{"id":"https://openalex.org/W7150928122","doi":"https://doi.org/10.48550/arxiv.2604.02846","title":"Adaptive Local Frequency Filtering for Fourier-Encoded Implicit Neural Representations","display_name":"Adaptive Local Frequency Filtering for Fourier-Encoded Implicit Neural Representations","publication_year":2026,"publication_date":"2026-04-03","ids":{"openalex":"https://openalex.org/W7150928122","doi":"https://doi.org/10.48550/arxiv.2604.02846"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2604.02846","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.02846","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","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.2604.02846","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5074746122","display_name":"Ligen Shi","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Shi, Ligen","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5133042662","display_name":"Jun Qiu","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Qiu, Jun","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5133030903","display_name":"Yuhang Zheng","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Zheng, Yuhang","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":null,"display_name":"Pang, Zengyu","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Pang, Zengyu","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":null,"display_name":"Liu, Chang","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Liu, Chang","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/T10719","display_name":"3D Shape Modeling and Analysis","score":0.3806999921798706,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10719","display_name":"3D Shape Modeling and Analysis","score":0.3806999921798706,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10775","display_name":"Generative Adversarial Networks and Image Synthesis","score":0.2433999925851822,"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/T11206","display_name":"Model Reduction and Neural Networks","score":0.10220000147819519,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/kernel","display_name":"Kernel (algebra)","score":0.5892000198364258},{"id":"https://openalex.org/keywords/filter","display_name":"Filter (signal processing)","score":0.5565999746322632},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.49880000948905945},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.46219998598098755},{"id":"https://openalex.org/keywords/distortion","display_name":"Distortion (music)","score":0.44999998807907104},{"id":"https://openalex.org/keywords/spatial-frequency","display_name":"Spatial frequency","score":0.44190001487731934},{"id":"https://openalex.org/keywords/fourier-transform","display_name":"Fourier transform","score":0.4361000061035156},{"id":"https://openalex.org/keywords/feature","display_name":"Feature (linguistics)","score":0.42899999022483826},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.42800000309944153},{"id":"https://openalex.org/keywords/kernel-adaptive-filter","display_name":"Kernel adaptive filter","score":0.4268999993801117}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5989000201225281},{"id":"https://openalex.org/C74193536","wikidata":"https://www.wikidata.org/wiki/Q574844","display_name":"Kernel (algebra)","level":2,"score":0.5892000198364258},{"id":"https://openalex.org/C106131492","wikidata":"https://www.wikidata.org/wiki/Q3072260","display_name":"Filter (signal processing)","level":2,"score":0.5565999746322632},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.5116000175476074},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.49880000948905945},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4699000120162964},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.46219998598098755},{"id":"https://openalex.org/C126780896","wikidata":"https://www.wikidata.org/wiki/Q899871","display_name":"Distortion (music)","level":4,"score":0.44999998807907104},{"id":"https://openalex.org/C100921725","wikidata":"https://www.wikidata.org/wiki/Q1650811","display_name":"Spatial frequency","level":2,"score":0.44190001487731934},{"id":"https://openalex.org/C102519508","wikidata":"https://www.wikidata.org/wiki/Q6520159","display_name":"Fourier transform","level":2,"score":0.4361000061035156},{"id":"https://openalex.org/C2776401178","wikidata":"https://www.wikidata.org/wiki/Q12050496","display_name":"Feature (linguistics)","level":2,"score":0.42899999022483826},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.42800000309944153},{"id":"https://openalex.org/C13107197","wikidata":"https://www.wikidata.org/wiki/Q6394192","display_name":"Kernel adaptive filter","level":4,"score":0.4268999993801117},{"id":"https://openalex.org/C153180895","wikidata":"https://www.wikidata.org/wiki/Q7148389","display_name":"Pattern recognition (psychology)","level":2,"score":0.42590001225471497},{"id":"https://openalex.org/C2781067378","wikidata":"https://www.wikidata.org/wiki/Q17027399","display_name":"Interpretability","level":2,"score":0.41029998660087585},{"id":"https://openalex.org/C12713177","wikidata":"https://www.wikidata.org/wiki/Q1900281","display_name":"Perspective (graphical)","level":2,"score":0.3977999985218048},{"id":"https://openalex.org/C36464697","wikidata":"https://www.wikidata.org/wiki/Q451553","display_name":"Visualization","level":2,"score":0.39570000767707825},{"id":"https://openalex.org/C102248274","wikidata":"https://www.wikidata.org/wiki/Q168388","display_name":"Adaptive