{"id":"https://openalex.org/W7164147372","doi":"https://doi.org/10.48550/arxiv.2606.09873","title":"Rotate2Think: Geometric Priming via Orthogonal Rotation to Improve Language Model Reasoning","display_name":"Rotate2Think: Geometric Priming via Orthogonal Rotation to Improve Language Model Reasoning","publication_year":2026,"publication_date":"2026-06-02","ids":{"openalex":"https://openalex.org/W7164147372","doi":"https://doi.org/10.48550/arxiv.2606.09873"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2606.09873","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2606.09873","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":"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.2606.09873","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5138325582","display_name":"Aditya Sharma","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Sharma, Aditya","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5075885606","display_name":"Christopher Pal","orcid":"https://orcid.org/0000-0001-6534-2114"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Pal, Christopher J.","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5075664559","display_name":"Amal Zouaq","orcid":"https://orcid.org/0000-0002-4791-0752"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Zouaq, Amal","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/T11714","display_name":"Multimodal Machine Learning Applications","score":0.4634999930858612,"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"}},"topics":[{"id":"https://openalex.org/T11714","display_name":"Multimodal Machine Learning Applications","score":0.4634999930858612,"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"}},{"id":"https://openalex.org/T10028","display_name":"Topic Modeling","score":0.15940000116825104,"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/T11273","display_name":"Advanced Graph Neural Networks","score":0.06650000065565109,"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/inference","display_name":"Inference","score":0.597599983215332},{"id":"https://openalex.org/keywords/embedding","display_name":"Embedding","score":0.5735999941825867},{"id":"https://openalex.org/keywords/representation","display_name":"Representation (politics)","score":0.5383999943733215},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.5187000036239624},{"id":"https://openalex.org/keywords/benchmark","display_name":"Benchmark (surveying)","score":0.459199994802475},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.45739999413490295},{"id":"https://openalex.org/keywords/cluster-analysis","display_name":"Cluster analysis","score":0.45260000228881836},{"id":"https://openalex.org/keywords/rotation","display_name":"Rotation (mathematics)","score":0.4422000050544739}],"concepts":[{"id":"https://openalex.org/C2776214188","wikidata":"https://www.wikidata.org/wiki/Q408386","display_name":"Inference","level":2,"score":0.597599983215332},{"id":"https://openalex.org/C41608201","wikidata":"https://www.wikidata.org/wiki/Q980509","display_name":"Embedding","level":2,"score":0.5735999941825867},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5734000205993652},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.5383999943733215},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.5187000036239624},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.4699999988079071},{"id":"https://openalex.org/C185798385","wikidata":"https://www.wikidata.org/wiki/Q1161707","display_name":"Benchmark (surveying)","level":2,"score":0.459199994802475},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.45739999413490295},{"id":"https://openalex.org/C73555534","wikidata":"https://www.wikidata.org/wiki/Q622825","display_name":"Cluster analysis","level":2,"score":0.45260000228881836},{"id":"https://openalex.org/C74050887","wikidata":"https://www.wikidata.org/wiki/Q848368","display_name":"Rotation (mathematics)","level":2,"score":0.4422000050544739},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.398499995470047},{"id":"https://openalex.org/C13336665","wikidata":"https://www.wikidata.org/wiki/Q125977","display_name":"Vector space","level":2,"score":0.37310001254081726},{"id":"https://openalex.org/C155911833","wikidata":"https://www.wikidata.org/wiki/Q3817354","display_name":"Spatial intelligence","level":2,"score":0.35280001163482666},{"id":"https://openalex.org/C195344581","wikidata":"https://www.wikidata.org/wiki/Q2555318","display_name":"Automated