenjie Li","orcid":null},"institutions":[{"id":"https://openalex.org/I14243506","display_name":"Hong Kong Polytechnic University","ror":"https://ror.org/0030zas98","country_code":"HK","type":"education","lineage":["https://openalex.org/I14243506"]}],"countries":["HK"],"is_corresponding":false,"raw_author_name":"Wenjie Li","raw_affiliation_strings":["The Hong Kong Polytechnic University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"The Hong Kong Polytechnic University","institution_ids":["https://openalex.org/I14243506"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5130174278","display_name":"Pengfei Liu","orcid":null},"institutions":[{"id":"https://openalex.org/I183067930","display_name":"Shanghai Jiao Tong University","ror":"https://ror.org/0220qvk04","country_code":"CN","type":"education","lineage":["https://openalex.org/I183067930"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Pengfei Liu","raw_affiliation_strings":["Shanghai Jiaotong University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Shanghai Jiaotong University","institution_ids":["https://openalex.org/I183067930"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":6,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.79344729,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"40","issue":"40","first_page":"34034","last_page":"34042"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10028","display_name":"Topic Modeling","score":0.35659998655319214,"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":0.35659998655319214,"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/T10181","display_name":"Natural Language Processing Techniques","score":0.11739999800920486,"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/T11948","display_name":"Machine Learning in Materials Science","score":0.07509999722242355,"subfield":{"id":"https://openalex.org/subfields/2505","display_name":"Materials Chemistry"},"field":{"id":"https://openalex.org/fields/25","display_name":"Materials Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/resource-allocation","display_name":"Resource allocation","score":0.6299999952316284},{"id":"https://openalex.org/keywords/scaling","display_name":"Scaling","score":0.5906000137329102},{"id":"https://openalex.org/keywords/context","display_name":"Context (archaeology)","score":0.5763999819755554},{"id":"https://openalex.org/keywords/scale","display_name":"Scale (ratio)","score":0.49300000071525574},{"id":"https://openalex.org/keywords/resource","display_name":"Resource (disambiguation)","score":0.4887000024318695},{"id":"https://openalex.org/keywords/mode","display_name":"Mode (computer interface)","score":0.47999998927116394},{"id":"https://openalex.org/keywords/computational-resource","display_name":"Computational resource","score":0.4498000144958496},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.4431000053882599}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.7580999732017517},{"id":"https://openalex.org/C29202148","wikidata":"https://www.wikidata.org/wiki/Q287260","display_name":"Resource allocation","level":2,"score":0.6299999952316284},{"id":"https://openalex.org/C99844830","wikidata":"https://www.wikidata.org/wiki/Q102441924","display_name":"Scaling","level":2,"score":0.5906000137329102},{"id":"https://openalex.org/C2779343474","wikidata":"https://www.wikidata.org/wiki/Q3109175","display_name":"Context (archaeology)","level":2,"score":0.5763999819755554},{"id":"https://openalex.org/C2778755073","wikidata":"https://www.wikidata.org/wiki/Q10858537","display_name":"Scale (ratio)","level":2,"score":0.49300000071525574},{"id":"https://openalex.org/C206345919","wikidata":"https://www.wikidata.org/wiki/Q20380951","display_name":"Resource (disambiguation)","level":2,"score":0.4887000024318695},{"id":"https://openalex.org/C48677424","wikidata":"https://www.wikidata.org/wiki/Q6888088","display_name":"Mode (computer interface)","level":2,"score":0.47999998927116394},{"id":"https://openalex.org/C127964446","wikidata":"https://www.wikidata.org/wiki/Q1092142","display_name":"Computational resource","level":3,"score":0.4498000144958496},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.4431000053882599},{"id":"https://openalex.org/C206729178","wikidata":"https://www.wikidata.org/wiki/Q2271896","display_name":"Scheduling (production processes)","level":2,"score":0.43779999017715454},{"id":"https://openalex.org/C111335779","wikidata":"https://www.wikidata.org/wiki/Q3454686","display_name":"Reduction (mathematics)","level":2,"score":0.4327999949455261},{"id":"https://openalex.org/C124681953","wikidata":"https://www.wikidata.org/wiki/Q339062","display_name":"Decomposition","level":2,"score":0.4203000068664551},{"id":"https://openalex.org/C120314980","wikidata":"https://www.wikidata.org/wiki/Q180634","display_name":"Distributed computing","level":1,"score":0.41760000586509705},{"id":"https://openalex.org/C2780513914","wikidata":"https://www.wikidata.org/wiki/Q18210350","display_name":"Bottleneck","level":2,"score":0.41190001368522644},{"id":"https://openalex.org/C2780609101","wikidata":"https://www.wikidata.org/wiki/Q17156588","display_name":"Resource management (computing)","level":2,"score":0.39250001311302185},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.37470000982284546},{"id":"https://openalex.org/C3019252630","wikidata":"https://www.wikidata.org/wiki/Q6549547","display_name":"Limited