{"id":"https://openalex.org/W7163219432","doi":"https://doi.org/10.48550/arxiv.2606.01244","title":"Efficient Approximation for Encoder--Decoder Neural Operators via Variation Spaces","display_name":"Efficient Approximation for Encoder--Decoder Neural Operators via Variation Spaces","publication_year":2026,"publication_date":"2026-05-31","ids":{"openalex":"https://openalex.org/W7163219432","doi":"https://doi.org/10.48550/arxiv.2606.01244"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2606.01244","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2606.01244","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.2606.01244","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5137653792","display_name":"Jia-Qi Yang","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Yang, Jia-Qi","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5137697953","display_name":"Lei Shi","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Shi, Lei","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/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.4332999885082245,"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/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.4332999885082245,"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":0.20550000667572021,"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/T11206","display_name":"Model Reduction and Neural Networks","score":0.05550000071525574,"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/encoding","display_name":"Encoding (memory)","score":0.6567999720573425},{"id":"https://openalex.org/keywords/lipschitz-continuity","display_name":"Lipschitz continuity","score":0.6550999879837036},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.5878999829292297},{"id":"https://openalex.org/keywords/differentiable-function","display_name":"Differentiable function","score":0.5623000264167786},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.5091999769210815},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.44920000433921814},{"id":"https://openalex.org/keywords/approximation-error","display_name":"Approximation error","score":0.3896999955177307},{"id":"https://openalex.org/keywords/constant","display_name":"Constant (computer programming)","score":0.37880000472068787}],"concepts":[{"id":"https://openalex.org/C125411270","wikidata":"https://www.wikidata.org/wiki/Q18653","display_name":"Encoding (memory)","level":2,"score":0.6567999720573425},{"id":"https://openalex.org/C22324862","wikidata":"https://www.wikidata.org/wiki/Q652707","display_name":"Lipschitz continuity","level":2,"score":0.6550999879837036},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6173999905586243},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.5878999829292297},{"id":"https://openalex.org/C202615002","wikidata":"https://www.wikidata.org/wiki/Q783507","display_name":"Differentiable function","level":2,"score":0.5623000264167786},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.5091999769210815},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.44920000433921814},{"id":"https://openalex.org/C122383733","wikidata":"https://www.wikidata.org/wiki/Q865920","display_name":"Approximation error","level":2,"score":0.3896999955177307},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.37880000472068787},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.3456000089645386},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3400000035762787},{"id":"https://openalex.org/C196697905","wikidata":"https://www.wikidata.org/wiki/Q2042052","display_name":"Input/output","level":2,"score":0.3368000090122223},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.3366999924182892},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.32100000977516174},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.3203999996185303},{"id":"https://openalex.org/C43929395","wikidata":"https://www.wikidata.org/wiki/Q1198874","display_name":"Operator theory","level":2,"score":0.30570000410079956},{"id":"https://openalex.org/C2778334786","wikidata":"https://www.wikidata.org/wiki/Q1586270","display_name":"Variation (astronomy)","level":2,"score":0.3037000000476837},{"id":"https://openalex.org/C145242015","wikidata":"https://www.wikidata.org/wiki/Q774123","display_name":"Approximation theory","level":2,"score":0.30079999566078186},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2937000095844269},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.2815999984741211},{"id":"https://openalex.org/C152306953","wikidata":"https://www.wikidata.org/wiki/Q621744","display_name":"Approximation property","level":3,"score":0.28110000491142273},{"id":"https://openalex.org/C91873725","wikidata":"https://www.wikidata.org/wiki/Q3445816","display_name":"Function approximation","level":3,"score":0.274399995803833},{"id":"https://openalex.org/C65630602","wikidata":"https://www.wikidata.org/wiki/Q2278680","display_name":"Shift operator","level":4,"score":0.2547999918460846},{"id":"https://openalex.org/C77618280","wikidata":"https://www.wikidata.org/wiki/Q1155772","display_name":"Scheme (mathematics)","level":2,"score":0.2547999918460846},{"id":"https://openalex.org/C147168706","wikidata":"https://www.wikidata.org/wiki/Q1457734","display_name":"Recurrent neural network","level":3,"score":0.25189998745918274}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2606.01244","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2606.01244","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.2606.01244","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2606.01244","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":[],"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],"study":[1],"operator":[2,124,132],"learning":[3,113,125],"using":[4],"encoder--decoder":[5,53],"neural":[6,14,123],"networks.":[7],"Inspired":[8],"by":[9],"the":[10,38,57,67,71,88,95,104],"function-space":[11],"theory":[12],"of":[13,80,87],"networks,":[15],"we":[16,48],"introduce":[17],"a":[18,76,84],"variation":[19],"space":[20,30],"as":[21],"an":[22,118],"infinite-dimensional":[23],"structural":[24],"class":[25],"for":[26,52,121],"nonlinear":[27],"operators.":[28],"This":[29],"is":[31],"defined":[32],"through":[33],"vector-valued":[34],"measures":[35],"directly":[36],"on":[37],"input":[39,68,89,96],"and":[40,75,90,97,112],"output":[41,72,91,98],"spaces.":[42],"For":[43],"operators":[44],"in":[45,56,103],"this":[46],"space,":[47],"establish":[49],"approximation":[50,78,111],"bounds":[51],"two-layer":[54],"networks":[55],"Bochner":[58],"$L^q$":[59],"norm.":[60],"The":[61,115],"resulting":[62],"error":[63],"bound":[64],"decomposes":[65],"into":[66],"encoding":[69,73,92,99,105],"error,":[70,74],"finite-width":[77],"term":[79],"order":[81],"$N^{-1/2}$,":[82],"with":[83],"constant":[85],"independent":[86],"dimensions.":[93],"When":[94],"errors":[100],"decay":[101],"polynomially":[102],"dimensions,":[106],"these":[107],"estimates":[108],"yield":[109],"algebraic":[110],"rates.":[114],"results":[116],"provide":[117],"theoretical":[119],"guarantees":[120],"efficient":[122],"beyond":[126],"general":[127],"Lipschitz":[128],"or":[129],"Fr\u00e9chet":[130],"differentiable":[131],"classes.":[133]},"counts_by_year":[],"updated_date":"2026-07-01T06:00:48.157686","created_date":"2026-06-03T00:00:00"}