reasoning","level":2,"score":0.33489999175071716},{"id":"https://openalex.org/C774472","wikidata":"https://www.wikidata.org/wiki/Q6760393","display_name":"Margin (machine learning)","level":2,"score":0.33320000767707825},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.33149999380111694},{"id":"https://openalex.org/C2776760102","wikidata":"https://www.wikidata.org/wiki/Q5139990","display_name":"Code (set theory)","level":3,"score":0.30970001220703125},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.2939999997615814},{"id":"https://openalex.org/C37335422","wikidata":"https://www.wikidata.org/wiki/Q6888134","display_name":"Model-based reasoning","level":3,"score":0.28859999775886536},{"id":"https://openalex.org/C83725634","wikidata":"https://www.wikidata.org/wiki/Q7268699","display_name":"Qualitative reasoning","level":2,"score":0.26930001378059387},{"id":"https://openalex.org/C125411270","wikidata":"https://www.wikidata.org/wiki/Q18653","display_name":"Encoding (memory)","level":2,"score":0.2563999891281128},{"id":"https://openalex.org/C204321447","wikidata":"https://www.wikidata.org/wiki/Q30642","display_name":"Natural language processing","level":1,"score":0.25220000743865967}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2606.09873","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2606.09873","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":"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.2606.09873","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2606.09873","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":"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":[{"score":0.8097949028015137,"display_name":"Quality Education","id":"https://metadata.un.org/sdg/4"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Reasoning":[0],"models":[1,117],"achieve":[2],"strong":[3],"performance":[4],"on":[5,210],"challenging":[6],"tasks":[7],"by":[8],"generating":[9],"explicit":[10],"intermediate":[11],"reasoning":[12,27,56,77,180,209],"traces":[13],"before":[14],"producing":[15],"a":[16,33,90,107,129,133,143,151,172],"final":[17],"answer.":[18],"Yet":[19],"the":[20,41,44,74,125,160,176,179],"internal":[21],"structure":[22,50],"of":[23,43,111,154,178,194],"representation":[24],"space":[25,113],"when":[26],"remains":[28],"poorly":[29],"understood:":[30],"how":[31],"do":[32],"model's":[34],"hidden":[35,71],"representations":[36],"differ":[37],"during":[38],"thinking":[39,67,99,104,163,166],"versus":[40],"embeddings":[42,65,68,105],"input":[45,64,97],"prompt,":[46],"and":[47,66,76,98,118,158,186,201,204],"can":[48],"this":[49,148],"be":[51],"exploited":[52],"to":[53,207],"elicit":[54],"stronger":[55],"at":[57,168,175],"inference":[58,169],"time?":[59],"We":[60,140],"show":[61],"that":[62,146],"both":[63],"(mean-pooled":[69],"last-layer":[70],"states":[72],"over":[73],"prompt":[75],"trace,":[78],"respectively)":[79],"exhibit":[80],"extremely":[81],"high":[82],"conicity,":[83],"with":[84,103],"all":[85],"vectors":[86],"clustering":[87],"tightly":[88],"around":[89],"single":[91],"mean":[92,96],"direction.":[93],"Crucially,":[94],"these":[95],"directions":[100],"are":[101],"non-collinear,":[102],"occupying":[106],"geometrically":[108],"distinct":[109],"region":[110],"embedding":[112],"across":[114,183,198],"many":[115],"different":[116],"benchmark":[119],"tasks.":[120],"This":[121],"observation":[122],"motivates":[123],"casting":[124],"input-to-thinking":[126],"transition":[127],"as":[128],"rotation":[130,149],"problem":[131],"admitting":[132],"closed-form":[134],"solution":[135],"via":[136],"orthogonal":[137],"Procrustes":[138],"analysis.":[139],"propose":[141],"Rotate2Think,":[142],"training-free":[144],"method":[145],"estimates":[147],"from":[150],"small":[152],"set":[153],"correctly":[155],"solved":[156],"examples":[157],"injects":[159],"resulting":[161],"synthetic":[162],"vector":[164],"between":[165],"delimiters":[167],"time,":[170],"providing":[171],"geometric":[173],"primer":[174],"onset":[177],"trace.":[181],"Evaluated":[182],"multiple":[184],"benchmarks":[185],"model":[187],"families,":[188],"Rotate2Think":[189],"improves":[190],"accuracy":[191],"in":[192],"30":[193],"32":[195],"model-benchmark":[196],"configurations":[197],"mathematics,":[199],"science,":[200],"code":[202],"tasks,":[203],"generalizes":[205],"zero-shot":[206],"multimodal":[208],"MATH-Vision.":[211]},"counts_by_year":[],"updated_date":"2026-07-01T06:00:48.157686","created_date":"2026-06-11T00:00:00"}