{"id":"https://openalex.org/W7131130848","doi":"https://doi.org/10.1109/tpami.2026.3667002","title":"Toward the Spectral Bias Alleviation by Normalizations in Coordinate Networks","display_name":"Toward the Spectral Bias Alleviation by Normalizations in Coordinate Networks","publication_year":2026,"publication_date":"2026-02-23","ids":{"openalex":"https://openalex.org/W7131130848","doi":"https://doi.org/10.1109/tpami.2026.3667002","pmid":"https://pubmed.ncbi.nlm.nih.gov/41729674"},"language":"en","primary_location":{"id":"doi:10.1109/tpami.2026.3667002","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tpami.2026.3667002","pdf_url":null,"source":{"id":"https://openalex.org/S199944782","display_name":"IEEE Transactions on Pattern Analysis and Machine Intelligence","issn_l":"0162-8828","issn":["0162-8828","1939-3539","2160-9292"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320439","host_organization_name":"IEEE Computer Society","host_organization_lineage":["https://openalex.org/P4310320439","https://openalex.org/P4310319808"],"host_organization_lineage_names":["IEEE Computer Society","Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Pattern Analysis and Machine Intelligence","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","pubmed"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5051336653","display_name":"Zhicheng Cai","orcid":"https://orcid.org/0000-0002-8702-6216"},"institutions":[{"id":"https://openalex.org/I881766915","display_name":"Nanjing University","ror":"https://ror.org/01rxvg760","country_code":"CN","type":"education","lineage":["https://openalex.org/I881766915"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zhicheng Cai","raw_affiliation_strings":["School of Electronic Science and Engineering, Nanjing University, Nanjing, China"],"raw_orcid":"https://orcid.org/0009-0000-7986-6269","affiliations":[{"raw_affiliation_string":"School of Electronic Science and Engineering, Nanjing University, Nanjing, China","institution_ids":["https://openalex.org/I881766915"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5058268359","display_name":"Hao Zhu","orcid":"https://orcid.org/0000-0003-4411-0933"},"institutions":[{"id":"https://openalex.org/I881766915","display_name":"Nanjing University","ror":"https://ror.org/01rxvg760","country_code":"CN","type":"education","lineage":["https://openalex.org/I881766915"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Hao Zhu","raw_affiliation_strings":["School of Electronic Science and Engineering, Nanjing University, Nanjing, China"],"raw_orcid":"https://orcid.org/0000-0002-6756-9571","affiliations":[{"raw_affiliation_string":"School of Electronic Science and Engineering, Nanjing University, Nanjing, China","institution_ids":["https://openalex.org/I881766915"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5126589649","display_name":"Qiu Shen","orcid":null},"institutions":[{"id":"https://openalex.org/I881766915","display_name":"Nanjing University","ror":"https://ror.org/01rxvg760","country_code":"CN","type":"education","lineage":["https://openalex.org/I881766915"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Qiu Shen","raw_affiliation_strings":["School of Electronic Science and Engineering, Nanjing University, Nanjing, China"],"raw_orcid":"https://orcid.org/0000-0002-3057-0608","affiliations":[{"raw_affiliation_string":"School of Electronic Science and Engineering, Nanjing University, Nanjing, China","institution_ids":["https://openalex.org/I881766915"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5126609373","display_name":"Xinran Wang","orcid":null},"institutions":[{"id":"https://openalex.org/I4210153682","display_name":"Intelligent Health (United Kingdom)","ror":"https://ror.org/0576zak10","country_code":"GB","type":"company","lineage":["https://openalex.org/I4210153682"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Xinran Wang","raw_affiliation_strings":["Interdisciplinary Research Center for Future Intelligent Chips (Chip-X), Nanjing University, Nanjing, China"],"raw_orcid":"https://orcid.org/0000-0002-3975-1667","affiliations":[{"raw_affiliation_string":"Interdisciplinary Research Center for Future Intelligent Chips (Chip-X), Nanjing University, Nanjing, China","institution_ids":["https://openalex.org/I4210153682"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5067778191","display_name":"Xun Cao","orcid":"https://orcid.org/0000-0003-1617-1501"},"institutions":[{"id":"https://openalex.org/I881766915","display_name":"Nanjing University","ror":"https://ror.org/01rxvg760","country_code":"CN","type":"education","lineage":["https://openalex.org/I881766915"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xun Cao","raw_affiliation_strings":["School of Electronic Science and Engineering, Nanjing University, Nanjing, China"],"raw_orcid":"https://orcid.org/0000-0003-3094-4371","affiliations":[{"raw_affiliation_string":"School of Electronic Science and Engineering, Nanjing University, Nanjing, China","institution_ids":["https://openalex.org/I881766915"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.23406262,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":95},"biblio":{"volume":"48","issue":"7","first_page":"7784","last_page":"7801"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10064","display_name":"Complex