{"id":"https://openalex.org/W4415961815","doi":"https://doi.org/10.48550/arxiv.2510.17072","title":"DFNN: A Deep Fr\u00e9chet Neural Network Framework for Learning Metric-Space-Valued Responses","display_name":"DFNN: A Deep Fr\u00e9chet Neural Network Framework for Learning Metric-Space-Valued Responses","publication_year":2025,"publication_date":"2025-10-20","ids":{"openalex":"https://openalex.org/W4415961815","doi":"https://doi.org/10.48550/arxiv.2510.17072"},"language":null,"primary_location":{"id":"pmh:oai:arXiv.org:2510.17072","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2510.17072","pdf_url":"https://arxiv.org/pdf/2510.17072","source":{"id":"https://openalex.org/S4393918464","display_name":"ArXiv.org","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"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/2510.17072","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Kim, Kyum","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Kim, Kyum","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100722049","display_name":"Yaqing Chen","orcid":"https://orcid.org/0000-0002-0566-6130"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Chen, Yaqing","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5067121866","display_name":"Paromita Dubey","orcid":"https://orcid.org/0000-0003-3362-0794"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Dubey, Paromita","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"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/T10775","display_name":"Generative Adversarial Networks and Image Synthesis","score":0.13760000467300415,"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/T10775","display_name":"Generative Adversarial Networks and Image Synthesis","score":0.13760000467300415,"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/T12814","display_name":"Gaussian Processes and Bayesian Inference","score":0.11069999635219574,"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/T12417","display_name":"Morphological variations and asymmetry","score":0.07689999788999557,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.6428999900817871},{"id":"https://openalex.org/keywords/deep-learning","display_name":"Deep learning","score":0.6427000164985657},{"id":"https://openalex.org/keywords/metric","display_name":"Metric (unit)","score":0.6353999972343445},{"id":"https://openalex.org/keywords/deep-neural-networks","display_name":"Deep neural networks","score":0.5372999906539917},{"id":"https://openalex.org/keywords/task","display_name":"Task (project management)","score":0.43630000948905945},{"id":"https://openalex.org/keywords/euclidean-geometry","display_name":"Euclidean geometry","score":0.365200012922287},{"id":"https://openalex.org/keywords/euclidean-space","display_name":"Euclidean space","score":0.3598000109195709},{"id":"https://openalex.org/keywords/euclidean-distance","display_name":"Euclidean distance","score":0.32679998874664307}],"concepts":[{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.7127000093460083},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.6428999900817871},{"id":"https://openalex.org/C108583219","wikidata":"https://www.wikidata.org/wiki/Q197536","display_name":"Deep learning","level":2,"score":0.6427000164985657},{"id":"https://openalex.org/C176217482","wikidata":"https://www.wikidata.org/wiki/Q860554","display_name":"Metric (unit)","level":2,"score":0.6353999972343445},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6014000177383423},{"id":"https://openalex.org/C2984842247","wikidata":"https://www.wikidata.org/wiki/Q197536","display_name":"Deep neural networks","level":3,"score":0.5372999906539917},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.5299999713897705},{"id":"https://openalex.org/C2780451532","wikidata":"https://www.wikidata.org/wiki/Q759676","display_name":"Task (project management)","level":2,"score":0.43630000948905945},{"id":"https://openalex.org/C129782007","wikidata":"https://www.wikidata.org/wiki/Q162886","display_name":"Euclidean geometry","level":2,"score":0.365200012922287},{"id":"https://openalex.org/C186450821","wikidata":"https://www.wikidata.org/wiki/Q17295","display_name":"Euclidean space","level":2,"score":0.3598000109195709},{"id":"https://openalex.org/C120174047","wikidata":"https://www.wikidata.org/wiki/Q847073","display_name":"Euclidean distance","level":2,"score":0.32679998874664307},{"id":"https://openalex.org/C163258240","wikidata":"https://www.wikidata.org/wiki/Q25342","display_name":"Power (physics)","level":2,"score":0.3197999894618988},{"id":"https://openalex.org/C120936955","wikidata":"https://www.wikidata.org/wiki/Q2155640","display_name":"Empirical research","level":2,"score":0.3077000081539154},{"id":"https://openalex.org/C97385483","wikidata":"https://www.wikidata.org/wiki/Q16954980","display_name":"Deep belief network","level":3,"score":0.30309998989105225},{"id":"https://openalex.org/C83546350","wikidata":"https://www.wikidata.org/wiki/Q1139051","display_name":"Regression","level":2,"score":0.28630000352859497},{"id":"https://openalex.org/C2776401178","wikidata":"https://www.wikidata.org/wiki/Q12050496","display_name":"Feature (linguistics)","level":2,"score":0.2808000147342682},{"id":"https://openalex.org/C44492722","wikidata":"https://www.wikidata.org/wiki/Q327069","display_name":"Conditional probability","level":2,"score":0.2752000093460083},{"id":"https://openalex.org/C149441793","wikidata":"https://www.wikidata.org/wiki/Q200726","display_name":"Probability distribution","level":2,"score":0.2727999985218048},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.2694000005722046},{"id":"https://openalex.org/C81363708","wikidata":"https://www.wikidata.org/wiki/Q17084460","display_name":"Convolutional neural network","level":2,"score":0.26179999113082886},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.2590000033378601},{"id":"https://openalex.org/C136389625","wikidata":"https://www.wikidata.org/wiki/Q334384","display_name":"Supervised learning","level":3,"score":0.2533999979496002}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2510.17072","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2510.17072","pdf_url":"https://arxiv.org/pdf/2510.17072","source":{"id":"https://openalex.org/S4393918464","display_name":"ArXiv.org","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"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.2510.17072","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2510.17072","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":"pmh:oai:arXiv.org:2510.17072","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2510.17072","pdf_url":"https://arxiv.org/pdf/2510.17072","source":{"id":"https://openalex.org/S4393918464","display_name":"ArXiv.org","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"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":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W4415961815.pdf"},"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Regression":[0],"with":[1],"non-Euclidean":[2,39],"responses":[3,40,122],"--":[4,14,41,52],"e.g.,":[5],"probability":[6],"distributions,":[7],"networks,":[8],"symmetric":[9],"positive-definite":[10],"matrices,":[11],"and":[12,100,137],"compositions":[13],"has":[15],"become":[16],"increasingly":[17],"important":[18],"in":[19,48],"modern":[20],"applications.":[21],"In":[22],"this":[23],"paper,":[24],"we":[25],"propose":[26],"deep":[27,34,63],"Fr\u00e9chet":[28,73,90],"neural":[29,64,115],"networks":[30,65],"(DFNNs),":[31],"an":[32],"end-to-end":[33],"learning":[35],"framework":[36,93],"for":[37,109],"predicting":[38,147],"which":[42],"are":[43],"considered":[44],"as":[45,140,142],"random":[46],"objects":[47],"a":[49,89,105,143],"metric":[50],"space":[51],"from":[53],"Euclidean":[54],"predictors.":[55,102],"Our":[56],"method":[57],"leverages":[58],"the":[59,68,76,79,81,112],"representation-learning":[60],"power":[61],"of":[62,70,75,84,114],"(DNNs)":[66],"to":[67,119,146],"task":[69],"approximating":[71],"conditional":[72,85],"means":[74],"response":[77],"given":[78],"predictors,":[80],"metric-space":[82],"analogue":[83],"expectations,":[86],"by":[87],"minimizing":[88],"risk.":[91],"The":[92],"is":[94],"highly":[95],"flexible,":[96],"accommodating":[97],"diverse":[98],"metrics":[99],"high-dimensional":[101],"We":[103],"establish":[104],"universal":[106],"approximation":[107,117],"theorem":[108],"DFNNs,":[110],"advancing":[111],"state-of-the-art":[113],"network":[116],"theory":[118],"general":[120],"metric-space-valued":[121],"without":[123],"making":[124],"model":[125],"assumptions":[126],"or":[127],"relying":[128],"on":[129,134],"local":[130],"smoothing.":[131],"Empirical":[132],"studies":[133],"synthetic":[135],"distributional":[136],"network-valued":[138],"responses,":[139],"well":[141],"real-world":[144],"application":[145],"employment":[148],"occupational":[149],"compositions,":[150],"demonstrate":[151],"that":[152],"DFNNs":[153],"consistently":[154],"outperform":[155],"existing":[156],"methods.":[157]},"counts_by_year":[],"updated_date":"2026-04-21T08:09:41.155169","created_date":"2025-10-22T00:00:00"}
