{"id":"https://openalex.org/W7166516601","doi":"https://doi.org/10.48550/arxiv.2606.27731","title":"Enhancing Numerical Prediction in LLMs via Smooth MMD Alignment","display_name":"Enhancing Numerical Prediction in LLMs via Smooth MMD Alignment","publication_year":2026,"publication_date":"2026-06-26","ids":{"openalex":"https://openalex.org/W7166516601","doi":"https://doi.org/10.48550/arxiv.2606.27731"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2606.27731","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2606.27731","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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.2606.27731","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5021918820","display_name":"Zhuo Zuo","orcid":"https://orcid.org/0000-0003-2341-177X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Zuo, Zhuo","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5139578734","display_name":"Li Yue","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Yue, Li","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5139583156","display_name":"Wenhao Zheng","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Zheng, Wenhao","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5139135714","display_name":"Chenpeng Wang","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Wang, Chenpeng","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5139571107","display_name":"Xianggen Liu","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Liu, Xianggen","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/T10028","display_name":"Topic Modeling","score":0.414000004529953,"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":0.414000004529953,"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/T13702","display_name":"Machine Learning in Healthcare","score":0.10890000313520432,"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":0.07150000333786011,"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/kernel","display_name":"Kernel (algebra)","score":0.6990000009536743},{"id":"https://openalex.org/keywords/smoothness","display_name":"Smoothness","score":0.6097999811172485},{"id":"https://openalex.org/keywords/residual","display_name":"Residual","score":0.6000000238418579},{"id":"https://openalex.org/keywords/metric","display_name":"Metric (unit)","score":0.5842999815940857},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.4699000120162964},{"id":"https://openalex.org/keywords/matching","display_name":"Matching (statistics)","score":0.46219998598098755},{"id":"https://openalex.org/keywords/kernel-method","display_name":"Kernel method","score":0.43380001187324524}],"concepts":[{"id":"https://openalex.org/C74193536","wikidata":"https://www.wikidata.org/wiki/Q574844","display_name":"Kernel (algebra)","level":2,"score":0.6990000009536743},{"id":"https://openalex.org/C102634674","wikidata":"https://www.wikidata.org/wiki/Q868473","display_name":"Smoothness","level":2,"score":0.6097999811172485},{"id":"https://openalex.org/C155512373","wikidata":"https://www.wikidata.org/wiki/Q287450","display_name":"Residual","level":2,"score":0.6000000238418579},{"id":"https://openalex.org/C176217482","wikidata":"https://www.wikidata.org/wiki/Q860554","display_name":"Metric (unit)","level":2,"score":0.5842999815940857},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5619999766349792},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5070000290870667},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.4699000120162964},{"id":"https://openalex.org/C165064840","wikidata":"https://www.wikidata.org/wiki/Q1321061","display_name":"Matching (statistics)","level":2,"score":0.46219998598098755},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.44609999656677246},{"id":"https://openalex.org/C122280245","wikidata":"https://www.wikidata.org/wiki/Q620622","display_name":"Kernel method","level":3,"score":0.43380001187324524},{"id":"https://openalex.org/C190812933","wikidata":"https://www.wikidata.org/wiki/Q28923","display_name":"Chart","level":2,"score":0.4196999967098236},{"id":"https://openalex.org/C26517878","wikidata":"https://www.wikidata.org/wiki/Q228039","display_name":"Key (lock)","level":2,"score":0.39980000257492065},{"id":"https://openalex.org/C71134354","wikidata":"https://www.wikidata.org/wiki/Q458825","display_name":"Kernel density estimation","level":3,"score":0.3955000042915344},{"id":"https://openalex.org/C195699287","wikidata":"https://www.wikidata.org/wiki/Q7915722","display_name":"Variable kernel density estimation","level":4,"score":0.3702000081539154},{"id":"https://openalex.org/C2776760102","wikidata":"https://www.wikidata.org/wiki/Q5139990","display_name":"Code (set theory)","level":3,"score":0.36399999260902405},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.34439998865127563},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.33230000734329224},{"id":"https://openalex.org/C110121322","wikidata":"https://www.wikidata.org/wiki/Q865811","display_name":"Distribution (mathematics)","level":2,"score":0.2969000041484833},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.2824000120162964},{"id":"https://openalex.org/C153180895","wikidata":"https://www.wikidata.org/wiki/Q7148389","display_name":"Pattern recognition (psychology)","level":2,"score":0.27549999952316284},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.26269999146461487},{"id":"https://openalex.org/C204323151","wikidata":"https://www.wikidata.org/wiki/Q905424","display_name":"Range (aeronautics)","level":2,"score":0.25780001282691956}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2606.27731","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2606.27731","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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.2606.27731","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2606.27731","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Despite":[0],"their":[1,39],"strong":[2],"general":[3],"capabilities,":[4],"large":[5],"language":[6],"models":[7],"(LLMs)":[8],"often":[9],"remain":[10],"unreliable":[11],"when":[12],"outputs":[13],"must":[14],"be":[15],"numerically":[16],"precise.":[17],"A":[18],"key":[19],"reason":[20],"is":[21,153],"the":[22,35,54,77,82,89,93,146],"training":[23],"objective:":[24],"standard":[25],"cross-entropy":[26,131],"treats":[27],"numeric":[28,62,73,79],"tokens":[29,63],"as":[30],"unstructured":[31],"categories":[32],"and":[33,64,87,114,122,132,142,144],"ignores":[34],"metric":[36],"structure":[37],"of":[38,148],"values.":[40],"We":[41,101],"address":[42],"this":[43,68],"mismatch":[44],"with":[45],"Smooth":[46],"Maximum":[47],"Mean":[48],"Discrepancy":[49],"(SMMD),":[50],"which":[51],"builds":[52],"on":[53,104],"classic":[55],"MMD":[56,141],"by":[57],"incorporating":[58],"value-distance":[59],"kernels":[60],"over":[61,71,92,129],"graph-based":[65],"smoothness.":[66],"With":[67],"kernel":[69,85,95,150],"defined":[70],"a":[72],"sub-vocabulary,":[74],"SMMD":[75,103,125],"aligns":[76],"predicted":[78],"distribution":[80],"to":[81,97],"target":[83],"via":[84],"matching":[86],"smooths":[88],"prediction-target":[90],"residual":[91],"induced":[94],"graph":[96],"encourage":[98],"local":[99],"consistency.":[100],"evaluate":[102],"four":[105],"numeric-target":[106,134],"tasks:":[107],"mathematical":[108],"reasoning,":[109],"arithmetic":[110],"calculation,":[111],"clock-time":[112],"recognition,":[113],"chart":[115],"question":[116],"answering,":[117],"across":[118],"multiple":[119],"open-weight":[120],"LLM":[121],"VLM":[123],"backbones.":[124],"consistently":[126],"improves":[127],"accuracy":[128],"both":[130],"recent":[133],"losses;":[135],"analyses":[136],"show":[137],"complementary":[138],"effects":[139],"between":[140],"smoothness":[143],"underscore":[145],"importance":[147],"distance-based":[149],"design.":[151],"Code":[152],"available":[154],"at":[155],"https://github.com/Zuozhuo/smmd-loss.":[156]},"counts_by_year":[],"updated_date":"2026-07-28T07:46:37.118299","created_date":"2026-06-30T00:00:00"}
