{"id":"https://openalex.org/W4391632063","doi":"https://doi.org/10.48550/arxiv.2402.04163","title":"Tempered Calculus for ML: Application to Hyperbolic Model Embedding","display_name":"Tempered Calculus for ML: Application to Hyperbolic Model Embedding","publication_year":2024,"publication_date":"2024-02-06","ids":{"openalex":"https://openalex.org/W4391632063","doi":"https://doi.org/10.48550/arxiv.2402.04163"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2402.04163","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2402.04163","pdf_url":"https://arxiv.org/pdf/2402.04163","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"type":"preprint","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2402.04163","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5082414223","display_name":"Richard Nock","orcid":"https://orcid.org/0000-0001-8384-9621"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Nock, Richard","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5056776503","display_name":"Ehsan Amid","orcid":"https://orcid.org/0000-0001-6097-0226"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Amid, Ehsan","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5061293973","display_name":"Frank Nielsen","orcid":"https://orcid.org/0000-0001-5728-0726"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Nielsen, Frank","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5027489404","display_name":"Alexander Soen","orcid":"https://orcid.org/0000-0002-2440-4814"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Soen, Alexander","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5108549518","display_name":"Manfred K. Warmuth","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Warmuth, Manfred K.","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":true,"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/T11206","display_name":"Model Reduction and Neural Networks","score":0.7426000237464905,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":0.7426000237464905,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T13650","display_name":"Computational Physics and Python Applications","score":0.6951000094413757,"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/embedding","display_name":"Embedding","score":0.7098754644393921},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.6564059853553772},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.44145289063453674},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.37643909454345703},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3412531614303589},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.10116389393806458},{"id":"https://openalex.org/keywords/medicine","display_name":"Medicine","score":0.09205156564712524},{"id":"https://openalex.org/keywords/dentistry","display_name":"Dentistry","score":0.07247981429100037}],"concepts":[{"id":"https://openalex.org/C41608201","wikidata":"https://www.wikidata.org/wiki/Q980509","display_name":"Embedding","level":2,"score":0.7098754644393921},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.6564059853553772},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.44145289063453674},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.37643909454345703},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3412531614303589},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.10116389393806458},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.09205156564712524},{"id":"https://openalex.org/C199343813","wikidata":"https://www.wikidata.org/wiki/Q12128","display_name":"Dentistry","level":1,"score":0.07247981429100037}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2402.04163","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2402.04163","pdf_url":"https://arxiv.org/pdf/2402.04163","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2402.04163","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2402.04163","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":"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":"pmh:oai:arXiv.org:2402.04163","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2402.04163","pdf_url":"https://arxiv.org/pdf/2402.04163","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4391632063.pdf","grobid_xml":"https://content.openalex.org/works/W4391632063.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2748952813","https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W4245490552","https://openalex.org/W4225152035","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W1587224694","https://openalex.org/W2911598644"],"abstract_inverted_index":{"Most":[0],"mathematical":[1],"distortions":[2,39],"used":[3],"in":[4,9,69,127,161,196],"ML":[5,44],"are":[6,59,141],"fundamentally":[7],"integral":[8,18,78],"nature:":[10],"$f$-divergences,":[11],"Bregman":[12],"divergences,":[13],"(regularized)":[14],"optimal":[15],"transport":[16],"distances,":[17,22],"probability":[19],"metrics,":[20],"geodesic":[21],"etc.":[23],"In":[24],"this":[25,74],"paper,":[26],"we":[27],"unveil":[28,178],"a":[29,49,80,101,109,128,132,154,166,179],"grounded":[30],"theory":[31,194],"and":[32,137,145,168,192,211],"tools":[33],"which":[34,183],"can":[35,116],"help":[36],"improve":[37],"these":[38],"to":[40,150,153],"better":[41],"cope":[42],"with":[43,48,100,131,165],"requirements.":[45],"We":[46,83,147,177],"start":[47],"generalization":[50],"of":[51,89,94,103,124,203],"Riemann":[52],"integration":[53],"that":[54,58,140,156],"also":[55],"encapsulates":[56],"functions":[57],"not":[60],"strictly":[61],"additive":[62],"but":[63],"are,":[64],"more":[65,104],"generally,":[66],"$t$-additive,":[67],"as":[68,79,108],"nonextensive":[70],"statistical":[71],"mechanics.":[72],"Notably,":[73],"recovers":[75],"Volterra's":[76],"product":[77],"special":[81,133],"case.":[82],"then":[84],"generalize":[85],"the":[86,95,142,172,184,208],"Fundamental":[87],"Theorem":[88],"calculus":[90],"using":[91,207],"an":[92],"extension":[93],"(Euclidean)":[96],"derivative.":[97],"This,":[98],"along":[99,171],"series":[102],"specific":[105],"Theorems,":[106],"serves":[107],"basis":[110],"for":[111,182,200],"results":[112],"showing":[113],"how":[114,149],"one":[115],"specifically":[117],"design,":[118],"alter,":[119],"or":[120],"change":[121],"fundamental":[122],"properties":[123,139],"distortion":[125],"measures":[126],"simple":[129],"way,":[130],"emphasis":[134],"on":[135],"geometric-":[136],"ML-related":[138],"metricity,":[143],"hyperbolicity,":[144],"encoding.":[146],"show":[148],"apply":[151],"it":[152],"problem":[155],"has":[157,188],"recently":[158],"gained":[159],"traction":[160],"ML:":[162],"hyperbolic":[163,173],"embeddings":[164,199],"\"cheap\"":[167],"accurate":[169],"encoding":[170],"vs":[174],"Euclidean":[175],"scale.":[176],"new":[180],"application":[181],"Poincar\u00e9":[185],"disk":[186],"model":[187],"very":[189],"appealing":[190],"features,":[191],"our":[193],"comes":[195],"handy:":[197],"\\textit{model}":[198],"boosted":[201],"combinations":[202],"decision":[204],"trees,":[205],"trained":[206],"log-loss":[209],"(trees)":[210],"logistic":[212],"loss":[213],"(combinations).":[214]},"counts_by_year":[],"updated_date":"2026-08-18T07:49:30.821534","created_date":"2025-10-10T00:00:00"}
