{"id":"https://openalex.org/W4415336375","doi":"https://doi.org/10.1007/s10994-025-06884-0","title":"Bridging XAI and spectral analysis to investigate the inductive biases of deep graph networks","display_name":"Bridging XAI and spectral analysis to investigate the inductive biases of deep graph networks","publication_year":2025,"publication_date":"2025-10-19","ids":{"openalex":"https://openalex.org/W4415336375","doi":"https://doi.org/10.1007/s10994-025-06884-0"},"language":"en","primary_location":{"id":"doi:10.1007/s10994-025-06884-0","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10994-025-06884-0","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10994-025-06884-0.pdf","source":{"id":"https://openalex.org/S62148650","display_name":"Machine Learning","issn_l":"0885-6125","issn":["0885-6125","1573-0565"],"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-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Machine Learning","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/s10994-025-06884-0.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5078841880","display_name":"Michele Fontanesi","orcid":"https://orcid.org/0009-0004-7566-903X"},"institutions":[{"id":"https://openalex.org/I108290504","display_name":"University of Pisa","ror":"https://ror.org/03ad39j10","country_code":"IT","type":"education","lineage":["https://openalex.org/I108290504"]}],"countries":["IT"],"is_corresponding":true,"raw_author_name":"Michele Fontanesi","raw_affiliation_strings":["Department of Computer Science, University of Pisa, Largo B. Pontecorvo 3, 56127, Pisa, Italy"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science, University of Pisa, Largo B. Pontecorvo 3, 56127, Pisa, Italy","institution_ids":["https://openalex.org/I108290504"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5010923663","display_name":"Alessio Micheli","orcid":"https://orcid.org/0000-0001-5764-5238"},"institutions":[{"id":"https://openalex.org/I108290504","display_name":"University of Pisa","ror":"https://ror.org/03ad39j10","country_code":"IT","type":"education","lineage":["https://openalex.org/I108290504"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Alessio Micheli","raw_affiliation_strings":["Department of Computer Science, University of Pisa, Largo B. Pontecorvo 3, 56127, Pisa, Italy"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science, University of Pisa, Largo B. Pontecorvo 3, 56127, Pisa, Italy","institution_ids":["https://openalex.org/I108290504"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5027095496","display_name":"Marco Podda","orcid":"https://orcid.org/0000-0003-1497-9515"},"institutions":[{"id":"https://openalex.org/I108290504","display_name":"University of Pisa","ror":"https://ror.org/03ad39j10","country_code":"IT","type":"education","lineage":["https://openalex.org/I108290504"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Marco Podda","raw_affiliation_strings":["Department of Computer Science, University of Pisa, Largo B. Pontecorvo 3, 56127, Pisa, Italy"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science, University of Pisa, Largo B. Pontecorvo 3, 56127, Pisa, Italy","institution_ids":["https://openalex.org/I108290504"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5068896301","display_name":"Domenico Tortorella","orcid":"https://orcid.org/0000-0003-3910-7713"},"institutions":[{"id":"https://openalex.org/I108290504","display_name":"University of Pisa","ror":"https://ror.org/03ad39j10","country_code":"IT","type":"education","lineage":["https://openalex.org/I108290504"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Domenico Tortorella","raw_affiliation_strings":["Department of Computer Science, University of Pisa, Largo B. Pontecorvo 3, 56127, Pisa, Italy"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science, University of Pisa, Largo B. Pontecorvo 3, 56127, Pisa, Italy","institution_ids":["https://openalex.org/I108290504"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5078841880"],"corresponding_institution_ids":["https://openalex.org/I108290504"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":{"value":2390,"currency":"EUR","value_usd":2990},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.15248011,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"114","issue":"11","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":0.9998999834060669,"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":0.9998999834060669,"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/T10064","display_name":"Complex Network Analysis Techniques","score":0.9990000128746033,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10887","display_name":"Bioinformatics and Genomic Networks","score":0.9952999949455261,"subfield":{"id":"https://openalex.org/subfields/1312","display_name":"Molecular Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/inductive-bias","display_name":"Inductive bias","score":0.6337000131607056},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.607200026512146},{"id":"https://openalex.org/keywords/granularity","display_name":"Granularity","score":0.5932999849319458},{"id":"https://openalex.org/keywords/centrality","display_name":"Centrality","score":0.5375999808311462},{"id":"https://openalex.org/keywords/network-science","display_name":"Network