{"id":"https://openalex.org/W4409158678","doi":"https://doi.org/10.1145/3690624.3709324","title":"Understanding Oversmoothing in Diffusion-Based GNNs From the Perspective of Operator Semigroup Theory","display_name":"Understanding Oversmoothing in Diffusion-Based GNNs From the Perspective of Operator Semigroup Theory","publication_year":2025,"publication_date":"2025-04-04","ids":{"openalex":"https://openalex.org/W4409158678","doi":"https://doi.org/10.1145/3690624.3709324"},"language":"en","primary_location":{"id":"doi:10.1145/3690624.3709324","is_oa":true,"landing_page_url":"https://doi.org/10.1145/3690624.3709324","pdf_url":null,"source":null,"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 31st ACM SIGKDD Conference on Knowledge Discovery and Data Mining V.1","raw_type":"proceedings-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://doi.org/10.1145/3690624.3709324","any_repository_has_fulltext":null},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5101416906","display_name":"Weichen Zhao","orcid":"https://orcid.org/0009-0005-1645-0860"},"institutions":[{"id":"https://openalex.org/I205237279","display_name":"Nankai University","ror":"https://ror.org/01y1kjr75","country_code":"CN","type":"education","lineage":["https://openalex.org/I205237279"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Weichen Zhao","raw_affiliation_strings":["The School of Statistics and Data Science, LPMC &amp; KLMDASR, Nankai University, Tianjin, China"],"raw_orcid":"https://orcid.org/0009-0005-1645-0860","affiliations":[{"raw_affiliation_string":"The School of Statistics and Data Science, LPMC &amp; KLMDASR, Nankai University, Tianjin, China","institution_ids":["https://openalex.org/I205237279"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5102783114","display_name":"Chenguang Wang","orcid":"https://orcid.org/0009-0008-4097-1174"},"institutions":[{"id":"https://openalex.org/I4210116924","display_name":"Chinese University of Hong Kong, Shenzhen","ror":"https://ror.org/02d5ks197","country_code":"CN","type":"education","lineage":["https://openalex.org/I177725633","https://openalex.org/I180726961","https://openalex.org/I4210116924"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Chenguang Wang","raw_affiliation_strings":["The School of Data Science, The Chinese University of Hong Kong, Shenzhen, Shenzhen, China"],"raw_orcid":"https://orcid.org/0009-0008-4097-1174","affiliations":[{"raw_affiliation_string":"The School of Data Science, The Chinese University of Hong Kong, Shenzhen, Shenzhen, China","institution_ids":["https://openalex.org/I4210116924"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5111473273","display_name":"X.-P. Wang","orcid":null},"institutions":[{"id":"https://openalex.org/I19820366","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35","country_code":"CN","type":"government","lineage":["https://openalex.org/I19820366"]},{"id":"https://openalex.org/I4210120485","display_name":"Academy of Mathematics and Systems Science","ror":"https://ror.org/02jkmyk67","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210120485"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xinyan Wang","raw_affiliation_strings":["The Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, China"],"raw_orcid":"https://orcid.org/0009-0007-4918-6466","affiliations":[{"raw_affiliation_string":"The Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, China","institution_ids":["https://openalex.org/I4210120485","https://openalex.org/I19820366"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5046469888","display_name":"Congying Han","orcid":"https://orcid.org/0000-0002-3445-4620"},"institutions":[{"id":"https://openalex.org/I4210165038","display_name":"University of Chinese Academy of Sciences","ror":"https://ror.org/05qbk4x57","country_code":"CN","type":"education","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210165038"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Congying Han","raw_affiliation_strings":["School of Mathematical Sciences, University of the Chinese Academy of Sciences, Beijing, China"],"raw_orcid":"https://orcid.org/0000-0002-3445-4620","affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, University of the Chinese Academy of