{"id":"https://openalex.org/W7077895164","doi":"https://doi.org/10.48550/arxiv.2508.18564","title":"A Note on Graphon-Signal Analysis of Graph Neural Networks","display_name":"A Note on Graphon-Signal Analysis of Graph Neural Networks","publication_year":2025,"publication_date":"2025-08-25","ids":{"openalex":"https://openalex.org/W7077895164","doi":"https://doi.org/10.48550/arxiv.2508.18564"},"language":"en","primary_location":{"id":"doi:10.48550/arxiv.2508.18564","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2508.18564","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":"Preprint"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2508.18564","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Rauchwerger, Levi","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Rauchwerger, Levi","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":null,"display_name":"Levie, Ron","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Levie, Ron","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":true,"primary_topic":{"id":"https://openalex.org/T12157","display_name":"Geochemistry and Geologic Mapping","score":0.3790000081062317,"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/T12157","display_name":"Geochemistry and Geologic Mapping","score":0.3790000081062317,"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/T13177","display_name":"Geological and Geophysical Studies","score":0.04280000180006027,"subfield":{"id":"https://openalex.org/subfields/1907","display_name":"Geology"},"field":{"id":"https://openalex.org/fields/19","display_name":"Earth and Planetary Sciences"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T13067","display_name":"Geological Modeling and Analysis","score":0.032600000500679016,"subfield":{"id":"https://openalex.org/subfields/1906","display_name":"Geochemistry and Petrology"},"field":{"id":"https://openalex.org/fields/19","display_name":"Earth and Planetary Sciences"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/lemma","display_name":"Lemma (botany)","score":0.6312000155448914},{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.6247000098228455},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.5784000158309937},{"id":"https://openalex.org/keywords/embedding","display_name":"Embedding","score":0.5543000102043152},{"id":"https://openalex.org/keywords/lipschitz-continuity","display_name":"Lipschitz continuity","score":0.5249999761581421},{"id":"https://openalex.org/keywords/limiting","display_name":"Limiting","score":0.5152999758720398}],"concepts":[{"id":"https://openalex.org/C2777759810","wikidata":"https://www.wikidata.org/wiki/Q149316","display_name":"Lemma (botany)","level":3,"score":0.6312000155448914},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.6247000098228455},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.5784000158309937},{"id":"https://openalex.org/C41608201","wikidata":"https://www.wikidata.org/wiki/Q980509","display_name":"Embedding","level":2,"score":0.5543000102043152},{"id":"https://openalex.org/C22324862","wikidata":"https://www.wikidata.org/wiki/Q652707","display_name":"Lipschitz continuity","level":2,"score":0.5249999761581421},{"id":"https://openalex.org/C188198153","wikidata":"https://www.wikidata.org/wiki/Q1613840","display_name":"Limiting","level":2,"score":0.5152999758720398},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5127000212669373},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.4903999865055084},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.38690000772476196},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.37929999828338623},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.3765999972820282},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.36800000071525574},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3596000075340271},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.2922999858856201},{"id":"https://openalex.org/C32946077","wikidata":"https://www.wikidata.org/wiki/Q618079","display_name":"Network analysis","level":2,"score":0.2849000096321106},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.26989999413490295},{"id":"https://openalex.org/C88230418","wikidata":"https://www.wikidata.org/wiki/Q131476","display_name":"Graph theory","level":2,"score":0.2612000107765198}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2508.18564","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2508.18564","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":"Preprint"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2508.18564","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2508.18564","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":"Preprint"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"A":[0],"recent":[1],"paper,":[2,68,82],"``A":[3],"Graphon-Signal":[4],"Analysis":[5],"of":[6,24,33,40,75],"Graph":[7],"Neural":[8],"Networks'',":[9],"by":[10,19,147],"Levie,":[11],"analyzed":[12],"message":[13],"passing":[14],"graph":[15,76],"neural":[16],"networks":[17],"(MPNNs)":[18],"embedding":[20],"the":[21,48,80,101,105,119,144,156],"input":[22],"space":[23,32],"MPNNs,":[25],"i.e.,":[26],"attributed":[27,34],"graphs":[28],"(graph-signals),":[29],"to":[30,46,89,107,122,128,138,158],"a":[31,51,55],"graphons":[35,160],"(graphon-signals).":[36],"Based":[37],"on":[38],"extensions":[39,88],"standard":[41],"results":[42,91,103],"in":[43,66,72,104],"graphon":[44],"analysis":[45,157],"graphon-signals,":[47],"paper":[49,106],"proved":[50],"generalization":[52,145,150],"bound":[53,146],"and":[54,87,152,161],"sampling":[56],"lemma":[57],"for":[58],"MPNNs.":[59],"However,":[60],"there":[61],"are":[62],"some":[63],"missing":[64],"ingredients":[65],"that":[67,92],"limiting":[69],"its":[70],"applicability":[71],"practical":[73],"settings":[74],"machine":[77],"learning.":[78],"In":[79,96],"current":[81],"we":[83,99,117,142,154],"introduce":[84],"several":[85],"refinements":[86],"existing":[90],"address":[93],"these":[94],"shortcomings.":[95],"detail,":[97],"1)":[98],"extend":[100,118,155],"main":[102],"graphon-signals":[108],"with":[109,124,126,136],"multidimensional":[110],"signals":[111],"(rather":[112,131],"than":[113,132],"1D":[114],"signals),":[115],"2)":[116],"Lipschitz":[120],"continuity":[121],"MPNNs":[123,133],"readout":[125,135],"respect":[127,137],"cut":[129,139],"distance":[130],"without":[134],"metric),":[140],"3)":[141],"improve":[143],"utilizing":[148],"robustness-type":[149],"bounds,":[151],"4)":[153],"non-symmetric":[159],"kernels.":[162]},"counts_by_year":[],"updated_date":"2026-07-01T06:00:48.157686","created_date":"2025-10-10T00:00:00"}