resources","level":2,"score":0.3702000081539154},{"id":"https://openalex.org/C179799912","wikidata":"https://www.wikidata.org/wiki/Q205084","display_name":"Computational complexity theory","level":2,"score":0.36809998750686646},{"id":"https://openalex.org/C125411270","wikidata":"https://www.wikidata.org/wiki/Q18653","display_name":"Encoding (memory)","level":2,"score":0.31470000743865967},{"id":"https://openalex.org/C66024118","wikidata":"https://www.wikidata.org/wiki/Q1122506","display_name":"Computational model","level":2,"score":0.30820000171661377},{"id":"https://openalex.org/C26517878","wikidata":"https://www.wikidata.org/wiki/Q228039","display_name":"Key (lock)","level":2,"score":0.2924000024795532},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.290800005197525},{"id":"https://openalex.org/C47822265","wikidata":"https://www.wikidata.org/wiki/Q854457","display_name":"Complex system","level":2,"score":0.26669999957084656},{"id":"https://openalex.org/C192209626","wikidata":"https://www.wikidata.org/wiki/Q190909","display_name":"Focus (optics)","level":2,"score":0.2653000056743622}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1609/aaai.v40i40.40697","is_oa":true,"landing_page_url":"https://doi.org/10.1609/aaai.v40i40.40697","pdf_url":"https://ojs.aaai.org/index.php/AAAI/article/download/40697/44658","source":{"id":"https://openalex.org/S4210191458","display_name":"Proceedings of the AAAI Conference on Artificial Intelligence","issn_l":"2159-5399","issn":["2159-5399","2374-3468"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/P4310320058","host_organization_name":"Association for the Advancement of Artificial Intelligence","host_organization_lineage":["https://openalex.org/P4310320058"],"host_organization_lineage_names":["Association for the Advancement of Artificial Intelligence"],"type":"conference"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the AAAI Conference on Artificial Intelligence","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1609/aaai.v40i40.40697","is_oa":true,"landing_page_url":"https://doi.org/10.1609/aaai.v40i40.40697","pdf_url":"https://ojs.aaai.org/index.php/AAAI/article/download/40697/44658","source":{"id":"https://openalex.org/S4210191458","display_name":"Proceedings of the AAAI Conference on Artificial Intelligence","issn_l":"2159-5399","issn":["2159-5399","2374-3468"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/P4310320058","host_organization_name":"Association for the Advancement of Artificial Intelligence","host_organization_lineage":["https://openalex.org/P4310320058"],"host_organization_lineage_names":["Association for the Advancement of Artificial Intelligence"],"type":"conference"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the AAAI Conference on Artificial Intelligence","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7139038209.pdf","grobid_xml":"https://content.openalex.org/works/W7139038209.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Test-time":[0],"compute":[1],"scaling":[2,164,192],"has":[3],"emerged":[4],"as":[5],"a":[6,74,187],"powerful":[7],"paradigm":[8],"for":[9,120,126],"enhancing":[10],"mathematical":[11],"reasoning":[12,34,95],"in":[13,190],"large":[14],"language":[15],"models":[16],"(LLMs)":[17],"by":[18,65,184],"allocating":[19],"additional":[20,58],"computational":[21,59,79,182],"resources":[22,60,80,138],"during":[23],"inference.":[24],"However,":[25],"current":[26,198],"methods":[27],"employ":[28],"uniform":[29,52,163],"resource":[30,154],"distribution":[31],"across":[32],"all":[33],"sub-problems,":[35,96,111],"creating":[36],"fundamental":[37,195],"bottlenecks":[38,56],"where":[39,57],"challenging":[40,110,140],"sub-problems":[41,122,141],"receive":[42],"insufficient":[43],"attention":[44],"while":[45,142,180],"routine":[46,106,144],"operations":[47,107,145],"consume":[48],"disproportionate":[49],"resources.":[50],"This":[51],"allocation":[53],"creates":[54],"performance":[55,150],"yield":[61],"diminishing":[62],"returns.":[63],"Inspired":[64],"dual-process":[66],"theory,":[67],"we":[68],"propose":[69],"SCALE":[70,85,147,160],"(Selective":[71],"Resource":[72],"Allocation),":[73],"framework":[75],"that":[76,159,193],"selectively":[77],"allocates":[78],"based":[81],"on":[82,139,178],"sub-problem":[83,102],"difficulty.":[84],"operates":[86],"through":[87],"four":[88],"stages:":[89],"(1)":[90],"problem":[91],"decomposition":[92],"into":[93],"sequential":[94,131],"(2)":[97],"difficulty":[98],"assessment":[99],"of":[100,169,197],"each":[101],"to":[103,171,176],"distinguish":[104],"between":[105,117],"and":[108,123,129],"computationally":[109],"(3)":[112],"selective":[113],"processing":[114,143],"mode":[115],"assignment":[116],"System":[118,124],"1":[119],"simple":[121],"2":[125],"complex":[127],"ones,":[128],"(4)":[130],"execution":[132],"with":[133,152],"context":[134],"propagation.":[135],"By":[136],"concentrating":[137],"efficiently,":[146],"achieves":[148],"substantial":[149],"improvements":[151,168],"superior":[153],"utilization.":[155],"Extensive":[156],"experiments":[157],"demonstrate":[158],"significantly":[161],"outperforms":[162],"baselines,":[165],"achieving":[166],"accuracy":[167],"up":[170],"13.75":[172],"percentage":[173],"points":[174],"(57.50%":[175],"71.25%":[177],"AIME25)":[179],"reducing":[181],"costs":[183],"33-53%,":[185],"representing":[186],"major":[188],"advance":[189],"test-time":[191],"addresses":[194],"limitations":[196],"approaches.":[199]},"counts_by_year":[],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2026-03-20T00:00:00"}
