{"id":"https://openalex.org/W7139947243","doi":"https://doi.org/10.48550/arxiv.2603.19198","title":"The Exponentially Weighted Signature","display_name":"The Exponentially Weighted Signature","publication_year":2026,"publication_date":"2026-03-19","ids":{"openalex":"https://openalex.org/W7139947243","doi":"https://doi.org/10.48550/arxiv.2603.19198"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2603.19198","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.19198","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.2603.19198","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5032455164","display_name":"Alexandre Bloch","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Bloch, Alexandre","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5060270542","display_name":"Samuel N. Cohen","orcid":"https://orcid.org/0000-0003-0539-6414"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Cohen, Samuel N.","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5130225054","display_name":"Terry Lyons","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Lyons, Terry","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5093855344","display_name":"Joel Mouterde","orcid":"https://orcid.org/0009-0005-0955-7440"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Mouterde, Jo\u00ebl","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5130236344","display_name":"Benjamin Walker","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Walker, Benjamin","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":5,"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/T10775","display_name":"Generative Adversarial Networks and Image Synthesis","score":0.20759999752044678,"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":0.20759999752044678,"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/T10028","display_name":"Topic Modeling","score":0.09430000185966492,"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/T12808","display_name":"Ferroelectric and Negative Capacitance Devices","score":0.08150000125169754,"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/signature","display_name":"Signature (topology)","score":0.6032999753952026},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.5112000107765198},{"id":"https://openalex.org/keywords/representation","display_name":"Representation (politics)","score":0.388700008392334},{"id":"https://openalex.org/keywords/interpretability","display_name":"Interpretability","score":0.3880000114440918},{"id":"https://openalex.org/keywords/tensor","display_name":"Tensor (intrinsic definition)","score":0.387800008058548},{"id":"https://openalex.org/keywords/diagonal","display_name":"Diagonal","score":0.38769999146461487},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.37299999594688416},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.3716999888420105},{"id":"https://openalex.org/keywords/weighting","display_name":"Weighting","score":0.36239999532699585},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.33489999175071716}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6854000091552734},{"id":"https://openalex.org/C2779696439","wikidata":"https://www.wikidata.org/wiki/Q7512811","display_name":"Signature (topology)","level":2,"score":0.6032999753952026},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.5112000107765198},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.388700008392334},{"id":"https://openalex.org/C2781067378","wikidata":"https://www.wikidata.org/wiki/Q17027399","display_name":"Interpretability","level":2,"score":0.3880000114440918},{"id":"https://openalex.org/C155281189","wikidata":"https://www.wikidata.org/wiki/Q3518150","display_name":"Tensor (intrinsic definition)","level":2,"score":0.387800008058548},{"id":"https://openalex.org/C130367717","wikidata":"https://www.wikidata.org/wiki/Q189791","display_name":"Diagonal","level":2,"score":0.38769999146461487},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.37299999594688416},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.3716999888420105},{"id":"https://openalex.org/C183115368","wikidata":"https://www.wikidata.org/wiki/Q856577","display_name":"Weighting","level":2,"score":0.36239999532699585},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.35679998993873596},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.34869998693466187},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.33489999175071716},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.33149999380111694},{"id":"https://openalex.org/C75235859","wikidata":"https://www.wikidata.org/wiki/Q582659","display_name":"Exponential growth","level":2,"score":0.321399986743927},{"id":"https://openalex.org/C2777735758","wikidata":"https://www.wikidata.org/wiki/Q817765","display_name":"Path (computing)","level":2,"score":0.321399986743927},{"id":"https://openalex.org/C207405024","wikidata":"https://www.wikidata.org/wiki/Q207348","display_name":"Semigroup","level":2,"score":0.3160000145435333},{"id":"https://openalex.org/C165700671","wikidata":"https://www.wikidata.org/wiki/Q203484","display_name":"Laplace operator","level":2,"score":0.3149000108242035},{"id":"https://openalex.org/C2776029896","wikidata":"https://www.wikidata.org/wiki/Q3935810","display_name":"Relaxation (psychology)","level":2,"score":0.3133000135421753},{"id":"https://openalex.org/C2776401178","wikidata":"https://www.wikidata.org/wiki/Q12050496","display_name":"Feature (linguistics)","level":2,"score":0.30660000443458557},{"id":"https://openalex.org/C97937538","wikidata":"https://www.wikidata.org/wiki/Q199691","display_name":"Laplace transform","level":2,"score":0.30059999227523804},{"id":"https://openalex.org/C42747912","wikidata":"https://www.wikidata.org/wiki/Q1048447","display_name":"Multiplicative function","level":2,"score":0.2939000129699707},{"id":"https://openalex.org/C28855332","wikidata":"https://www.wikidata.org/wiki/Q198099","display_name":"Quantization (signal processing)","level":2,"score":0.2903999984264374},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.29019999504089355},{"id":"https://openalex.org/C149364088","wikidata":"https://www.wikidata.org/wiki/Q185917","display_name":"Translation (biology)","level":4,"score":0.2815999984741211},{"id":"https://openalex.org/C55439883","wikidata":"https://www.wikidata.org/wiki/Q360812","display_name":"Correctness","level":2,"score":0.2775000035762787},{"id":"https://openalex.org/C77246614","wikidata":"https://www.wikidata.org/wiki/Q1409400","display_name":"Gramian matrix","level":3,"score":0.2743000090122223},{"id":"https://openalex.org/C158154518","wikidata":"https://www.wikidata.org/wiki/Q7310970","display_name":"Relevance (law)","level":2,"score":0.26809999346733093},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.26190000772476196},{"id":"https://openalex.org/C81539297","wikidata":"https://www.wikidata.org/wiki/Q33456","display_name":"Exponentiation","level":2,"score":0.25850000977516174},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2565000057220459},{"id":"https://openalex.org/C2780791683","wikidata":"https://www.wikidata.org/wiki/Q846785","display_name":"Action (physics)","level":2,"score":0.2515000104904175},{"id":"https://openalex.org/C179117685","wikidata":"https://www.wikidata.org/wiki/Q328998","display_name":"Complex plane","level":2,"score":0.25040000677108765}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2603.19198","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.19198","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.2603.19198","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.19198","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":{"The":[0,121],"signature":[1,47,166],"is":[2,91],"a":[3,7,96],"canonical":[4],"representation":[5],"of":[6,28,63,82,118,124],"multidimensional":[8],"path":[9],"over":[10],"an":[11],"interval.":[12],"However,":[13],"it":[14,107],"treats":[15],"all":[16],"historical":[17],"information":[18],"uniformly,":[19],"offering":[20],"no":[21],"intrinsic":[22],"mechanism":[23],"for":[24],"contextualising":[25],"the":[26,29,36,42,61,79,83,89,92,102,113,119,125,132,139,157,161,165],"relevance":[27],"past.":[30],"To":[31],"address":[32],"this,":[33],"we":[34],"introduce":[35],"Exponentially":[37,43],"Weighted":[38],"Signature":[39],"(EWS),":[40],"generalising":[41],"Fading":[44],"Memory":[45],"(EFM)":[46],"from":[48],"diagonal":[49],"to":[50,95,135,154],"general":[51],"bounded":[52],"linear":[53,97],"operators.":[54],"These":[55],"operators":[56],"enable":[57],"cross-channel":[58],"coupling":[59],"at":[60],"level":[62],"temporal":[64],"weighting":[65],"together":[66],"with":[67,138],"richer":[68],"memory":[69],"dynamics":[70],"including":[71],"oscillatory,":[72],"growth,":[73],"and":[74,105,112,115,130,145,163,167],"regime-dependent":[75],"behaviour,":[76],"while":[77],"preserving":[78],"algebraic":[80],"strengths":[81],"classical":[84],"signature.":[85],"We":[86,150],"show":[87],"that":[88,106],"EWS":[90,126,162],"unique":[93],"solution":[94],"controlled":[98],"differential":[99],"equation":[100],"on":[101,169],"tensor":[103],"algebra,":[104],"generalises":[108],"both":[109,164],"state-space":[110],"models":[111],"Laplace":[114],"Fourier":[116],"transforms":[117],"path.":[120],"group-like":[122],"structure":[123],"enables":[127],"efficient":[128],"computation":[129],"makes":[131],"framework":[133,153],"amenable":[134],"gradient-based":[136],"learning,":[137],"full":[140],"semigroup":[141],"action":[142],"parametrised":[143],"by":[144],"learned":[146],"through":[147],"its":[148],"generator.":[149],"use":[151],"this":[152],"empirically":[155],"demonstrate":[156],"expressivity":[158],"gap":[159],"between":[160],"EFM":[168],"two":[170],"SDE-based":[171],"regression":[172],"tasks.":[173]},"counts_by_year":[],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2026-03-21T00:00:00"}