{"id":"https://openalex.org/W7164696291","doi":"https://doi.org/10.1007/s10044-026-01701-3","title":"Preserving node representation diversity in deep graph neural networks through R\u00e9nyi entropy regularization","display_name":"Preserving node representation diversity in deep graph neural networks through R\u00e9nyi entropy regularization","publication_year":2026,"publication_date":"2026-06-13","ids":{"openalex":"https://openalex.org/W7164696291","doi":"https://doi.org/10.1007/s10044-026-01701-3"},"language":"en","primary_location":{"id":"doi:10.1007/s10044-026-01701-3","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10044-026-01701-3","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10044-026-01701-3.pdf","source":{"id":"https://openalex.org/S45497385","display_name":"Pattern Analysis and Applications","issn_l":"1433-7541","issn":["1433-7541","1433-755X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Pattern Analysis and Applications","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s10044-026-01701-3.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5034350635","display_name":"Ahmed Begga","orcid":"https://orcid.org/0009-0000-8733-2072"},"institutions":[{"id":"https://openalex.org/I130194489","display_name":"University of Alicante","ror":"https://ror.org/05t8bcz72","country_code":"ES","type":"education","lineage":["https://openalex.org/I130194489"]}],"countries":["ES"],"is_corresponding":true,"raw_author_name":"Ahmed Begga","raw_affiliation_strings":["Department of Computer Science and Artificial Intelligence, University of Alicante, San Vicente del Raspeig, 03690, Alicante, Spain"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science and Artificial Intelligence, University of Alicante, San Vicente del Raspeig, 03690, Alicante, Spain","institution_ids":["https://openalex.org/I130194489"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5138586567","display_name":"Francisco Escolano","orcid":null},"institutions":[{"id":"https://openalex.org/I130194489","display_name":"University of Alicante","ror":"https://ror.org/05t8bcz72","country_code":"ES","type":"education","lineage":["https://openalex.org/I130194489"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Francisco Escolano","raw_affiliation_strings":["Department of Computer Science and Artificial Intelligence, University of Alicante, San Vicente del Raspeig, 03690, Alicante, Spain"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science and Artificial Intelligence, University of Alicante, San Vicente del Raspeig, 03690, Alicante, Spain","institution_ids":["https://openalex.org/I130194489"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5138580788","display_name":"Miguel \u00c1ngel Lozano","orcid":null},"institutions":[{"id":"https://openalex.org/I130194489","display_name":"University of Alicante","ror":"https://ror.org/05t8bcz72","country_code":"ES","type":"education","lineage":["https://openalex.org/I130194489"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Miguel \u00c1ngel Lozano","raw_affiliation_strings":["Department of Computer Science and Artificial Intelligence, University of Alicante, San Vicente del Raspeig, 03690, Alicante, Spain"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science and Artificial Intelligence, University of Alicante, San Vicente del Raspeig, 03690, Alicante, Spain","institution_ids":["https://openalex.org/I130194489"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5034350635"],"corresponding_institution_ids":["https://openalex.org/I130194489"],"apc_list":{"value":2990,"currency":"USD","value_usd":2990},"apc_paid":{"value":2990,"currency":"USD","value_usd":2990},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.74907398,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"29","issue":"3","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":0.9915000200271606,"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":0.9915000200271606,"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/T12292","display_name":"Graph Theory and Algorithms","score":0.0007999999797903001,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"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/T13702","display_name":"Machine Learning in Healthcare","score":0.000699999975040555,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/entropy","display_name":"Entropy (arrow of time)","score":0.5307000279426575},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.519599974155426},{"id":"https://openalex.org/keywords/discriminative-model","display_name":"Discriminative model","score":0.4577000141143799},{"id":"https://openalex.org/keywords/gaussian","display_name":"Gaussian","score":0.43209999799728394},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.4104999899864197},{"id":"https://openalex.org/keywords/regularization","display_name":"Regularization (linguistics)","score":0.40310001373291016}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6643999814987183},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.5428000092506409},{"id":"https://openalex.org/C106301342","wikidata":"https://www.wikidata.org/wiki/Q4117933","display_name":"Entropy (arrow of time)","level":2,"score":0.5307000279426575},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.519599974155426},{"id":"https://openalex.org/C97931131","wikidata":"https://www.wikidata.org/wiki/Q5282087","display_name":"Discriminative model","level":2,"score":0.4577000141143799},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.43209999799728394},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.4104999899864197},{"id":"https://openalex.org/C2776135515","wikidata":"https://www.wikidata.org/wiki/Q17143721","display_name":"Regularization (linguistics)","level":2,"score":0.40310001373291016},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.4023999869823456},{"id":"https://openalex.org/C153180895","wikidata":"https://www.wikidata.org/wiki/Q7148389","display_name":"Pattern recognition (psychology)","level":2,"score":0.37630000710487366},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3700999915599823},{"id":"https://openalex.org/C2984842247","wikidata":"https://www.wikidata.org/wiki/Q197536","display_name":"Deep neural networks","level":3,"score":0.3646000027656555},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.34290000796318054},{"id":"https://openalex.org/C86251818","wikidata":"https://www.wikidata.org/wiki/Q816754","display_name":"Benchmarking","level":2,"score":0.31859999895095825},{"id":"https://openalex.org/C71134354","wikidata":"https://www.wikidata.org/wiki/Q458825","display_name":"Kernel density estimation","level":3,"score":0.29440000653266907},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.2867000102996826},{"id":"https://openalex.org/C185798385","wikidata":"https://www.wikidata.org/wiki/Q1161707","display_name":"Benchmark (surveying)","level":2,"score":0.274399995803833},{"id":"https://openalex.org/C108583219","wikidata":"https://www.wikidata.org/wiki/Q197536","display_name":"Deep learning","level":2,"score":0.25690001249313354}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s10044-026-01701-3","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10044-026-01701-3","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10044-026-01701-3.pdf","source":{"id":"https://openalex.org/S45497385","display_name":"Pattern Analysis and Applications","issn_l":"1433-7541","issn":["1433-7541","1433-755X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Pattern Analysis and Applications","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1007/s10044-026-01701-3","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10044-026-01701-3","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10044-026-01701-3.pdf","source":{"id":"https://openalex.org/S45497385","display_name":"Pattern Analysis and Applications","issn_l":"1433-7541","issn":["1433-7541","1433-755X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Pattern Analysis and Applications","raw_type":"journal-article"},"sustainable_development_goals":[{"display_name":"Reduced inequalities","score":0.7956236004829407,"id":"https://metadata.un.org/sdg/10"}],"awards":[],"funders":[{"id":"https://openalex.org/F4320311011","display_name":"Universidad de Alicante","ror":"https://ror.org/05t8bcz72"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7164696291.pdf","grobid_xml":"https://content.openalex.org/works/W7164696291.grobid-xml"},"referenced_works_count":18,"referenced_works":["https://openalex.org/W2116341502","https://openalex.org/W2118439480","https://openalex.org/W2964051675","https://openalex.org/W2990045899","https://openalex.org/W3128443161","https://openalex.org/W3187483004","https://openalex.org/W4200566466","https://openalex.org/W4303833139","https://openalex.org/W4320060387","https://openalex.org/W4323314209","https://openalex.org/W4388721381","https://openalex.org/W4390547902","https://openalex.org/W4392203343","https://openalex.org/W4396220739","https://openalex.org/W4402114425","https://openalex.org/W4411048537","https://openalex.org/W4413490502","https://openalex.org/W4414811748"],"related_works":[],"abstract_inverted_index":{"Abstract":[0],"Graph":[1],"Neural":[2],"Networks":[3],"have":[4],"demonstrated":[5],"remarkable":[6],"performance":[7,121],"across":[8,58,122],"diverse":[9],"domains,":[10],"yet":[11],"they":[12],"face":[13],"significant":[14,133],"limitations":[15],"in":[16],"deeper":[17],"architectures":[18],"due":[19],"to":[20,83,103,154],"oversmoothing\u2014the":[21],"phenomenon":[22],"where":[23],"node":[24,56],"representations":[25,57],"become":[26],"increasingly":[27],"indistinguishable":[28],"through":[29,44],"successive":[30],"message-passing":[31],"operations.":[32],"We":[33],"propose":[34],"a":[35,70,167],"novel":[36],"information-theoretic":[37],"approach":[38,93],"that":[39,75,114,144],"addresses":[40],"this":[41],"fundamental":[42],"challenge":[43],"R\u00e9nyi":[45,116],"entropy":[46,72,117],"optimization.":[47],"Our":[48,140],"method":[49,146],"quantifies":[50],"and":[51,131,165],"maximizes":[52],"the":[53,77,104,145,159],"diversity":[54],"of":[55,129,162],"network":[59,149],"layers":[60,153],"using":[61],"kernel":[62],"density":[63],"estimation":[64],"with":[65,96,126],"Gaussian":[66],"kernels.":[67],"By":[68],"formulating":[69],"graph-structured":[71],"regularization":[73,118],"term":[74],"respects":[76],"underlying":[78],"topology,":[79],"we":[80],"encourage":[81],"networks":[82],"maintain":[84],"discriminative":[85],"features":[86],"while":[87],"preserving":[88],"essential":[89],"structural":[90],"information.":[91],"This":[92],"integrates":[94],"seamlessly":[95],"existing":[97],"GNN":[98,124],"architectures,":[99],"requiring":[100],"minimal":[101],"modifications":[102],"training":[105],"procedure.":[106],"Extensive":[107],"experiments":[108],"on":[109,135],"ten":[110],"benchmark":[111],"datasets":[112],"demonstrate":[113],"our":[115],"consistently":[119],"improves":[120],"multiple":[123],"variants,":[125],"average":[127],"gains":[128],"1.89%":[130],"particularly":[132],"improvements":[134],"heterophilic":[136],"graphs":[137],"exceeding":[138],"2.5%.":[139],"depth":[141,150],"analysis":[142],"shows":[143],"extends":[147],"viable":[148],"from":[151],"2\u20133":[152],"8\u201310":[155],"layers,":[156],"effectively":[157],"countering":[158],"homogenization":[160],"tendency":[161],"deep":[163],"GNNs":[164],"establishing":[166],"principled":[168],"foundation":[169],"for":[170],"more":[171],"expressive":[172],"graph":[173],"neural":[174],"networks.":[175]},"counts_by_year":[],"updated_date":"2026-07-23T08:03:31.855105","created_date":"2026-06-14T00:00:00"}
