{"id":"https://openalex.org/W7220436115","doi":"https://doi.org/10.48550/arxiv.2610.03169","title":"Cup and Cap Topological Neural Network","display_name":"Cup and Cap Topological Neural Network","publication_year":2026,"publication_date":"2026-10-02","ids":{"openalex":"https://openalex.org/W7220436115","doi":"https://doi.org/10.48550/arxiv.2610.03169"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.03169","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.03169","pdf_url":"https://arxiv.org/pdf/2610.03169","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2610.03169","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5095900511","display_name":"Marta Niedostatek","orcid":"https://orcid.org/0009-0000-1137-3441","observed_orcids":["https://orcid.org/0009-0000-1137-3441"]},"institutions":[{"id":"https://openalex.org/I166337079","display_name":"Queen Mary University of London","ror":"https://ror.org/026zzn846","country_code":"GB","type":"education","lineage":["https://openalex.org/I124357947","https://openalex.org/I166337079"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Niedostatek, Marta","raw_affiliation_strings":["Queen Mary University of London"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Queen Mary University of London","institution_ids":["https://openalex.org/I166337079"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5106113123","display_name":"Ferran Hernandez Caralt","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I166337079","display_name":"Queen Mary University of London","ror":"https://ror.org/026zzn846","country_code":"GB","type":"education","lineage":["https://openalex.org/I124357947","https://openalex.org/I166337079"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Caralt, Ferran Hernandez","raw_affiliation_strings":["Queen Mary University of London"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Queen Mary University of London","institution_ids":["https://openalex.org/I166337079"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5034510535","display_name":"Runyue Wang","orcid":"https://orcid.org/0009-0005-9386-1655","observed_orcids":["https://orcid.org/0009-0005-9386-1655"]},"institutions":[{"id":"https://openalex.org/I241749","display_name":"University of Cambridge","ror":"https://ror.org/013meh722","country_code":"GB","type":"education","lineage":["https://openalex.org/I241749"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Wang, Runyue","raw_affiliation_strings":["University of Cambridge"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Cambridge","institution_ids":["https://openalex.org/I241749"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5028688027","display_name":"Federica Baccini","orcid":"https://orcid.org/0000-0001-6107-9611","observed_orcids":["https://orcid.org/0000-0001-6107-9611"]},"institutions":[{"id":"https://openalex.org/I861853513","display_name":"Sapienza University of Rome","ror":"https://ror.org/02be6w209","country_code":"IT","type":"education","lineage":["https://openalex.org/I861853513"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Baccini, Federica","raw_affiliation_strings":["Sapienza University of Rome"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Sapienza University of Rome","institution_ids":["https://openalex.org/I861853513"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5072726627","display_name":"Lorenzo Giambagli","orcid":"https://orcid.org/0000-0002-0045-6839","observed_orcids":["https://orcid.org/0000-0002-0045-6839"]},"institutions":[{"id":"https://openalex.org/I75951250","display_name":"Freie Universit\u00e4t Berlin","ror":"https://ror.org/046ak2485","country_code":"DE","type":"education","lineage":["https://openalex.org/I75951250"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Giambagli, Lorenzo","raw_affiliation_strings":["Freie Universit\u00e4t Berlin"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Freie Universit\u00e4t Berlin","institution_ids":["https://openalex.org/I75951250"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5127785355","display_name":"Pietro Li\u00f2","orcid":"https://orcid.org/0000-0002-0540-5053","observed_orcids":["https://orcid.org/0000-0002-0540-5053"]},"institutions":[{"id":"https://openalex.org/I241749","display_name":"University of Cambridge","ror":"https://ror.org/013meh722","country_code":"GB","type":"education","lineage":["https://openalex.org/I241749"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Li\u00f3, Pietro","raw_affiliation_strings":["University of Cambridge"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Cambridge","institution_ids":["https://openalex.org/I241749"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5022368086","display_name":"Ginestra Bianconi","orcid":"https://orcid.org/0000-0002-3380-887X","observed_orcids":["https://orcid.org/0000-0002-3380-887X"]},"institutions":[{"id":"https://openalex.org/I166337079","display_name":"Queen Mary University of London","ror":"https://ror.org/026zzn846","country_code":"GB","type":"education","lineage":["https://openalex.org/I124357947","https://openalex.org/I166337079"]},{"id":"https://openalex.org/I241749","display_name":"University of Cambridge","ror":"https://ror.org/013meh722","country_code":"GB","type":"education","lineage":["https://openalex.org/I241749"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Bianconi, Ginestra","raw_affiliation_strings":["Queen Mary University of London","University of Cambridge"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Queen Mary University of London","institution_ids":["https://openalex.org/I166337079"]},{"raw_affiliation_string":"University of Cambridge","institution_ids":["https://openalex.org/I241749"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":4,"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/T12536","display_name":"Topological and Geometric Data Analysis","score":0.9994999766349792,"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"}},"topics":[{"id":"https://openalex.org/T12536","display_name":"Topological and Geometric Data