science","score":0.5109000205993652},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.48030000925064087},{"id":"https://openalex.org/keywords/bridging","display_name":"Bridging (networking)","score":0.4569999873638153},{"id":"https://openalex.org/keywords/spectral-graph-theory","display_name":"Spectral graph theory","score":0.45489999651908875},{"id":"https://openalex.org/keywords/network-analysis","display_name":"Network analysis","score":0.37540000677108765}],"concepts":[{"id":"https://openalex.org/C197352929","wikidata":"https://www.wikidata.org/wiki/Q1074074","display_name":"Inductive bias","level":4,"score":0.6337000131607056},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.607200026512146},{"id":"https://openalex.org/C177774035","wikidata":"https://www.wikidata.org/wiki/Q1246948","display_name":"Granularity","level":2,"score":0.5932999849319458},{"id":"https://openalex.org/C53811970","wikidata":"https://www.wikidata.org/wiki/Q5062194","display_name":"Centrality","level":2,"score":0.5375999808311462},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5231000185012817},{"id":"https://openalex.org/C137753397","wikidata":"https://www.wikidata.org/wiki/Q2434424","display_name":"Network science","level":3,"score":0.5109000205993652},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.4828000068664551},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.48030000925064087},{"id":"https://openalex.org/C174348530","wikidata":"https://www.wikidata.org/wiki/Q188635","display_name":"Bridging (networking)","level":2,"score":0.4569999873638153},{"id":"https://openalex.org/C74003402","wikidata":"https://www.wikidata.org/wiki/Q3180727","display_name":"Spectral graph theory","level":5,"score":0.45489999651908875},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.43540000915527344},{"id":"https://openalex.org/C32946077","wikidata":"https://www.wikidata.org/wiki/Q618079","display_name":"Network analysis","level":2,"score":0.37540000677108765},{"id":"https://openalex.org/C106937863","wikidata":"https://www.wikidata.org/wiki/Q7236518","display_name":"Power graph analysis","level":3,"score":0.36059999465942383},{"id":"https://openalex.org/C108583219","wikidata":"https://www.wikidata.org/wiki/Q197536","display_name":"Deep learning","level":2,"score":0.3424000144004822},{"id":"https://openalex.org/C104267543","wikidata":"https://www.wikidata.org/wiki/Q208163","display_name":"Signal processing","level":3,"score":0.328000009059906},{"id":"https://openalex.org/C88230418","wikidata":"https://www.wikidata.org/wiki/Q131476","display_name":"Graph theory","level":2,"score":0.32749998569488525},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3228999972343445},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3203999996185303},{"id":"https://openalex.org/C64339825","wikidata":"https://www.wikidata.org/wiki/Q722659","display_name":"Graph property","level":5,"score":0.30880001187324524},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.2928999960422516},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.2892000079154968},{"id":"https://openalex.org/C160920958","wikidata":"https://www.wikidata.org/wiki/Q7662746","display_name":"Synthetic data","level":2,"score":0.28619998693466187},{"id":"https://openalex.org/C59404180","wikidata":"https://www.wikidata.org/wiki/Q17013334","display_name":"Feature learning","level":2,"score":0.2777999937534332},{"id":"https://openalex.org/C153180895","wikidata":"https://www.wikidata.org/wiki/Q7148389","display_name":"Pattern recognition (psychology)","level":2,"score":0.26989999413490295},{"id":"https://openalex.org/C104122410","wikidata":"https://www.wikidata.org/wiki/Q1416406","display_name":"Network model","level":2,"score":0.26249998807907104},{"id":"https://openalex.org/C47458327","wikidata":"https://www.wikidata.org/wiki/Q910404","display_name":"Random graph","level":3,"score":0.25920000672340393},{"id":"https://openalex.org/C3018234147","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Undirected graph","level":3,"score":0.25029999017715454}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/s10994-025-06884-0","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10994-025-06884-0","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10994-025-06884-0.pdf","source":{"id":"https://openalex.org/S62148650","display_name":"Machine Learning","issn_l":"0885-6125","issn":["0885-6125","1573-0565"],"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-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Machine Learning","raw_type":"journal-article"},{"id":"pmh:oai:arpi.unipi.it:11568/1328204","is_oa":true,"landing_page_url":"https://link.springer.com/article/10.1007/s10994-025-06884-0","pdf_url":null,"source":{"id":"https://openalex.org/S4377196265","display_name":"CINECA IRIS Institutial research information system (University of Pisa)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I108290504","host_organization_name":"University