{"id":"https://openalex.org/W7161985774","doi":"https://doi.org/10.48550/arxiv.2605.21435","title":"Gaussian Sheaf Neural Networks","display_name":"Gaussian Sheaf Neural Networks","publication_year":2026,"publication_date":"2026-05-20","ids":{"openalex":"https://openalex.org/W7161985774","doi":"https://doi.org/10.48550/arxiv.2605.21435"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2605.21435","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.21435","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.2605.21435","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5136646095","display_name":"Andr\u00e9 Ribeiro","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Ribeiro, Andr\u00e9","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5136672100","display_name":"Ana Luiza Ten\u00f3rio","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Ten\u00f3rio, Ana Luiza","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5079545086","display_name":"Tiago da Silva","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"da Silva, Tiago","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5120320559","display_name":"Diego Mesquita","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Mesquita, Diego","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/T11273","display_name":"Advanced Graph Neural Networks","score":0.8122000098228455,"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":0.8122000098228455,"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/T12676","display_name":"Machine Learning and ELM","score":0.03060000017285347,"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":0.02449999935925007,"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/complement","display_name":"Complement (music)","score":0.5580000281333923},{"id":"https://openalex.org/keywords/laplace-operator","display_name":"Laplace operator","score":0.5077999830245972},{"id":"https://openalex.org/keywords/gaussian","display_name":"Gaussian","score":0.5029000043869019},{"id":"https://openalex.org/keywords/node","display_name":"Node (physics)","score":0.501800000667572},{"id":"https://openalex.org/keywords/covariance","display_name":"Covariance","score":0.4925999939441681},{"id":"https://openalex.org/keywords/sheaf","display_name":"Sheaf","score":0.48899999260902405},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.4717000126838684},{"id":"https://openalex.org/keywords/laplacian-matrix","display_name":"Laplacian matrix","score":0.3610999882221222},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.3497999906539917}],"concepts":[{"id":"https://openalex.org/C112313634","wikidata":"https://www.wikidata.org/wiki/Q7886648","display_name":"Complement (music)","level":5,"score":0.5580000281333923},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5494999885559082},{"id":"https://openalex.org/C165700671","wikidata":"https://www.wikidata.org/wiki/Q203484","display_name":"Laplace operator","level":2,"score":0.5077999830245972},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.5029000043869019},{"id":"https://openalex.org/C62611344","wikidata":"https://www.wikidata.org/wiki/Q1062658","display_name":"Node (physics)","level":2,"score":0.501800000667572},{"id":"https://openalex.org/C178650346","wikidata":"https://www.wikidata.org/wiki/Q201984","display_name":"Covariance","level":2,"score":0.4925999939441681},{"id":"https://openalex.org/C4017995","wikidata":"https://www.wikidata.org/wiki/Q595298","display_name":"Sheaf","level":2,"score":0.48899999260902405},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.4717000126838684},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.42160001397132874},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.3961000144481659},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.38600000739097595},{"id":"https://openalex.org/C115178988","wikidata":"https://www.wikidata.org/wiki/Q772067","display_name":"Laplacian matrix","level":3,"score":0.3610999882221222},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.35740000009536743},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.3497999906539917},{"id":"https://openalex.org/C7948225","wikidata":"https://www.wikidata.org/wiki/Q4723998","display_name":"Algebraic connectivity","level":4,"score":0.3441999852657318},{"id":"https://openalex.org/C158154518","wikidata":"https://www.wikidata.org/wiki/Q7310970","display_name":"Relevance (law)","level":2,"score":0.34200000762939453},{"id":"https://openalex.org/C97931131","wikidata":"https://www.wikidata.org/wiki/Q5282087","display_name":"Discriminative model","level":2,"score":0.3327000141143799},{"id":"https://openalex.org/C26517878","wikidata":"https://www.wikidata.org/wiki/Q228039","display_name":"Key (lock)","level":2,"score":0.33000001311302185},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.3215000033378601},{"id":"https://openalex.org/C149441793","wikidata":"https://www.wikidata.org/wiki/Q200726","display_name":"Probability distribution","level":2,"score":0.3116999864578247},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.30979999899864197},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.28619998693466187},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.27869999408721924},{"id":"https://openalex.org/C122203268","wikidata":"https://www.wikidata.org/wiki/Q5862903","display_name":"Probability theory","level":2,"score":0.27559998631477356},{"id":"https://openalex.org/C13336665","wikidata":"https://www.wikidata.org/wiki/Q125977","display_name":"Vector space","level":2,"score":0.27480000257492065},{"id":"https://openalex.org/C155846161","wikidata":"https://www.wikidata.org/wiki/Q1143367","display_name":"Graphical model","level":2,"score":0.26820001006126404},{"id":"https://openalex.org/C153180895","wikidata":"https://www.wikidata.org/wiki/Q7148389","display_name":"Pattern recognition (psychology)","level":2,"score":0.26409998536109924},{"id":"https://openalex.org/C122123141","wikidata":"https://www.wikidata.org/wiki/Q176623","display_name":"Random variable","level":2,"score":0.2596000134944916}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2605.21435","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.21435","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.2605.21435","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.21435","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":{"Graph":[0],"Neural":[1,85],"Networks":[2,86],"(GNNs)":[3],"have":[4],"become":[5],"the":[6,71,101,114,139],"de":[7],"facto":[8],"standard":[9,67],"for":[10,23],"learning":[11],"on":[12,100,132],"relational":[13],"data.":[14],"While":[15],"traditional":[16],"GNNs'":[17],"message":[18,68],"passing":[19,69],"is":[20],"well":[21],"suited":[22],"vector-valued":[24],"node":[25,32,45],"features,":[26],"there":[27],"are":[28,34,47],"cases":[29],"in":[30],"which":[31],"features":[33,46],"better":[35],"represented":[36],"by":[37,50],"probability":[38],"distributions":[39],"than":[40],"real":[41],"vectors.":[42],"Concretely,":[43],"when":[44],"Gaussians,":[48],"characterized":[49],"a":[51,54,62,88,108],"mean":[52],"and":[53,65,73,79,120,134],"covariance":[55],"matrix,":[56],"naively":[57],"concatenating":[58],"their":[59],"parameters":[60],"into":[61,96],"single":[63],"vector":[64],"applying":[66],"discards":[70],"geometric":[72],"algebraic":[74],"structure":[75],"that":[76,91,112,137],"governs":[77],"means":[78],"covariances.":[80],"We":[81,125],"propose":[82],"Gaussian":[83],"Sheaf":[84],"(GSNNs),":[87],"principled":[89],"framework":[90],"incorporates":[92],"these":[93],"inductive":[94],"biases":[95],"graph-based":[97],"learning.":[98],"Building":[99],"theory":[102],"of":[103,142],"cellular":[104],"sheaves,":[105],"we":[106],"derive":[107],"new":[109],"Laplacian":[110,116],"operator":[111],"generalizes":[113],"sheaf":[115],"to":[117],"this":[118],"setting":[119],"preserves":[121],"its":[122],"key":[123],"properties.":[124],"complement":[126],"our":[127],"theoretical":[128],"contributions":[129],"with":[130],"experiments":[131],"synthetic":[133],"real-world":[135],"data":[136],"illustrate":[138],"practical":[140],"relevance":[141],"GSNNs.":[143]},"counts_by_year":[],"updated_date":"2026-07-28T07:46:37.118299","created_date":"2026-05-22T00:00:00"}