Sciences, Beijing, China","institution_ids":["https://openalex.org/I4210165038"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5059320585","display_name":"Tiande Guo","orcid":"https://orcid.org/0000-0002-3804-9163"},"institutions":[{"id":"https://openalex.org/I4210165038","display_name":"University of Chinese Academy of Sciences","ror":"https://ror.org/05qbk4x57","country_code":"CN","type":"education","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210165038"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Tiande Guo","raw_affiliation_strings":["School of Mathematical Sciences, University of the Chinese Academy of Sciences, Beijing, China"],"raw_orcid":"https://orcid.org/0000-0002-3804-9163","affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, University of the Chinese Academy of Sciences, Beijing, China","institution_ids":["https://openalex.org/I4210165038"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5101448070","display_name":"Tianshu Yu","orcid":"https://orcid.org/0000-0002-6537-1924"},"institutions":[{"id":"https://openalex.org/I4210116924","display_name":"Chinese University of Hong Kong, Shenzhen","ror":"https://ror.org/02d5ks197","country_code":"CN","type":"education","lineage":["https://openalex.org/I177725633","https://openalex.org/I180726961","https://openalex.org/I4210116924"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Tianshu Yu","raw_affiliation_strings":["The School of Data Science, The Chinese University of Hong Kong, Shenzhen, Shenzhen, China"],"raw_orcid":"https://orcid.org/0000-0002-6537-1924","affiliations":[{"raw_affiliation_string":"The School of Data Science, The Chinese University of Hong Kong, Shenzhen, Shenzhen, China","institution_ids":["https://openalex.org/I4210116924"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":6,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.7588,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.85882353,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":95},"biblio":{"volume":null,"issue":null,"first_page":"2043","last_page":"2054"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10320","display_name":"Neural Networks and Applications","score":0.7271000146865845,"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/T10320","display_name":"Neural Networks and Applications","score":0.7271000146865845,"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/T12162","display_name":"Cellular Automata and Applications","score":0.6833000183105469,"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/perspective","display_name":"Perspective (graphical)","score":0.6531476378440857},{"id":"https://openalex.org/keywords/semigroup","display_name":"Semigroup","score":0.5234339237213135},{"id":"https://openalex.org/keywords/diffusion-theory","display_name":"Diffusion theory","score":0.4791400134563446},{"id":"https://openalex.org/keywords/diffusion","display_name":"Diffusion","score":0.4729701578617096},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.46536946296691895},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.42376261949539185},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.35788917541503906},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.23418372869491577},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.23243007063865662},{"id":"https://openalex.org/keywords/thermodynamics","display_name":"Thermodynamics","score":0.1353650689125061},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.09007975459098816}],"concepts":[{"id":"https://openalex.org/C12713177","wikidata":"https://www.wikidata.org/wiki/Q1900281","display_name":"Perspective (graphical)","level":2,"score":0.6531476378440857},{"id":"https://openalex.org/C207405024","wikidata":"https://www.wikidata.org/wiki/Q207348","display_name":"Semigroup","level":2,"score":0.5234339237213135},{"id":"https://openalex.org/C2986659545","wikidata":"https://www.wikidata.org/wiki/Q7280376","display_name":"Diffusion