filter","level":2,"score":0.3952000141143799},{"id":"https://openalex.org/C138187205","wikidata":"https://www.wikidata.org/wiki/Q131251","display_name":"Tangent","level":2,"score":0.39169999957084656},{"id":"https://openalex.org/C57733114","wikidata":"https://www.wikidata.org/wiki/Q1006032","display_name":"Discrete Fourier transform (general)","level":5,"score":0.38040000200271606},{"id":"https://openalex.org/C137798554","wikidata":"https://www.wikidata.org/wiki/Q6038852","display_name":"Instantaneous phase","level":3,"score":0.3610000014305115},{"id":"https://openalex.org/C23548689","wikidata":"https://www.wikidata.org/wiki/Q5282049","display_name":"Discrete frequency domain","level":3,"score":0.35359999537467957},{"id":"https://openalex.org/C527412718","wikidata":"https://www.wikidata.org/wiki/Q855395","display_name":"Interpretation (philosophy)","level":2,"score":0.3433000147342682},{"id":"https://openalex.org/C31972630","wikidata":"https://www.wikidata.org/wiki/Q844240","display_name":"Computer vision","level":1,"score":0.32350000739097595},{"id":"https://openalex.org/C19118579","wikidata":"https://www.wikidata.org/wiki/Q786423","display_name":"Frequency domain","level":2,"score":0.32249999046325684},{"id":"https://openalex.org/C142433447","wikidata":"https://www.wikidata.org/wiki/Q7806653","display_name":"Time\u2013frequency analysis","level":3,"score":0.3221000134944916},{"id":"https://openalex.org/C11930861","wikidata":"https://www.wikidata.org/wiki/Q181417","display_name":"Frequency modulation","level":3,"score":0.3212999999523163},{"id":"https://openalex.org/C58489278","wikidata":"https://www.wikidata.org/wiki/Q1172284","display_name":"Data set","level":2,"score":0.31450000405311584},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.31200000643730164},{"id":"https://openalex.org/C157157409","wikidata":"https://www.wikidata.org/wiki/Q909601","display_name":"Tangent space","level":2,"score":0.28850001096725464},{"id":"https://openalex.org/C141379421","wikidata":"https://www.wikidata.org/wiki/Q6094427","display_name":"Iterative reconstruction","level":2,"score":0.2825999855995178},{"id":"https://openalex.org/C121475858","wikidata":"https://www.wikidata.org/wiki/Q2735911","display_name":"Spatial filter","level":2,"score":0.2639999985694885},{"id":"https://openalex.org/C160920958","wikidata":"https://www.wikidata.org/wiki/Q7662746","display_name":"Synthetic data","level":2,"score":0.2567000091075897}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2604.02846","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.02846","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2604.02846","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.02846","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Fourier-encoded":[0,65,192],"implicit":[1],"neural":[2,106],"representations":[3],"(INRs)":[4],"have":[5],"shown":[6],"strong":[7],"capability":[8],"in":[9],"modeling":[10],"continuous":[11],"signals":[12,37],"from":[13,104],"discrete":[14],"samples.":[15],"However,":[16],"conventional":[17],"Fourier":[18,79],"feature":[19],"mappings":[20],"use":[21],"a":[22,71,82,188],"fixed":[23],"set":[24],"of":[25,49,100,116,163,173],"frequencies":[26],"over":[27],"the":[28,98,101,105,120,138,156,171,174],"entire":[29],"spatial":[30,93],"domain,":[31],"making":[32],"them":[33],"poorly":[34],"suited":[35],"to":[36,46,76,147],"with":[38,151],"spatially":[39,72,164],"varying":[40,73,165],"local":[41,60,184],"spectra":[42],"and":[43,88,111,132,145],"often":[44],"leading":[45],"slow":[47],"convergence":[48],"high-frequency":[50],"details.":[51],"To":[52],"address":[53],"this":[54],"issue,":[55],"we":[56],"propose":[57],"an":[58,113,160],"adaptive":[59,183],"frequency":[61,166,185],"filtering":[62],"method":[63,69,140],"for":[64,191],"INRs.":[66,193],"The":[67],"proposed":[68,102,139],"introduces":[70],"parameter":[74],"$\u03b1(\\mathbf{x})$":[75,158],"modulate":[77],"encoded":[78],"components,":[80],"enabling":[81],"smooth":[83],"transition":[84],"among":[85],"low-pass,":[86],"band-pass,":[87],"high-pass":[89],"behaviors":[90],"at":[91],"different":[92],"locations.":[94],"We":[95],"further":[96],"analyze":[97],"effect":[99],"filter":[103],"tangent":[107],"kernel":[108,122],"(NTK)":[109],"perspective":[110],"provide":[112],"NTK-inspired":[114],"interpretation":[115],"how":[117],"it":[118],"reshapes":[119],"effective":[121],"spectrum.":[123],"Experiments":[124],"on":[125,176],"2D":[126],"image":[127],"fitting,":[128],"3D":[129],"shape":[130],"representation,":[131],"sparse":[133],"data":[134],"reconstruction":[135,143],"demonstrate":[136],"that":[137,182],"consistently":[141],"improves":[142],"quality":[144],"leads":[146],"faster":[148],"optimization":[149],"compared":[150],"fixed-frequency":[152],"baselines.":[153],"In":[154],"addition,":[155],"learned":[157],"provides":[159],"intuitive":[161],"visualization":[162],"preferences,":[167],"which":[168],"helps":[169],"explain":[170],"behavior":[172],"model":[175],"non-stationary":[177],"signals.":[178],"These":[179],"results":[180],"indicate":[181],"modulation":[186],"is":[187],"practical":[189],"enhancement":[190]},"counts_by_year":[],"updated_date":"2026-07-01T06:00:48.157686","created_date":"2026-04-07T00:00:00"}