{"id":"https://openalex.org/W7165659923","doi":"https://doi.org/10.48550/arxiv.2606.23572","title":"A Spectral Theory of Normalized Corrected GNN Propagation","display_name":"A Spectral Theory of Normalized Corrected GNN Propagation","publication_year":2026,"publication_date":"2026-06-22","ids":{"openalex":"https://openalex.org/W7165659923","doi":"https://doi.org/10.48550/arxiv.2606.23572"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2606.23572","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2606.23572","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.2606.23572","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5102941837","display_name":"Qihan Chen","orcid":"https://orcid.org/0000-0003-0819-3786"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Chen, Qihan","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5139149741","display_name":"Wei Li","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Li, Wei","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5139157317","display_name":"Meng Qin","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Qin, Meng","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5101971243","display_name":"Jianfeng Hou","orcid":"https://orcid.org/0000-0002-5221-003X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Hou, Jianfeng","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":false,"primary_topic":{"id":"https://openalex.org/T11273","display_name":"Advanced Graph Neural Networks","score":0.2533999979496002,"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":0.2533999979496002,"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/T10320","display_name":"Neural Networks and Applications","score":0.09149999916553497,"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/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.09149999916553497,"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/normalization","display_name":"Normalization (sociology)","score":0.5256999731063843},{"id":"https://openalex.org/keywords/adjacency-list","display_name":"Adjacency list","score":0.5192999839782715},{"id":"https://openalex.org/keywords/binary-number","display_name":"Binary number","score":0.42559999227523804},{"id":"https://openalex.org/keywords/central-limit-theorem","display_name":"Central limit theorem","score":0.38920000195503235},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.3799999952316284},{"id":"https://openalex.org/keywords/graph-theory","display_name":"Graph theory","score":0.35589998960494995},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.353300005197525},{"id":"https://openalex.org/keywords/matching","display_name":"Matching (statistics)","score":0.33570000529289246}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.734499990940094},{"id":"https://openalex.org/C136886441","wikidata":"https://www.wikidata.org/wiki/Q926129","display_name":"Normalization (sociology)","level":2,"score":0.5256999731063843},{"id":"https://openalex.org/C110484373","wikidata":"https://www.wikidata.org/wiki/Q264398","display_name":"Adjacency list","level":2,"score":0.5192999839782715},{"id":"https://openalex.org/C48372109","wikidata":"https://www.wikidata.org/wiki/Q3913","display_name":"Binary number","level":2,"score":0.42559999227523804},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4032000005245209},{"id":"https://openalex.org/C166785042","wikidata":"https://www.wikidata.org/wiki/Q190391","display_name":"Central limit theorem","level":2,"score":0.38920000195503235},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.3799999952316284},{"id":"https://openalex.org/C88230418","wikidata":"https://www.wikidata.org/wiki/Q131476","display_name":"Graph theory","level":2,"score":0.35589998960494995},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.353300005197525},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3370000123977661},{"id":"https://openalex.org/C165064840","wikidata":"https://www.wikidata.org/wiki/Q1321061","display_name":"Matching (statistics)","level":2,"score":0.33570000529289246},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.3280999958515167},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.31929999589920044},{"id":"https://openalex.org/C163415756","wikidata":"https://www.wikidata.org/wiki/Q126473","display_name":"Contraction (grammar)","level":2,"score":0.3100000023841858},{"id":"https://openalex.org/C65180967","wikidata":"https://www.wikidata.org/wiki/Q130901","display_name":"Binary relation","level":2,"score":0.3066999912261963},{"id":"https://openalex.org/C78913703","wikidata":"https://www.wikidata.org/wiki/Q5597087","display_name":"Graph energy","level":5,"score":0.2964000105857849},{"id":"https://openalex.org/C180356752","wikidata":"https://www.wikidata.org/wiki/Q727035","display_name":"Adjacency matrix","level":3,"score":0.2791000008583069},{"id":"https://openalex.org/C72169020","wikidata":"https://www.wikidata.org/wiki/Q194404","display_name":"Monotonic function","level":2,"score":0.2786000072956085},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.27639999985694885},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.27309998869895935},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.26109999418258667},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.26100000739097595},{"id":"https://openalex.org/C2777210771","wikidata":"https://www.wikidata.org/wiki/Q4927124","display_name":"Block (permutation group theory)","level":2,"score":0.259799987077713},{"id":"https://openalex.org/C43711488","wikidata":"https://www.wikidata.org/wiki/Q7534783","display_name":"Skew","level":2,"score":0.2590000033378601},{"id":"https://openalex.org/C98306654","wikidata":"https://www.wikidata.org/wiki/Q2409122","display_name":"Spectral theory","level":3,"score":0.2590000033378601},{"id":"https://openalex.org/C2781238097","wikidata":"https://www.wikidata.org/wiki/Q175026","display_name":"Object (grammar)","level":2,"score":0.2574999928474426},{"id":"https://openalex.org/C168110828","wikidata":"https://www.wikidata.org/wiki/Q1331626","display_name":"Spectral density","level":2,"score":0.25119999051094055}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2606.23572","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2606.23572","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.2606.23572","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2606.23572","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":[{"score":0.7989049553871155,"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"We":[0,97],"develop":[1],"a":[2,63,100],"spectral":[3],"theory":[4],"for":[5,67,87,110],"\\emph{normalized":[6],"corrected":[7,49],"GNN":[8],"propagation}.":[9],"The":[10,42],"object":[11],"of":[12,123],"study":[13],"is":[14,46,62],"the":[15,25,34,68,80,124],"symmetric":[16],"normalized":[17,50],"adjacency":[18],"with":[19],"its":[20],"degree-stationary":[21],"component":[22],"removed,":[23],"matching":[24],"normalization":[26],"used":[27],"by":[28],"standard":[29],"GCN-style":[30],"models":[31],"while":[32],"isolating":[33],"stationary":[35],"direction":[36],"most":[37,111],"directly":[38],"tied":[39],"to":[40],"oversmoothing.":[41],"central":[43],"theoretical":[44],"question":[45],"whether":[47],"this":[48],"operator":[51],"preserves":[52],"class-discriminative":[53],"signal":[54],"after":[55,74],"many":[56],"propagation":[57,77],"layers.":[58],"Our":[59],"main":[60],"result":[61],"high-probability":[64],"exact-recovery":[65],"theorem":[66,104],"binary":[69],"Contextual":[70],"Stochastic":[71],"Block":[72],"Model":[73],"\\(k=O(\\log":[75],"n)\\)":[76],"steps":[78],"in":[79],"dense":[81],"polylogarithmic":[82],"regime":[83],"\\(p\\ge":[84],"C\\log^B":[85],"n/n\\),":[86],"any":[88],"fixed":[89],"\\(B&gt;4\\),":[90],"under":[91],"explicit":[92],"graph-signal":[93],"and":[94,114,132],"feature-SNR":[95],"conditions.":[96],"also":[98],"establish":[99],"multi-class":[101],"partial":[102],"recovery":[103],"showing":[105],"contraction":[106],"toward":[107],"class":[108],"centers":[109],"nodes.":[112],"Synthetic":[113],"real":[115],"node-classification":[116],"experiments":[117],"are":[118],"included":[119],"as":[120],"empirical":[121],"checks":[122],"theory's":[125],"predicted":[126],"dependence":[127],"on":[128],"depth,":[129],"graph":[130],"signal,":[131],"feature":[133],"noise.":[134]},"counts_by_year":[],"updated_date":"2026-07-01T06:00:48.157686","created_date":"2026-06-24T00:00:00"}