Network Analysis Techniques","score":0.0892999991774559,"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"}},"topics":[{"id":"https://openalex.org/T10064","display_name":"Complex Network Analysis Techniques","score":0.0892999991774559,"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/T11321","display_name":"Error Correcting Code Techniques","score":0.04969999939203262,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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/T10148","display_name":"Advanced MIMO Systems Optimization","score":0.04740000143647194,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/normalization","display_name":"Normalization (sociology)","score":0.8435999751091003},{"id":"https://openalex.org/keywords/coordinate-system","display_name":"Coordinate system","score":0.595300018787384},{"id":"https://openalex.org/keywords/convolutional-neural-network","display_name":"Convolutional neural network","score":0.5454999804496765},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.5216000080108643},{"id":"https://openalex.org/keywords/pattern-recognition","display_name":"Pattern recognition (psychology)","score":0.4708999991416931},{"id":"https://openalex.org/keywords/tangent","display_name":"Tangent","score":0.44920000433921814},{"id":"https://openalex.org/keywords/inverse-problem","display_name":"Inverse problem","score":0.3828999996185303},{"id":"https://openalex.org/keywords/inverse","display_name":"Inverse","score":0.3619999885559082}],"concepts":[{"id":"https://openalex.org/C136886441","wikidata":"https://www.wikidata.org/wiki/Q926129","display_name":"Normalization (sociology)","level":2,"score":0.8435999751091003},{"id":"https://openalex.org/C80551277","wikidata":"https://www.wikidata.org/wiki/Q11210","display_name":"Coordinate system","level":2,"score":0.595300018787384},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.5561000108718872},{"id":"https://openalex.org/C81363708","wikidata":"https://www.wikidata.org/wiki/Q17084460","display_name":"Convolutional neural network","level":2,"score":0.5454999804496765},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5429999828338623},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.5216000080108643},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.49720001220703125},{"id":"https://openalex.org/C153180895","wikidata":"https://www.wikidata.org/wiki/Q7148389","display_name":"Pattern recognition (psychology)","level":2,"score":0.4708999991416931},{"id":"https://openalex.org/C138187205","wikidata":"https://www.wikidata.org/wiki/Q131251","display_name":"Tangent","level":2,"score":0.44920000433921814},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4036000072956085},{"id":"https://openalex.org/C135252773","wikidata":"https://www.wikidata.org/wiki/Q1567213","display_name":"Inverse problem","level":2,"score":0.3828999996185303},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.3619999885559082},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.3418000042438507},{"id":"https://openalex.org/C34736171","wikidata":"https://www.wikidata.org/wiki/Q918333","display_name":"Preprocessor","level":2,"score":0.32659998536109924},{"id":"https://openalex.org/C94360122","wikidata":"https://www.wikidata.org/wiki/Q1967557","display_name":"Spectral power distribution","level":2,"score":0.32589998841285706},{"id":"https://openalex.org/C9417928","wikidata":"https://www.wikidata.org/wiki/Q1070689","display_name":"Image processing","level":3,"score":0.2996000051498413},{"id":"https://openalex.org/C31972630","wikidata":"https://www.wikidata.org/wiki/Q844240","display_name":"Computer vision","level":1,"score":0.29589998722076416},{"id":"https://openalex.org/C49766605","wikidata":"https://www.wikidata.org/wiki/Q207643","display_name":"Linear map","level":2,"score":0.27799999713897705},{"id":"https://openalex.org/C110121322","wikidata":"https://www.wikidata.org/wiki/Q865811","display_name":"Distribution (mathematics)","level":2,"score":0.2623000144958496},{"id":"https://openalex.org/C116580362","wikidata":"https://www.wikidata.org/wiki/Q3878457","display_name":"Spatial normalization","level":3,"score":0.26100000739097595},{"id":"https://openalex.org/C104267543","wikidata":"https://www.wikidata.org/wiki/Q208163","display_name":"Signal processing","level":3,"score":0.2547000050544739},{"id":"https://openalex.org/C169756996","wikidata":"https://www.wikidata.org/wiki/Q194919","display_name":"Eigendecomposition of a matrix","level":3,"score":0.250900000333786}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/tpami.2026.3667002","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tpami.2026.3667002","pdf_url":null,"source":{"id":"https://openalex.org/S199944782","display_name":"IEEE Transactions on Pattern Analysis and Machine Intelligence","issn_l":"0162-8828","issn":["0162-8828","1939-3539","2160-9292"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320439","host_organization_name":"IEEE Computer Society","host_organization_lineage":["https://openalex.org/P4310320439","https://openalex.org/P4310319808"],"host_organization_lineage_names":["IEEE Computer Society","Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Pattern