{"id":"https://openalex.org/W2979863392","doi":null,"title":"Inferring Dynamical Systems with Long-Range Dependencies through Line Attractor Regularization.","display_name":"Inferring Dynamical Systems with Long-Range Dependencies through Line Attractor Regularization.","publication_year":2019,"publication_date":"2019-09-25","ids":{"openalex":"https://openalex.org/W2979863392","mag":"2979863392"},"language":"en","primary_location":{"id":"mag:2979863392","doi":null,"is_oa":true,"landing_page_url":"http://export.arxiv.org/pdf/1910.03471","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":[],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"http://export.arxiv.org/pdf/1910.03471","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Dominik Schmidt","orcid":"https://orcid.org/0000-0001-8208-6087","observed_orcids":["https://orcid.org/0000-0001-8208-6087"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Dominik Schmidt","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0001-8208-6087","affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5012894482","display_name":"Georgia Koppe","orcid":"https://orcid.org/0000-0003-2941-9238","observed_orcids":["https://orcid.org/0000-0003-2941-9238"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Georgia Koppe","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0003-2941-9238","affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5032433296","display_name":"Max Beutelspacher","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Max Beutelspacher","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5056788018","display_name":"Daniel Durstewitz","orcid":"https://orcid.org/0000-0002-9340-3786","observed_orcids":["https://orcid.org/0000-0002-9340-3786"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Daniel Durstewitz","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0002-9340-3786","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":6,"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/T10320","display_name":"Neural Networks and Applications","score":0.926800012588501,"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/T10320","display_name":"Neural Networks and Applications","score":0.926800012588501,"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/T12611","display_name":"Neural Networks and Reservoir Computing","score":0.011900000274181366,"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":0.007899999618530273,"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/recurrent-neural-networks","display_name":"recurrent neural networks","score":0.875},{"id":"https://openalex.org/keywords/long-term-dependencies","display_name":"long-range dependencies","score":0.8610000014305115},{"id":"https://openalex.org/keywords/relu","display_name":"ReLU","score":0.5080000162124634},{"id":"https://openalex.org/keywords/long-short-term-memory","display_name":"long short-term memory","score":0.7710000276565552},{"id":"https://openalex.org/keywords/slow-time-scale","display_name":"slow time scale","score":0.8159999847412109},{"id":"https://openalex.org/keywords/chaos","display_name":"chaos","score":0.8569999933242798},{"id":"https://openalex.org/keywords/multistability","display_name":"multistability","score":0.875},{"id":"https://openalex.org/keywords/latent-subspace","display_name":"latent subspace","score":0.5740000009536743},{"id":"https://openalex.org/keywords/multiplication","display_name":"multiplication","score":0.31200000643730164}],"concepts":[{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.7307267189025879},{"id":"https://openalex.org/C164380108","wikidata":"https://www.wikidata.org/wiki/Q507187","display_name":"Attractor","level":2,"score":0.6917723417282104},{"id":"https://openalex.org/C190502265","wikidata":"https://www.wikidata.org/wiki/Q17069496","display_name":"MNIST database","level":3,"score":0.6164820194244385},{"id":"https://openalex.org/C2776135515","wikidata":"https://www.wikidata.org/wiki/Q17143721","display_name":"Regularization (linguistics)","level":2,"score":0.5863664746284485},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5630922317504883},{"id":"https://openalex.org/C114466953","wikidata":"https://www.wikidata.org/wiki/Q6034165","display_name":"Initialization","level":2,"score":0.5555896759033203},{"id":"https://openalex.org/C32834561","wikidata":"https://www.wikidata.org/wiki/Q660730","display_name":"Subspace topology","level":2,"score":0.5049503445625305},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.45014622807502747},{"id":"https://openalex.org/C33962884","wikidata":"https://www.wikidata.org/wiki/Q378637","display_name":"Dynamical system (definition)","level":3,"score":0.4250989258289337},{"id":"https://openalex.org/C17137986","wikidata":"https://www.wikidata.org/wiki/Q215067","display_name":"Orthogonality","level":2,"score":0.41412559151649475},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3678216338157654},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.3339334726333618},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.32119274139404297},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.30614322423934937},{"id":"https://openalex.org/C108583219","wikidata":"https://www.wikidata.org/wiki/Q197536","display_name":"Deep learning","level":2,"score":0.19396820664405823},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.14190930128097534},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.12295177578926086},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"mag:2979863392","doi":null,"is_oa":true,"landing_page_url":"http://export.arxiv.org/pdf/1910.03471","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null}],"best_oa_location":{"id":"mag:2979863392","doi":null,"is_oa":true,"landing_page_url":"http://export.arxiv.org/pdf/1910.03471","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":51,"referenced_works":["https://openalex.org/W592244745","https://openalex.org/W1498436455","https://openalex.org/W1966841546","https://openalex.org/W1980324747","https://openalex.org/W2004021828","https://openalex.org/W2016589492","https://openalex.org/W2032535902","https://openalex.org/W2033178790","https://openalex.org/W2046278043","https://openalex.org/W2050076818","https://openalex.org/W2052296894","https://openalex.org/W2054100637","https://openalex.org/W2058580716","https://openalex.org/W2060958440","https://openalex.org/W2067619114","https://openalex.org/W2068665590","https://openalex.org/W2072139234","https://openalex.org/W2092124742","https://openalex.org/W2132904166","https://openalex.org/W2143503258","https://openalex.org/W2147269409","https://openalex.org/W2156168178","https://openalex.org/W2157331557","https://openalex.org/W2157518752","https://openalex.org/W2175402905","https://openalex.org/W2239232218","https://openalex.org/W2243249356","https://openalex.org/W2278773995","https://openalex.org/W2280725856","https://openalex.org/W2474920236","https://openalex.org/W2495782740","https://openalex.org/W2509445763","https://openalex.org/W2561857267","https://openalex.org/W2584388207","https://openalex.org/W2605288757","https://openalex.org/W2618767566","https://openalex.org/W2626194254","https://openalex.org/W2740137140","https://openalex.org/W2754341698","https://openalex.org/W2785024182","https://openalex.org/W2798649148","https://openalex.org/W2899771611","https://openalex.org/W2945174756","https://openalex.org/W2962727772","https://openalex.org/W2963279312","https://openalex.org/W2968695582","https://openalex.org/W2969708557","https://openalex.org/W2970053421","https://openalex.org/W3034577438","https://openalex.org/W3105919389","https://openalex.org/W3124661333"],"related_works":["https://openalex.org/W3132271517","https://openalex.org/W7133220912","https://openalex.org/W4409281647","https://openalex.org/W6884980550","https://openalex.org/W631352912","https://openalex.org/W4284899738","https://openalex.org/W1980324747","https://openalex.org/W4415798100","https://openalex.org/W7038800016","https://openalex.org/W4309795870"],"abstract_inverted_index":{"Vanilla":[0],"RNN":[1],"with":[2,57,63],"ReLU":[3],"activation":[4],"have":[5],"a":[6,77,89,110],"simple":[7],"structure":[8],"that":[9,80,93,105],"lends":[10],"itself":[11],"to":[12,31,59,65],"systematic":[13],"dynamical":[14,66,125],"systems":[15,67,126],"analysis":[16],"and":[17,98,121],"interpretation,":[18],"but":[19],"they":[20],"suffer":[21],"from":[22],"the":[23,37,50,84,115],"exploding":[24],"vs.":[25],"vanishing":[26],"gradients":[27],"problem.":[28],"Recent":[29],"attempts":[30],"retain":[32],"this":[33],"simplicity":[34],"while":[35],"alleviating":[36],"gradient":[38],"problem":[39],"are":[40],"based":[41],"on":[42,49,109],"proper":[43],"initialization":[44],"schemes":[45],"or":[46,71,118],"orthogonality/unitary":[47],"constraints":[48],"RNN's":[51,85],"recurrence":[52],"matrix,":[53],"which,":[54],"however,":[55],"comes":[56],"limitations":[58],"its":[60],"expressive":[61],"power":[62],"regards":[64],"phenomena":[68],"like":[69,114],"chaos":[70],"multi-stability.":[72],"Here,":[73],"we":[74],"instead":[75],"suggest":[76],"regularization":[78],"scheme":[79],"pushes":[81],"part":[82],"of":[83,112,124],"latent":[86],"subspace":[87],"toward":[88],"line":[90],"attractor":[91],"configuration":[92],"enables":[94,122],"long":[95],"short-term":[96],"memory":[97],"arbitrarily":[99],"slow":[100],"time":[101,131],"scales.":[102,132],"We":[103],"show":[104],"our":[106],"approach":[107],"excels":[108],"number":[111],"benchmarks":[113],"sequential":[116],"MNIST":[117],"multiplication":[119],"problems,":[120],"reconstruction":[123],"which":[127],"harbor":[128],"widely":[129],"different":[130]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":3}],"updated_date":"2026-11-03T10:50:19.383937","created_date":"2019-10-18T00:00:00"}