{"id":"https://openalex.org/W7140114905","doi":"https://doi.org/10.48550/arxiv.2603.19847","title":"Transformer Causality Regularization for Dynamic Inverse Problems","display_name":"Transformer Causality Regularization for Dynamic Inverse Problems","publication_year":2026,"publication_date":"2026-03-20","ids":{"openalex":"https://openalex.org/W7140114905","doi":"https://doi.org/10.48550/arxiv.2603.19847"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2603.19847","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.19847","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":"article"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2603.19847","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5130377708","display_name":"Gesa Sarnighausen","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Sarnighausen, Gesa","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5024356887","display_name":"Anne Wald","orcid":"https://orcid.org/0000-0001-6149-8576"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Wald, Anne","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5052463438","display_name":"Andreas Hauptmann","orcid":"https://orcid.org/0000-0002-3756-8121"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Hauptmann, Andreas","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5130377708"],"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/T10775","display_name":"Generative Adversarial Networks and Image Synthesis","score":0.1404999941587448,"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"}},"topics":[{"id":"https://openalex.org/T10775","display_name":"Generative Adversarial Networks and Image Synthesis","score":0.1404999941587448,"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/T10241","display_name":"Functional Brain Connectivity Studies","score":0.10050000250339508,"subfield":{"id":"https://openalex.org/subfields/2805","display_name":"Cognitive Neuroscience"},"field":{"id":"https://openalex.org/fields/28","display_name":"Neuroscience"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},{"id":"https://openalex.org/T12814","display_name":"Gaussian Processes and Bayesian Inference","score":0.07569999992847443,"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/regularization","display_name":"Regularization (linguistics)","score":0.5573999881744385},{"id":"https://openalex.org/keywords/transformer","display_name":"Transformer","score":0.5437999963760376},{"id":"https://openalex.org/keywords/inverse-problem","display_name":"Inverse problem","score":0.4478999972343445},{"id":"https://openalex.org/keywords/causality","display_name":"Causality (physics)","score":0.35089999437332153},{"id":"https://openalex.org/keywords/inverse","display_name":"Inverse","score":0.34299999475479126},{"id":"https://openalex.org/keywords/grid","display_name":"Grid","score":0.31450000405311584},{"id":"https://openalex.org/keywords/regularization-perspectives-on-support-vector-machines","display_name":"Regularization perspectives on support vector machines","score":0.28110000491142273}],"concepts":[{"id":"https://openalex.org/C2776135515","wikidata":"https://www.wikidata.org/wiki/Q17143721","display_name":"Regularization (linguistics)","level":2,"score":0.5573999881744385},{"id":"https://openalex.org/C66322947","wikidata":"https://www.wikidata.org/wiki/Q11658","display_name":"Transformer","level":3,"score":0.5437999963760376},{"id":"https://openalex.org/C135252773","wikidata":"https://www.wikidata.org/wiki/Q1567213","display_name":"Inverse problem","level":2,"score":0.4478999972343445},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.44369998574256897},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4388999938964844},{"id":"https://openalex.org/C64357122","wikidata":"https://www.wikidata.org/wiki/Q1149766","display_name":"Causality (physics)","level":2,"score":0.35089999437332153},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.34299999475479126},{"id":"https://openalex.org/C187691185","wikidata":"https://www.wikidata.org/wiki/Q2020720","display_name":"Grid","level":2,"score":0.31450000405311584},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.31279999017715454},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.30720001459121704},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.2921000123023987},{"id":"https://openalex.org/C141718189","wikidata":"https://www.wikidata.org/wiki/Q7309628","display_name":"Regularization perspectives on support vector machines","level":4,"score":0.28110000491142273},{"id":"https://openalex.org/C2780695315","wikidata":"https://www.wikidata.org/wiki/Q3799040","display_name":"Unobservable","level":2,"score":0.2750999927520752},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.27309998869895935},{"id":"https://openalex.org/C197352929","wikidata":"https://www.wikidata.org/wiki/Q1074074","display_name":"Inductive bias","level":4,"score":0.2728999853134155},{"id":"https://openalex.org/C129537906","wikidata":"https://www.wikidata.org/wiki/Q7603913","display_name":"State variable","level":2,"score":0.26579999923706055},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.26249998807907104},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.2621000111103058}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2603.19847","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.19847","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":"article"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2603.19847","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.19847","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":"article"},"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":[0,113],"study":[1],"the":[2,6,12,70,87,97,106,117,130,136,165,181],"concept":[3],"of":[4,14,62,99,120,135,167,180],"including":[5],"causality":[7,36,40,93],"principle":[8,41],"as":[9,142],"regularizer":[10,186],"into":[11],"solution":[13,157],"linear":[15],"time-dependent":[16],"inverse":[17],"problems.":[18],"This":[19],"is":[20,60,139],"achieved":[21],"by":[22],"combining":[23],"transformer-based":[24],"predictions":[25],"with":[26,80,116],"classical":[27,150],"variational":[28,146,200],"regularization,":[29,147],"resulting":[30],"in":[31],"what":[32],"we":[33,171],"call":[34],"transformer":[35,71,138],"regularization":[37,153],"(TCR).":[38],"The":[39,133,192],"states":[42,54,64,108],"that":[43,95,149,195],"an":[44,100],"object":[45,101],"at":[46,55,65,102,109],"time":[47,103],"$t'$":[48,104],"depends":[49],"only":[50],"on":[51,152],"its":[52],"previous":[53,107],"$t":[56,66,110],"&lt;":[57,111],"t'$":[58],"and":[59,76,154,177,189,205],"independent":[61],"future":[63],"&gt;":[67],"t'$.":[68,112],"Since":[69],"architecture":[72],"represents":[73],"sequence-to-sequence":[74],"functions":[75],"can":[77],"be":[78],"equipped":[79],"a":[81,91,143,175,199],"causal":[82],"attention":[83],"mask,":[84],"transformers":[85],"are":[86],"natural":[88],"choice":[89],"for":[90,125,145,156,187],"learned":[92],"function":[94],"predicts":[96],"state":[98],"given":[105],"combine":[114],"this":[115],"inductive":[118],"bias":[119],"convolutional":[121],"neural":[122],"networks":[123],"(CNNs)":[124],"imaging":[126],"tasks":[127],"to":[128,161,174],"treat":[129],"spatial":[131],"variable.":[132],"output":[134],"spatial-temporal":[137],"then":[140],"used":[141],"prior":[144],"such":[148],"results":[151,193,204],"convergence":[155],"methods":[158],"directly":[159],"transfer":[160],"our":[162],"case.":[163],"Using":[164],"example":[166],"dynamic":[168,178],"computerized":[169],"tomography,":[170],"compare":[172],"TCR":[173,197],"static":[176],"version":[179],"earlier":[182],"introduced":[183],"unrolled":[184],"adversarial":[185],"simulated":[188],"measured":[190],"data.":[191],"show":[194],"using":[196],"within":[198],"framework":[201],"improves":[202],"reconstruction":[203],"data-consistency.":[206]},"counts_by_year":[],"updated_date":"2026-03-24T06:04:31.470712","created_date":"2026-03-24T00:00:00"}