Analysis and Machine Intelligence","raw_type":"journal-article"},{"id":"pmid:41729674","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/41729674","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE transactions on pattern analysis and machine intelligence","raw_type":null}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities","score":0.4311383068561554}],"awards":[{"id":"https://openalex.org/G4469794710","display_name":null,"funder_award_id":"U25B2046","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G505992543","display_name":null,"funder_award_id":"T2221003","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G6127711580","display_name":null,"funder_award_id":"62231002","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":55,"referenced_works":["https://openalex.org/W2083927153","https://openalex.org/W2085905957","https://openalex.org/W2122572959","https://openalex.org/W2178629455","https://openalex.org/W2194775991","https://openalex.org/W2962849139","https://openalex.org/W2963596039","https://openalex.org/W2963627347","https://openalex.org/W2963743626","https://openalex.org/W2963926543","https://openalex.org/W2981657250","https://openalex.org/W2989630530","https://openalex.org/W2993158195","https://openalex.org/W3003922491","https://openalex.org/W3034968345","https://openalex.org/W3035515538","https://openalex.org/W3095682719","https://openalex.org/W3153220274","https://openalex.org/W3163993681","https://openalex.org/W3175967923","https://openalex.org/W3179022832","https://openalex.org/W3184957317","https://openalex.org/W3195875706","https://openalex.org/W3203281102","https://openalex.org/W3215434375","https://openalex.org/W3215589927","https://openalex.org/W4200150166","https://openalex.org/W4221151978","https://openalex.org/W4225305714","https://openalex.org/W4250482878","https://openalex.org/W4287660544","https://openalex.org/W4294691181","https://openalex.org/W4296209293","https://openalex.org/W4312325284","https://openalex.org/W4312349930","https://openalex.org/W4312443924","https://openalex.org/W4312796583","https://openalex.org/W4313147859","https://openalex.org/W4313156152","https://openalex.org/W4379382937","https://openalex.org/W4381165433","https://openalex.org/W4382464509","https://openalex.org/W4385245566","https://openalex.org/W4386047745","https://openalex.org/W4386066223","https://openalex.org/W4386066812","https://openalex.org/W4386076276","https://openalex.org/W4390190370","https://openalex.org/W4391854909","https://openalex.org/W4400073365","https://openalex.org/W4402703005","https://openalex.org/W4402797665","https://openalex.org/W4402816953","https://openalex.org/W4415120057","https://openalex.org/W7133183852"],"related_works":[],"abstract_inverted_index":{"Representing":[0],"signals":[1],"using":[2,66],"coordinate":[3,30,55,87,181],"networks":[4,82,182],"dominates":[5],"the":[6,33,44,48,96,106,110,117,138,171,187],"area":[7],"of":[8,26,47,54,100,126,164],"inverse":[9],"problems":[10],"recently,":[11],"and":[12,72,98,174,201],"is":[13,41,113,168],"widely":[14],"applied":[15],"in":[16,29,79,86,123,159],"various":[17,184],"scientific":[18],"computing":[19],"tasks.":[20],"Still,":[21],"there":[22],"exists":[23],"an":[24],"issue":[25],"spectral":[27,139],"bias":[28,140],"networks,":[31],"limiting":[32],"capacity":[34],"to":[35,133,183],"learn":[36],"high-frequency":[37],"components.":[38],"This":[39],"problem":[40],"caused":[42],"by":[43,154,170,178],"pathological":[45,61],"distribution":[46,62,128],"neural":[49,81],"tangent":[50],"kernel's":[51],"(NTK's)":[52],"eigenvalues":[53,102],"networks.":[56,88],"We":[57,89],"find":[58],"that,":[59],"this":[60,119],"could":[63,141],"be":[64,142],"improved":[65],"classical":[67],"normalization":[68,71,92,152,166],"techniques":[69,93,153,158,167],"(batch":[70],"layer":[73],"normalization),":[74],"which":[75],"are":[76],"commonly":[77],"used":[78,85],"convolutional":[80],"but":[83],"rarely":[84],"prove":[90],"that":[91],"greatly":[94],"reduces":[95],"maximum":[97],"variance":[99,120],"NTK's":[101],"while":[103],"slightly":[104],"modifies":[105],"mean":[107],"value,":[108],"considering":[109],"max":[111],"eigenvalue":[112],"much":[114],"larger":[115],"than":[116],"most,":[118],"change":[121],"results":[122],"a":[124,130,134],"shift":[125],"eigenvalues'":[127],"from":[129],"lower":[131],"one":[132],"higher":[135],"one,":[136],"therefore":[137],"alleviated":[143],"(see":[144],"Fig.":[145],"1).":[146],"Furthermore,":[147],"we":[148],"propose":[149],"two":[150,157],"new":[151,175],"combining":[155],"these":[156,165],"different":[160],"ways.":[161],"The":[162],"efficacy":[163],"substantiated":[169],"significant":[172],"improvements":[173],"state-of-the-arts":[176],"achieved":[177],"applying":[179],"normalization-based":[180],"tasks,":[185],"including":[186],"image":[188],"compression,":[189],"computed":[190],"tomography":[191],"reconstruction,":[192],"shape":[193],"representation,":[194],"magnetic":[195],"resonance":[196],"imaging,":[197],"novel":[198],"view":[199],"synthesis":[200],"multi-view":[202],"stereo":[203],"reconstruction.":[204]},"counts_by_year":[{"year":2025,"cited_by_count":1}],"updated_date":"2026-06-07T06:13:29.825681","created_date":"2026-02-24T00:00:00"}