{"id":"https://openalex.org/W6966826110","doi":"https://doi.org/10.48550/arxiv.2507.17787","title":"Hyperbolic Deep Learning for Foundation Models: A Survey","display_name":"Hyperbolic Deep Learning for Foundation Models: A Survey","publication_year":2025,"publication_date":"2025-07-23","ids":{"openalex":"https://openalex.org/W6966826110","doi":"https://doi.org/10.48550/arxiv.2507.17787"},"language":"en","primary_location":{"id":"doi:10.48550/arxiv.2507.17787","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2507.17787","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":null,"license_id":null,"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.2507.17787","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"He, Neil","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"He, Neil","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":null,"display_name":"Madhu, Hiren","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Madhu, Hiren","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":null,"display_name":"Bui, Ngoc","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Bui, Ngoc","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":null,"display_name":"Yang, Menglin","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Yang, Menglin","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":null,"display_name":"Ying, Rex","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Ying, Rex","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":5,"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":true,"primary_topic":{"id":"https://openalex.org/T11714","display_name":"Multimodal Machine Learning Applications","score":0.49970000982284546,"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":0.49970000982284546,"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/T11273","display_name":"Advanced Graph Neural Networks","score":0.1979999989271164,"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/T10028","display_name":"Topic Modeling","score":0.07180000096559525,"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/foundation","display_name":"Foundation (evidence)","score":0.7358999848365784},{"id":"https://openalex.org/keywords/euclidean-geometry","display_name":"Euclidean geometry","score":0.6571999788284302},{"id":"https://openalex.org/keywords/key","display_name":"Key (lock)","score":0.54830002784729},{"id":"https://openalex.org/keywords/deep-learning","display_name":"Deep learning","score":0.529699981212616},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.4271000027656555},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.40959998965263367},{"id":"https://openalex.org/keywords/non-euclidean-geometry","display_name":"Non-Euclidean geometry","score":0.40059998631477356}],"concepts":[{"id":"https://openalex.org/C2780966255","wikidata":"https://www.wikidata.org/wiki/Q5474306","display_name":"Foundation (evidence)","level":2,"score":0.7358999848365784},{"id":"https://openalex.org/C129782007","wikidata":"https://www.wikidata.org/wiki/Q162886","display_name":"Euclidean geometry","level":2,"score":0.6571999788284302},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.5570999979972839},{"id":"https://openalex.org/C26517878","wikidata":"https://www.wikidata.org/wiki/Q228039","display_name":"Key (lock)","level":2,"score":0.54830002784729},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5374000072479248},{"id":"https://openalex.org/C108583219","wikidata":"https://www.wikidata.org/wiki/Q197536","display_name":"Deep learning","level":2,"score":0.529699981212616},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.4271000027656555},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.40959998965263367},{"id":"https://openalex.org/C10784197","wikidata":"https://www.wikidata.org/wiki/Q233858","display_name":"Non-Euclidean geometry","level":3,"score":0.40059998631477356},{"id":"https://openalex.org/C206352148","wikidata":"https://www.wikidata.org/wiki/Q209306","display_name":"Hyperbolic geometry","level":3,"score":0.38269999623298645},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.34220001101493835},{"id":"https://openalex.org/C2776542497","wikidata":"https://www.wikidata.org/wiki/Q5266672","display_name":"Development (topology)","level":2,"score":0.3165999948978424},{"id":"https://openalex.org/C67186912","wikidata":"https://www.wikidata.org/wiki/Q367664","display_name":"Data modeling","level":2,"score":0.31610000133514404},{"id":"https://openalex.org/C2984842247","wikidata":"https://www.wikidata.org/wiki/Q197536","display_name":"Deep neural networks","level":3,"score":0.3082999885082245},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.30820000171661377},{"id":"https://openalex.org/C2522767166","wikidata":"https://www.wikidata.org/wiki/Q2374463","display_name":"Data science","level":1,"score":0.30300000309944153},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.27630001306533813},{"id":"https://openalex.org/C539667460","wikidata":"https://www.wikidata.org/wiki/Q2414942","display_name":"Management science","level":1,"score":0.2721000015735626},{"id":"https://openalex.org/C184337299","wikidata":"https://www.wikidata.org/wiki/Q1437428","display_name":"Semantics (computer science)","level":2,"score":0.26930001378059387},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.26600000262260437}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2507.17787","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2507.17787","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":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2507.17787","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2507.17787","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":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},"sustainable_development_goals":[{"display_name":"Peace, Justice and strong institutions","score":0.6331166625022888,"id":"https://metadata.un.org/sdg/16"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Foundation":[0],"models":[1,9,12,72],"pre-trained":[2],"on":[3],"massive":[4],"datasets,":[5],"including":[6,140],"large":[7,15],"language":[8],"(LLMs),":[10],"vision-language":[11],"(VLMs),":[13],"and":[14,43,83,119,149,167,179],"multimodal":[16],"models,":[17,64,139],"have":[18,29,132],"demonstrated":[19],"remarkable":[20],"success":[21],"in":[22],"diverse":[23],"downstream":[24],"tasks.":[25],"However,":[26],"recent":[27,169],"studies":[28],"shown":[30],"fundamental":[31],"limitations":[32],"of":[33,80,91,113,163],"these":[34,134],"models:":[35],"(1)":[36],"limited":[37],"representational":[38],"capacity,":[39],"(2)":[40],"lower":[41],"adaptability,":[42],"(3)":[44],"diminishing":[45],"scalability.":[46],"These":[47,108],"shortcomings":[48],"raise":[49],"a":[50,89,104,160],"critical":[51],"question:":[52],"is":[53],"Euclidean":[54,128],"geometry":[55],"truly":[56],"the":[57,77,184],"optimal":[58],"inductive":[59],"bias":[60],"for":[61,171],"all":[62],"foundation":[63,138,172],"or":[65],"could":[66],"incorporating":[67],"alternative":[68],"geometric":[69],"spaces":[70,109],"enable":[71,110],"to":[73,101,127,136,182],"better":[74],"align":[75],"with":[76,99,122],"intrinsic":[78],"structure":[79],"real-world":[81],"data":[82],"improve":[84],"reasoning":[85,144],"processes?":[86],"Hyperbolic":[87],"spaces,":[88],"class":[90],"non-Euclidean":[92],"manifolds":[93],"characterized":[94],"by":[95],"exponential":[96],"volume":[97],"growth":[98],"respect":[100],"distance,":[102],"offer":[103],"mathematically":[105],"grounded":[106],"solution.":[107],"low-distortion":[111],"embeddings":[112],"hierarchical":[114],"structures":[115],"(e.g.,":[116],"trees,":[117],"taxonomies)":[118],"power-law":[120],"distributions":[121],"substantially":[123],"fewer":[124],"dimensions":[125],"compared":[126],"counterparts.":[129],"Recent":[130],"advances":[131],"leveraged":[133],"properties":[135],"enhance":[137],"improving":[141],"LLMs'":[142],"complex":[143],"ability,":[145],"VLMs'":[146],"zero-shot":[147],"generalization,":[148],"cross-modal":[150],"semantic":[151],"alignment,":[152],"while":[153],"maintaining":[154],"parameter":[155],"efficiency.":[156],"This":[157],"paper":[158],"provides":[159],"comprehensive":[161],"review":[162],"hyperbolic":[164],"neural":[165],"networks":[166],"their":[168],"development":[170],"models.":[173],"We":[174],"further":[175],"outline":[176],"key":[177],"challenges":[178],"research":[180],"directions":[181],"advance":[183],"field.":[185]},"counts_by_year":[],"updated_date":"2025-11-06T06:51:31.235846","created_date":"2025-10-10T00:00:00"}