Analysis","score":0.9994999766349792,"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"}},{"id":"https://openalex.org/T10320","display_name":"Neural Networks and Applications","score":0.00019999999494757503,"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/T10896","display_name":"Homotopy and Cohomology in Algebraic Topology","score":0.0,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/topological-deep-learning","display_name":"topological deep learning","score":0.9269999861717224},{"id":"https://openalex.org/keywords/simplicial-complex","display_name":"simplicial complexes","score":0.9290000200271606},{"id":"https://openalex.org/keywords/many-body-interactions","display_name":"many-body interactions","score":0.6679999828338623}],"concepts":[{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.6399000287055969},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.5922999978065491},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.5271999835968018},{"id":"https://openalex.org/C2776477805","wikidata":"https://www.wikidata.org/wiki/Q4460773","display_name":"Topological data analysis","level":2,"score":0.5105000138282776},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.5077999830245972},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5042999982833862},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.4507000148296356},{"id":"https://openalex.org/C108583219","wikidata":"https://www.wikidata.org/wiki/Q197536","display_name":"Deep learning","level":2,"score":0.38749998807907104},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.37290000915527344},{"id":"https://openalex.org/C199845137","wikidata":"https://www.wikidata.org/wiki/Q145490","display_name":"Network topology","level":2,"score":0.34709998965263367},{"id":"https://openalex.org/C2984842247","wikidata":"https://www.wikidata.org/wiki/Q197536","display_name":"Deep neural networks","level":3,"score":0.3352999985218048},{"id":"https://openalex.org/C123657996","wikidata":"https://www.wikidata.org/wiki/Q12271","display_name":"Architecture","level":2,"score":0.334199994802475},{"id":"https://openalex.org/C2776401178","wikidata":"https://www.wikidata.org/wiki/Q12050496","display_name":"Feature (linguistics)","level":2,"score":0.3140999972820282},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.27090001106262207},{"id":"https://openalex.org/C81332173","wikidata":"https://www.wikidata.org/wiki/Q179899","display_name":"Topological space","level":2,"score":0.26339998841285706}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.03169","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.03169","pdf_url":"https://arxiv.org/pdf/2610.03169","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2610.03169","doi":"https://doi.org/10.48550/arxiv.2610.03169","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.03169","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":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2610.03169","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.03169","pdf_url":"https://arxiv.org/pdf/2610.03169","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320311061","display_name":"Queen Mary University of London","ror":"https://ror.org/026zzn846"},{"id":"https://openalex.org/F4320314731","display_name":"UK Research and Innovation","ror":"https://ror.org/001aqnf71"},{"id":"https://openalex.org/F4320334629","display_name":"Biotechnology and Biological Sciences Research Council","ror":"https://ror.org/00cwqg982"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7220436115.pdf","grobid_xml":"https://content.openalex.org/works/W7220436115.grobid-xml"},"referenced_works_count":9,"referenced_works":["https://openalex.org/W2116341502","https://openalex.org/W2588670633","https://openalex.org/W3202715456","https://openalex.org/W4318350419","https://openalex.org/W4384887216","https://openalex.org/W4401202981","https://openalex.org/W4406316664","https://openalex.org/W4417498005","https://openalex.org/W7128518190"],"related_works":["https://openalex.org/W4404524624","https://openalex.org/W4281710343","https://openalex.org/W4403345239","https://openalex.org/W4402386647","https://openalex.org/W4399062346","https://openalex.org/W7204750925","https://openalex.org/W7211866305","https://openalex.org/W4415142848","https://openalex.org/W4408354445","https://openalex.org/W7214563012"],"abstract_inverted_index":{"Topological":[0,78],"Deep":[1],"Learning":[2],"(TDL)":[3],"is":[4],"designed":[5,87],"to":[6,88,124],"learn":[7,89],"features":[8,39],"associated":[9],"not":[10],"only":[11],"with":[12,16,122],"nodes":[13],"but":[14],"also":[15],"edges,":[17],"triangles":[18],"and":[19,32,40,68,76],"higher":[20],"dimensional":[21],"simplices.":[22],"However,":[23],"most":[24],"TDL":[25],"approaches,":[26],"being":[27],"based":[28],"on":[29,114],"boundary":[30],"operators":[31],"Hodge":[33],"Laplacians,":[34],"have":[35],"the":[36,63,66,74,105,115],"limitation":[37],"that":[38],"signals":[41],"cannot":[42],"be":[43],"lifted":[44],"or":[45],"lowered":[46],"across":[47],"more":[48],"than":[49],"one":[50],"dimension":[51],"per":[52],"layer.":[53],"To":[54],"overcome":[55],"this":[56,59],"limitation,":[57],"in":[58,104],"work,":[60],"we":[61,72],"propose":[62],"adoption":[64],"of":[65],"cup":[67],"cap":[69],"products.":[70],"Specifically,":[71],"formulate":[73],"Cup":[75],"Cap":[77],"Neural":[79],"Network":[80],"(CCNN),":[81],"a":[82],"topological":[83],"deep":[84],"learning":[85],"architecture":[86],"node-based":[90],"variables":[91],"(or":[92],"0-cochains)":[93],"by":[94,110],"taking":[95],"into":[96],"account":[97],"their":[98],"many-body":[99],"interactions":[100],"(e.g.":[101],"triangles)":[102],"present":[103],"data.":[106],"We":[107],"validate":[108],"CCNN":[109],"assessing":[111],"its":[112,119],"performance":[113,121],"TopoBench":[116],"datasets,":[117],"demonstrating":[118],"competitive":[120],"respect":[123],"other":[125],"simplicial":[126],"complex":[127],"neural":[128],"networks.":[129]},"counts_by_year":[],"updated_date":"2026-11-08T12:12:28.789561","created_date":"2026-10-06T00:00:00"}
