{"id":"https://openalex.org/W7133236465","doi":"https://doi.org/10.48550/arxiv.2602.23959","title":"Thinking with Images as Continuous Actions: Numerical Visual Chain-of-Thought","display_name":"Thinking with Images as Continuous Actions: Numerical Visual Chain-of-Thought","publication_year":2026,"publication_date":"2026-02-27","ids":{"openalex":"https://openalex.org/W7133236465","doi":"https://doi.org/10.48550/arxiv.2602.23959"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2602.23959","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2602.23959","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":"article"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2602.23959","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5124909181","display_name":"Kesen Zhao","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Zhao, Kesen","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5009738035","display_name":"Beier Zhu","orcid":"https://orcid.org/0000-0002-7900-6979"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Zhu, Beier","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5082187586","display_name":"Junbao Zhou","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Zhou, Junbao","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5127808960","display_name":"Xingyu Zhu","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Zhu, Xingyu","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5127834758","display_name":"Zhongqi Yue","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Yue, Zhongqi","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5127847717","display_name":"Hanwang Zhang","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Zhang, Hanwang","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":6,"corresponding_author_ids":["https://openalex.org/A5124909181"],"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":0.9761000275611877,"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":0.9761000275611877,"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/T10775","display_name":"Generative Adversarial Networks and Image Synthesis","score":0.0032999999821186066,"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/T11307","display_name":"Domain Adaptation and Few-Shot Learning","score":0.0027000000700354576,"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/visual-reasoning","display_name":"Visual reasoning","score":0.6617000102996826},{"id":"https://openalex.org/keywords/categorical-variable","display_name":"Categorical variable","score":0.46970000863075256},{"id":"https://openalex.org/keywords/reinforcement-learning","display_name":"Reinforcement learning","score":0.40310001373291016},{"id":"https://openalex.org/keywords/vocabulary","display_name":"Vocabulary","score":0.3831000030040741},{"id":"https://openalex.org/keywords/grasp","display_name":"GRASP","score":0.37229999899864197},{"id":"https://openalex.org/keywords/encoding","display_name":"Encoding (memory)","score":0.33340001106262207},{"id":"https://openalex.org/keywords/security-token","display_name":"Security token","score":0.33070001006126404},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.3156999945640564},{"id":"https://openalex.org/keywords/leverage","display_name":"Leverage (statistics)","score":0.3012999892234802}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.7361000180244446},{"id":"https://openalex.org/C2777508537","wikidata":"https://www.wikidata.org/wiki/Q7936620","display_name":"Visual reasoning","level":2,"score":0.6617000102996826},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.6080999970436096},{"id":"https://openalex.org/C5274069","wikidata":"https://www.wikidata.org/wiki/Q2285707","display_name":"Categorical variable","level":2,"score":0.46970000863075256},{"id":"https://openalex.org/C97541855","wikidata":"https://www.wikidata.org/wiki/Q830687","display_name":"Reinforcement learning","level":2,"score":0.40310001373291016},{"id":"https://openalex.org/C2777601683","wikidata":"https://www.wikidata.org/wiki/Q6499736","display_name":"Vocabulary","level":2,"score":0.3831000030040741},{"id":"https://openalex.org/C31972630","wikidata":"https://www.wikidata.org/wiki/Q844240","display_name":"Computer vision","level":1,"score":0.3752000033855438},{"id":"https://openalex.org/C171268870","wikidata":"https://www.wikidata.org/wiki/Q1486676","display_name":"GRASP","level":2,"score":0.37229999899864197},{"id":"https://openalex.org/C125411270","wikidata":"https://www.wikidata.org/wiki/Q18653","display_name":"Encoding (memory)","level":2,"score":0.33340001106262207},{"id":"https://openalex.org/C48145219","wikidata":"https://www.wikidata.org/wiki/Q1335365","display_name":"Security token","level":2,"score":0.33070001006126404},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.3156999945640564},{"id":"https://openalex.org/C153083717","wikidata":"https://www.wikidata.org/wiki/Q6535263","display_name":"Leverage (statistics)","level":2,"score":0.3012999892234802},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.298799991607666},{"id":"https://openalex.org/C2776459999","wikidata":"https://www.wikidata.org/wiki/Q2119376","display_name":"Fidelity","level":2,"score":0.288100004196167},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.287200003862381},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.28450000286102295},{"id":"https://openalex.org/C2780791683","wikidata":"https://www.wikidata.org/wiki/Q846785","display_name":"Action (physics)","level":2,"score":0.2806999981403351},{"id":"https://openalex.org/C137293760","wikidata":"https://www.wikidata.org/wiki/Q3621696","display_name":"Language model","level":2,"score":0.2685999870300293},{"id":"https://openalex.org/C94124525","wikidata":"https://www.wikidata.org/wiki/Q912550","display_name":"Categorization","level":2,"score":0.26339998841285706},{"id":"https://openalex.org/C184337299","wikidata":"https://www.wikidata.org/wiki/Q1437428","display_name":"Semantics (computer science)","level":2,"score":0.26179999113082886},{"id":"https://openalex.org/C61326573","wikidata":"https://www.wikidata.org/wiki/Q1496376","display_name":"Gaussian process","level":3,"score":0.26010000705718994},{"id":"https://openalex.org/C146849305","wikidata":"https://www.wikidata.org/wiki/Q370766","display_name":"Ground truth","level":2,"score":0.2522999942302704},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.2522999942302704},{"id":"https://openalex.org/C2780226545","wikidata":"https://www.wikidata.org/wiki/Q6888030","display_name":"Modality (human\u2013computer interaction)","level":2,"score":0.2522999942302704},{"id":"https://openalex.org/C81917197","wikidata":"https://www.wikidata.org/wiki/Q628760","display_name":"Selection (genetic algorithm)","level":2,"score":0.25029999017715454}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2602.23959","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2602.23959","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":"article"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2602.23959","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2602.23959","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":"article"},"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":{"Recent":[0],"multimodal":[1],"large":[2],"language":[3],"models":[4,84],"(MLLMs)":[5],"increasingly":[6],"rely":[7],"on":[8,137],"visual":[9,143,167],"chain-of-thought":[10],"to":[11,60,78,85],"perform":[12],"region-grounded":[13],"reasoning":[14,144,168],"over":[15,62,119],"images.":[16],"However,":[17],"existing":[18],"approaches":[19],"ground":[20],"regions":[21],"via":[22,124],"either":[23],"textified":[24],"coordinates-causing":[25],"modality":[26],"mismatch":[27],"and":[28,40,103,121,153],"semantic":[29],"fragmentation":[30],"or":[31],"fixed-granularity":[32],"patches":[33],"that":[34,57,147],"both":[35,100],"limit":[36],"precise":[37],"region":[38],"selection":[39],"often":[41],"require":[42],"non-trivial":[43],"architectural":[44,95],"changes.":[45],"In":[46,106],"this":[47],"paper,":[48],"we":[49,108],"propose":[50],"Numerical":[51],"Visual":[52],"Chain-of-Thought":[53],"(NV-CoT),":[54],"a":[55,79,114],"framework":[56,98],"enables":[58],"MLLMs":[59],"reason":[61],"images":[63],"using":[64],"continuous":[65,80],"numerical":[66],"coordinates.":[67],"NV-CoT":[68,128,148],"expands":[69],"the":[70,163],"MLLM":[71],"action":[72],"space":[73],"from":[74],"discrete":[75],"vocabulary":[76],"tokens":[77],"Euclidean":[81],"space,":[82],"allowing":[83],"directly":[86],"generate":[87],"bounding-box":[88],"coordinates":[89,120],"as":[90],"actions":[91],"with":[92,113,131],"only":[93],"minimal":[94],"modification.":[96],"The":[97,171],"supports":[99],"supervised":[101],"fine-tuning":[102],"reinforcement":[104],"learning.":[105],"particular,":[107],"replace":[109],"categorical":[110],"token":[111],"policies":[112],"Gaussian":[115],"(or":[116],"Laplace)":[117],"policy":[118,133],"introduce":[122],"stochasticity":[123],"reparameterized":[125],"sampling,":[126],"making":[127],"fully":[129],"compatible":[130],"GRPO-style":[132],"optimization.":[134],"Extensive":[135],"experiments":[136],"three":[138],"benchmarks":[139],"against":[140],"eight":[141],"representative":[142],"baselines":[145],"demonstrate":[146],"significantly":[149],"improves":[150],"localization":[151],"precision":[152],"final":[154],"answer":[155],"accuracy,":[156],"while":[157],"also":[158],"accelerating":[159],"training":[160],"convergence,":[161],"validating":[162],"effectiveness":[164],"of":[165],"continuous-action":[166],"in":[169,175],"MLLMs.":[170],"code":[172],"is":[173],"available":[174],"https://github.com/kesenzhao/NV-CoT.":[176]},"counts_by_year":[],"updated_date":"2026-03-03T06:18:10.843953","created_date":"2026-03-03T00:00:00"}