of Pisa","host_organization_lineage":["https://openalex.org/I108290504"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"doi:10.1007/s10994-025-06884-0","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10994-025-06884-0","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10994-025-06884-0.pdf","source":{"id":"https://openalex.org/S62148650","display_name":"Machine Learning","issn_l":"0885-6125","issn":["0885-6125","1573-0565"],"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-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Machine Learning","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G100767060","display_name":null,"funder_award_id":"T4-AN-07","funder_id":"https://openalex.org/F4320321781","funder_display_name":"Ministero della Salute"},{"id":"https://openalex.org/G6788846316","display_name":null,"funder_award_id":"I53C22001300001","funder_id":"https://openalex.org/F4320321781","funder_display_name":"Ministero della Salute"},{"id":"https://openalex.org/G7022670847","display_name":null,"funder_award_id":"POS 2014-2020","funder_id":"https://openalex.org/F4320321781","funder_display_name":"Ministero della Salute"}],"funders":[{"id":"https://openalex.org/F4320321781","display_name":"Ministero della Salute","ror":"https://ror.org/00789fa95"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4415336375.pdf","grobid_xml":"https://content.openalex.org/works/W4415336375.grobid-xml"},"referenced_works_count":33,"referenced_works":["https://openalex.org/W1512522810","https://openalex.org/W2012724202","https://openalex.org/W2016423476","https://openalex.org/W2026417691","https://openalex.org/W2101491865","https://openalex.org/W2116341502","https://openalex.org/W2132914434","https://openalex.org/W2139906443","https://openalex.org/W2153513200","https://openalex.org/W2295107390","https://openalex.org/W2781888589","https://openalex.org/W2907492528","https://openalex.org/W2912636151","https://openalex.org/W2962810718","https://openalex.org/W2964051675","https://openalex.org/W2979481854","https://openalex.org/W2990138404","https://openalex.org/W2997785591","https://openalex.org/W3101413764","https://openalex.org/W3116637551","https://openalex.org/W4223413649","https://openalex.org/W4224309172","https://openalex.org/W4229000221","https://openalex.org/W4312410287","https://openalex.org/W4327813569","https://openalex.org/W4382405183","https://openalex.org/W4388235537","https://openalex.org/W4393906067","https://openalex.org/W4393972734","https://openalex.org/W4402365128","https://openalex.org/W4402778834","https://openalex.org/W4405925602","https://openalex.org/W4406844753"],"related_works":[],"abstract_inverted_index":{"Understanding":[0],"the":[1,32,48,56,89,92,98,113,157,161,166,174,202],"inductive":[2,50,189],"bias":[3],"of":[4,52,70,91,112,160,201],"Deep":[5],"Graph":[6],"Networks":[7],"(DGNs)":[8],"is":[9,104,140,184],"crucial":[10],"because":[11],"it":[12],"reveals":[13],"how":[14],"these":[15,25],"models":[16],"generalize":[17,122,132],"from":[18],"training":[19],"data":[20],"to":[21,31,65,84,178,199],"unseen":[22],"data.":[23],"Discovering":[24],"learning":[26],"assumptions,":[27],"and":[28,40,73,117,169],"their":[29],"alignment":[30],"task\u2019s":[33],"characteristics,":[34],"allows":[35],"informed":[36],"architectural":[37],"design":[38],"choices":[39],"facilitates":[41],"interpretation.":[42],"With":[43],"this":[44,86,182],"goal,":[45],"we":[46],"analyze":[47],"different":[49,106,110],"biases":[51,190],"DGNs":[53,107,121,131],"by":[54,60,97,123,133,146,186],"relating":[55],"node-level":[57],"explanations":[58,149],"produced":[59],"explainable":[61],"AI":[62],"(XAI)":[63],"methods":[64],"known":[66],"network":[67,152],"science":[68,153],"measures":[69,154],"lower-order":[71,126],"(local)":[72],"higher-order":[74,135],"(increasingly":[75],"global)":[76],"connectivity.":[77],"We":[78],"then":[79],"apply":[80],"graph":[81,93,114,127,136],"signal":[82],"processing":[83],"refine":[85],"analysis":[87],"at":[88,156],"granularity":[90],"frequency":[94,115,203],"spectrum":[95,162],"spanned":[96],"explanation":[99],"signals.":[100],"Our":[101],"main":[102],"finding":[103],"that":[105,148,188,197],"focus":[108],"on":[109,125,143,194],"regions":[111],"spectrum,":[116],"in":[118,165,173],"particular,":[119],"high-frequency":[120],"focusing":[124],"connectivity,":[128],"while":[129],"low-frequency":[130],"recognizing":[134],"structures.":[137],"This":[138],"characterization":[139],"first":[141],"derived":[142],"synthetic":[144],"benchmarks":[145],"showing":[147,187],"align":[150],"with":[151],"sitting":[155],"two":[158],"extremes":[159],"(Katz":[163],"centrality":[164],"high":[167],"frequencies,":[168],"Fiedler":[170],"eigenvector":[171],"scores":[172],"low":[175],"frequencies).":[176],"Moving":[177],"real-world":[179],"chemical":[180],"benchmarks,":[181],"result":[183],"generalized":[185],"do":[191],"indeed":[192],"lie":[193],"a":[195],"continuum":[196],"corresponds":[198],"sub-regions":[200],"spectrum.":[204]},"counts_by_year":[],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2025-10-19T00:00:00"}