{"id":"https://openalex.org/W4387929666","doi":"https://doi.org/10.48550/arxiv.2310.15003","title":"Neural Snowflakes: Universal Latent Graph Inference via Trainable Latent Geometries","display_name":"Neural Snowflakes: Universal Latent Graph Inference via Trainable Latent Geometries","publication_year":2023,"publication_date":"2023-10-23","ids":{"openalex":"https://openalex.org/W4387929666","doi":"https://doi.org/10.48550/arxiv.2310.15003"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2310.15003","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2310.15003","pdf_url":"https://arxiv.org/pdf/2310.15003","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,"listed_in":[],"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"},"volume":null,"type":"preprint","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2310.15003","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5022524322","display_name":"Haitz S\u00e1ez de Oc\u00e1riz Borde","orcid":"https://orcid.org/0009-0000-2297-7750","observed_orcids":["https://orcid.org/0009-0000-2297-7750"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Borde, Haitz S\u00e1ez de Oc\u00e1riz","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5036113771","display_name":"Anastasis Kratsios","orcid":"https://orcid.org/0000-0001-6791-3371","observed_orcids":["https://orcid.org/0000-0001-6791-3371"]},"institutions":[{"id":"https://openalex.org/I4210127509","display_name":"Vector Institute","ror":"https://ror.org/03kqdja62","country_code":"CA","type":"facility","lineage":["https://openalex.org/I4210127509"]},{"id":"https://openalex.org/I98251732","display_name":"McMaster University","ror":"https://ror.org/02fa3aq29","country_code":"CA","type":"education","lineage":["https://openalex.org/I98251732"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Kratsios, Anastasis","raw_affiliation_strings":["Department of Mathematics McMaster University and the Vector Institute Ontario , Canada"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics McMaster University and the Vector Institute Ontario , Canada","institution_ids":["https://openalex.org/I4210127509","https://openalex.org/I98251732"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":2,"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/T11273","display_name":"Advanced Graph Neural Networks","score":0.9976000189781189,"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/T11273","display_name":"Advanced Graph Neural Networks","score":0.9976000189781189,"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/T10320","display_name":"Neural Networks and Applications","score":0.0005000000237487257,"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/T12536","display_name":"Topological and Geometric Data Analysis","score":0.00039999998989515007,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/graph-neural-networks","display_name":"graph neural networks","score":0.8709999918937683},{"id":"https://openalex.org/keywords/latent-geometry","display_name":"latent geometry","score":0.6430000066757202},{"id":"https://openalex.org/keywords/isometric-embedding","display_name":"isometric embedding","score":0.8230000138282776},{"id":"https://openalex.org/keywords/metric-learning","display_name":"metric learning","score":0.9470000267028809},{"id":"https://openalex.org/keywords/fractal-metric","display_name":"fractal metric","score":0.7459999918937683},{"id":"https://openalex.org/keywords/inductive-bias","display_name":"inductive bias","score":0.6639999747276306},{"id":"https://openalex.org/keywords/curse-of-dimensionality","display_name":"curse of dimensionality","score":0.7829999923706055},{"id":"https://openalex.org/keywords/kernel-methods","display_name":"kernel methods","score":0.656000018119812}],"concepts":[{"id":"https://openalex.org/C41608201","wikidata":"https://www.wikidata.org/wiki/Q980509","display_name":"Embedding","level":2,"score":0.6304872035980225},{"id":"https://openalex.org/C75564084","wikidata":"https://www.wikidata.org/wiki/Q5597085","display_name":"Graph embedding","level":3,"score":0.6066516041755676},{"id":"https://openalex.org/C2776214188","wikidata":"https://www.wikidata.org/wiki/Q408386","display_name":"Inference","level":2,"score":0.5477470755577087},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5347427725791931},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.5132181644439697},{"id":"https://openalex.org/C111030470","wikidata":"https://www.wikidata.org/wiki/Q1430460","display_name":"Curse of dimensionality","level":2,"score":0.47912025451660156},{"id":"https://openalex.org/C54059038","wikidata":"https://www.wikidata.org/wiki/Q550147","display_name":"Snowflake","level":3,"score":0.472788542509079},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.46757179498672485},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.46628499031066895},{"id":"https://openalex.org/C153180895","wikidata":"https://www.wikidata.org/wiki/Q7148389","display_name":"Pattern recognition (psychology)","level":2,"score":0.4506545066833496},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.42159926891326904},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3751892149448395},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3468247056007385},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C153294291","wikidata":"https://www.wikidata.org/wiki/Q25261","display_name":"Meteorology","level":1,"score":0.0},{"id":"https://openalex.org/C197046000","wikidata":"https://www.wikidata.org/wiki/Q7561","display_name":"Snow","level":2,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2310.15003","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2310.15003","pdf_url":"https://arxiv.org/pdf/2310.15003","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,"listed_in":[],"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.2310.15003","doi":"https://doi.org/10.48550/arxiv.2310.15003","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2310.15003","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,"listed_in":[],"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":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2310.15003","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2310.15003","pdf_url":"https://arxiv.org/pdf/2310.15003","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,"listed_in":[],"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":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G6938737173","display_name":"Geometric Deep Learning with Applications to Stochastic Finance","funder_award_id":"rgpin-2023-04482","funder_id":"https://openalex.org/F4320334593","funder_display_name":"Natural Sciences and Engineering Research Council of Canada"}],"funders":[{"id":"https://openalex.org/F4320311526","display_name":"McMaster University","ror":"https://ror.org/02fa3aq29"},{"id":"https://openalex.org/F4320334593","display_name":"Natural Sciences and Engineering Research Council of Canada","ror":"https://ror.org/01h531d29"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4387929666.pdf","grobid_xml":"https://content.openalex.org/works/W4387929666.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W4310513139","https://openalex.org/W4353115078","https://openalex.org/W4388926333","https://openalex.org/W3036884729","https://openalex.org/W3102209588","https://openalex.org/W3214420534","https://openalex.org/W6941486428","https://openalex.org/W4297731700","https://openalex.org/W2794980531","https://openalex.org/W7075326843"],"abstract_inverted_index":{"The":[0],"inductive":[1],"bias":[2],"of":[3,47,103,124,133,138,147,162,199],"a":[4,29,58,87,104,129,143,229],"graph":[5,17,31,81,95,179,183,203],"neural":[6,64,113,163,187,222],"network":[7],"(GNN)":[8],"is":[9,210],"largely":[10],"encoded":[11],"in":[12,45,99,135,228],"its":[13],"specified":[14],"graph.":[15,150],"Latent":[16],"inference":[18,180,204],"relies":[19],"on":[20,72,182],"latent":[21,94,149,178,202,218],"geometric":[22],"representations":[23],"to":[24,32,121,155,167],"dynamically":[25],"rewire":[26],"or":[27,196],"infer":[28],"GNN's":[30,35],"maximize":[33],"the":[34,93,100,111,122,136,148,157,186,200,221],"predictive":[36,191],"downstream":[37],"performance,":[38],"but":[39],"it":[40],"lacks":[41],"solid":[42],"theoretical":[43],"foundations":[44],"terms":[46],"embedding-based":[48],"representation":[49],"guarantees.":[50],"This":[51,140],"paper":[52],"addresses":[53],"this":[54,207,226],"issue":[55],"by":[56,86,126],"introducing":[57],"trainable":[59],"deep":[60],"learning":[61,160],"architecture,":[62],"coined":[63],"snowflake,":[65],"that":[66,76,110,193,198],"can":[67,82,96],"adaptively":[68],"implement":[69],"fractal-like":[70],"metrics":[71],"$\\mathbb{R}^d$.":[73],"We":[74,151],"prove":[75],"any":[77],"given":[78],"finite":[79],"weights":[80],"be":[83,97],"isometrically":[84],"embedded":[85],"standard":[88],"MLP":[89,116],"encoder.":[90],"Furthermore,":[91],"when":[92,165],"represented":[98],"feature":[101],"space":[102],"sufficiently":[105],"regular":[106],"kernel,":[107],"we":[108,175],"show":[109],"combined":[112],"snowflake":[114,188,223],"and":[115],"encoder":[117],"do":[118],"not":[119],"succumb":[120],"curse":[123],"dimensionality":[125],"using":[127],"only":[128],"low-degree":[130],"polynomial":[131],"number":[132,137],"parameters":[134],"nodes.":[139],"implementation":[141],"enables":[142],"low-dimensional":[144],"isometric":[145],"embedding":[146],"conduct":[152],"synthetic":[153],"experiments":[154,181],"demonstrate":[156],"superior":[158],"metric":[159],"capabilities":[161],"snowflakes":[164],"compared":[166],"more":[168],"familiar":[169],"spaces":[170],"like":[171],"Euclidean":[172],"space.":[173],"Additionally,":[174],"carry":[176],"out":[177],"benchmarks.":[184],"Consistently,":[185],"model":[189,224],"achieves":[190,225],"performance":[192,208],"either":[194],"matches":[195],"surpasses":[197],"state-of-the-art":[201],"models.":[205],"Importantly,":[206],"improvement":[209],"achieved":[211],"without":[212],"requiring":[213],"random":[214],"search":[215],"for":[216],"optimal":[217],"geometry.":[219],"Instead,":[220],"enhancement":[227],"differentiable":[230],"manner.":[231]},"counts_by_year":[{"year":2024,"cited_by_count":2}],"updated_date":"2026-10-16T09:59:22.235173","created_date":"2023-10-25T00:00:00"}
