{"id":"https://openalex.org/W7163353681","doi":"https://doi.org/10.48550/arxiv.2606.03227","title":"Learning Temporal Causal Structure via Smooth Differentiable Optimization","display_name":"Learning Temporal Causal Structure via Smooth Differentiable Optimization","publication_year":2026,"publication_date":"2026-06-02","ids":{"openalex":"https://openalex.org/W7163353681","doi":"https://doi.org/10.48550/arxiv.2606.03227"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2606.03227","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2606.03227","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.2606.03227","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5137797038","display_name":"Tong Zhao","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Zhao, Tong","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5137794628","display_name":"Ce Guo","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Guo, Ce","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5043749887","display_name":"Wayne Luk","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Luk, Wayne","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5123894148","display_name":"Emil Lupu","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Lupu, Emil","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5137714863","display_name":"Ray Dipojjwal","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Dipojjwal, Ray","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/T11303","display_name":"Bayesian Modeling and Causal Inference","score":0.7361999750137329,"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/T11303","display_name":"Bayesian Modeling and Causal Inference","score":0.7361999750137329,"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/T13702","display_name":"Machine Learning in Healthcare","score":0.08399999886751175,"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/T12205","display_name":"Time Series Analysis and Forecasting","score":0.024900000542402267,"subfield":{"id":"https://openalex.org/subfields/1711","display_name":"Signal Processing"},"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/differentiable-function","display_name":"Differentiable function","score":0.59579998254776},{"id":"https://openalex.org/keywords/augmented-lagrangian-method","display_name":"Augmented Lagrangian method","score":0.5559999942779541},{"id":"https://openalex.org/keywords/constraint","display_name":"Constraint (computer-aided design)","score":0.534600019454956},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.5335000157356262},{"id":"https://openalex.org/keywords/autoregressive-model","display_name":"Autoregressive model","score":0.4652000069618225},{"id":"https://openalex.org/keywords/speedup","display_name":"Speedup","score":0.44369998574256897},{"id":"https://openalex.org/keywords/series","display_name":"Series (stratigraphy)","score":0.3783000111579895},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.35359999537467957},{"id":"https://openalex.org/keywords/permutation","display_name":"Permutation (music)","score":0.3409000039100647}],"concepts":[{"id":"https://openalex.org/C202615002","wikidata":"https://www.wikidata.org/wiki/Q783507","display_name":"Differentiable function","level":2,"score":0.59579998254776},{"id":"https://openalex.org/C150452318","wikidata":"https://www.wikidata.org/wiki/Q4820432","display_name":"Augmented Lagrangian method","level":2,"score":0.5559999942779541},{"id":"https://openalex.org/C2776036281","wikidata":"https://www.wikidata.org/wiki/Q48769818","display_name":"Constraint (computer-aided design)","level":2,"score":0.534600019454956},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.5335000157356262},{"id":"https://openalex.org/C159877910","wikidata":"https://www.wikidata.org/wiki/Q2202883","display_name":"Autoregressive model","level":2,"score":0.4652000069618225},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.460999995470047},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.44670000672340393},{"id":"https://openalex.org/C68339613","wikidata":"https://www.wikidata.org/wiki/Q1549489","display_name":"Speedup","level":2,"score":0.44369998574256897},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4388999938964844},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.43860000371932983},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.40059998631477356},{"id":"https://openalex.org/C143724316","wikidata":"https://www.wikidata.org/wiki/Q312468","display_name":"Series (stratigraphy)","level":2,"score":0.3783000111579895},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.35359999537467957},{"id":"https://openalex.org/C21308566","wikidata":"https://www.wikidata.org/wiki/Q7169365","display_name":"Permutation (music)","level":2,"score":0.3409000039100647},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.3400999903678894},{"id":"https://openalex.org/C151406439","wikidata":"https://www.wikidata.org/wiki/Q186588","display_name":"Time series","level":2,"score":0.33550000190734863},{"id":"https://openalex.org/C161584116","wikidata":"https://www.wikidata.org/wiki/Q1952580","display_name":"Multivariate statistics","level":2,"score":0.3296000063419342},{"id":"https://openalex.org/C163504300","wikidata":"https://www.wikidata.org/wiki/Q2364925","display_name":"Causal structure","level":2,"score":0.3100000023841858},{"id":"https://openalex.org/C57493831","wikidata":"https://www.wikidata.org/wiki/Q3134666","display_name":"Projection (relational algebra)","level":2,"score":0.30480000376701355},{"id":"https://openalex.org/C137798554","wikidata":"https://www.wikidata.org/wiki/Q6038852","display_name":"Instantaneous phase","level":3,"score":0.3041999936103821},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.2897000014781952},{"id":"https://openalex.org/C55660270","wikidata":"https://www.wikidata.org/wiki/Q5164377","display_name":"Constrained optimization","level":2,"score":0.2874000072479248},{"id":"https://openalex.org/C43521106","wikidata":"https://www.wikidata.org/wiki/Q2165493","display_name":"Pipeline (software)","level":2,"score":0.27000001072883606},{"id":"https://openalex.org/C147764199","wikidata":"https://www.wikidata.org/wiki/Q6865248","display_name":"Minification","level":2,"score":0.2603999972343445},{"id":"https://openalex.org/C133029050","wikidata":"https://www.wikidata.org/wiki/Q385593","display_name":"Vector autoregression","level":2,"score":0.25920000672340393},{"id":"https://openalex.org/C168167062","wikidata":"https://www.wikidata.org/wiki/Q1117970","display_name":"Component (thermodynamics)","level":2,"score":0.2542000114917755},{"id":"https://openalex.org/C64357122","wikidata":"https://www.wikidata.org/wiki/Q1149766","display_name":"Causality (physics)","level":2,"score":0.2513999938964844}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2606.03227","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2606.03227","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.2606.03227","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2606.03227","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":{"Causal":[0],"discovery":[1,138],"with":[2,110,133],"instantaneous":[3,13,25,71],"effects":[4],"in":[5,81,117,136],"multivariate":[6],"time":[7],"series":[8],"is":[9],"challenging,":[10],"as":[11],"the":[12,65,70,82,128,143],"structure":[14],"must":[15],"be":[16],"acyclic.":[17],"Prior":[18],"methods":[19],"enforce":[20],"this":[21,50],"by":[22],"either":[23],"separating":[24],"and":[26,68,95,140],"lagged":[27],"estimation":[28],"into":[29,92],"multi-stage":[30],"pipelines":[31],"or":[32],"imposing":[33],"algebraic":[34],"acyclicity":[35,87],"constraints":[36],"via":[37],"complex":[38],"augmented":[39],"Lagrangian":[40],"optimization,":[41],"both":[42,137],"of":[43,62,74],"which":[44],"incur":[45],"high":[46],"computational":[47],"cost.":[48],"In":[49,101],"work,":[51],"we":[52,57],"propose":[53],"a":[54,59,75,89,93,154],"different":[55],"approach:":[56],"learn":[58],"differentiable":[60],"permutation":[61],"variables":[63],"using":[64],"Gumbel--Sinkhorn":[66],"operator":[67],"triangularize":[69],"coefficient":[72],"matrix":[73],"Structural":[76],"Vector":[77],"Autoregressive":[78],"(SVAR)":[79],"model":[80],"learned":[83],"order.":[84],"This":[85],"converts":[86],"from":[88],"hard":[90],"constraint":[91],"parameterization":[94],"keeps":[96],"it":[97,146],"valid":[98],"throughout":[99],"optimization.":[100],"doing":[102],"so,":[103],"our":[104,125],"method":[105,126],"enables":[106],"unified,":[107],"continuous":[108],"optimization":[109],"gradient-based":[111],"learning,":[112],"leading":[113],"to":[114],"improved":[115],"efficiency":[116],"time--series":[118],"causal":[119],"discovery.":[120],"Across":[121],"three":[122],"real-world":[123],"benchmarks,":[124],"achieves":[127],"best":[129],"overall":[130],"performance":[131],"compared":[132],"12":[134],"baselines":[135],"accuracy":[139],"efficiency.":[141],"On":[142],"large-scale":[144],"benchmark,":[145],"further":[147],"demonstrates":[148],"strong":[149],"scalability,":[150],"achieving":[151],"more":[152],"than":[153],"6x":[155],"speedup":[156],"over":[157],"competing":[158],"methods.":[159]},"counts_by_year":[],"updated_date":"2026-07-01T06:00:48.157686","created_date":"2026-06-04T00:00:00"}