theory","level":3,"score":0.4791400134563446},{"id":"https://openalex.org/C69357855","wikidata":"https://www.wikidata.org/wiki/Q163214","display_name":"Diffusion","level":2,"score":0.4729701578617096},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.46536946296691895},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.42376261949539185},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.35788917541503906},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.23418372869491577},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.23243007063865662},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.1353650689125061},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.09007975459098816},{"id":"https://openalex.org/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C86339819","wikidata":"https://www.wikidata.org/wiki/Q407384","display_name":"Transcription factor","level":3,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1145/3690624.3709324","is_oa":true,"landing_page_url":"https://doi.org/10.1145/3690624.3709324","pdf_url":null,"source":null,"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 31st ACM SIGKDD Conference on Knowledge Discovery and Data Mining V.1","raw_type":"proceedings-article"}],"best_oa_location":{"id":"doi:10.1145/3690624.3709324","is_oa":true,"landing_page_url":"https://doi.org/10.1145/3690624.3709324","pdf_url":null,"source":null,"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 31st ACM SIGKDD Conference on Knowledge Discovery and Data Mining V.1","raw_type":"proceedings-article"},"sustainable_development_goals":[{"score":0.5400000214576721,"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":13,"referenced_works":["https://openalex.org/W423603040","https://openalex.org/W2027731328","https://openalex.org/W2107559689","https://openalex.org/W2162630660","https://openalex.org/W2170316986","https://openalex.org/W2964051675","https://openalex.org/W2990138404","https://openalex.org/W3160872503","https://openalex.org/W4296414251","https://openalex.org/W4385567824","https://openalex.org/W4385567890","https://openalex.org/W4390534655","https://openalex.org/W6803753837"],"related_works":["https://openalex.org/W2899084033","https://openalex.org/W2018871932","https://openalex.org/W641279757","https://openalex.org/W370975646","https://openalex.org/W1670566515","https://openalex.org/W4242022592","https://openalex.org/W2017303116","https://openalex.org/W1985186062","https://openalex.org/W2421796019","https://openalex.org/W2114138732"],"abstract_inverted_index":{"This":[0,36,95],"paper":[1],"presents":[2],"an":[3],"analytical":[4],"study":[5],"of":[6,52,66,75,84,93,133],"the":[7,50,53,64,76,106,144],"oversmoothing":[8,45,123,157],"issue":[9],"in":[10,21,124,166],"diffusion-based":[11,125],"Graph":[12],"Neural":[13],"Networks":[14],"(GNNs).":[15],"Generalizing":[16],"beyond":[17],"extant":[18],"approaches":[19],"grounded":[20,119],"random":[22],"walk":[23],"analysis":[24],"or":[25],"particle":[26],"systems,":[27],"we":[28,60,128],"approach":[29,120],"this":[30,152],"problem":[31],"through":[32],"operator":[33],"semigroup":[34,58],"theory.":[35],"theoretical":[37,145],"framework":[38],"allows":[39],"us":[40],"to":[41,49,121],"rigorously":[42],"prove":[43],"that":[44,151],"is":[46],"intrinsically":[47],"linked":[48],"ergodicity":[51,80],"diffusion":[54,68],"operator.":[55],"Relying":[56],"on":[57],"method,":[59],"can":[61],"quantitatively":[62],"analyze":[63],"dynamic":[65],"graph":[67],"and":[69,81,101,117,142,162],"give":[70],"a":[71,99,114,130,137],"specific":[72,108],"mathematical":[73],"form":[74],"smoothing":[77],"feature":[78],"by":[79,159],"invariant":[82],"measure":[83],"operator,":[85],"which":[86],"improves":[87],"previous":[88],"works":[89,141],"only":[90],"show":[91],"existence":[92],"oversmoothing.":[94],"finding":[96],"further":[97],"poses":[98],"general":[100],"mild":[102],"ergodicity-breaking":[103,153],"condition,":[104],"encompassing":[105],"various":[107],"solutions":[109],"previously":[110],"offered,":[111],"thereby":[112],"presenting":[113],"more":[115],"universal":[116],"theoretically":[118],"relieve":[122],"GNNs.":[126],"Additionally,":[127],"offer":[129],"probabilistic":[131],"interpretation":[132],"our":[134],"theory,":[135],"forging":[136],"link":[138],"with":[139],"prior":[140],"broadening":[143],"horizon.":[146],"Our":[147],"experimental":[148],"results":[149],"reveal":[150],"term":[154],"effectively":[155],"mitigates":[156],"measured":[158],"Dirichlet":[160],"energy,":[161],"simultaneously":[163],"enhances":[164],"performance":[165],"node":[167],"classification":[168],"tasks.":[169]},"counts_by_year":[{"year":2025,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
