Impact of Time-History Terms on Reservoir Dynamics and Prediction Accuracy in Echo State Networks

Impact of Time-History Terms on Reservoir Dynamics and Prediction Accuracy in Echo State Networks | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Article Impact of Time-History Terms on Reservoir Dynamics and Prediction Accuracy in Echo State Networks Yudai Ebato, Sou Nobukawa, Yusuke Sakemi, Haruhiko Nishimura, and 3 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-3834443/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 15 Apr, 2024 Read the published version in Scientific Reports → Version 1 posted 11 You are reading this latest preprint version Abstract The echo state network (ESN) is an excellent machine learning model for processing time series data. This model, utilizing the response of a recurrent neural network called a reservoir to input signals, achieves high training efficiency. Introducing time-history terms into the neuron model of the reservoir is known to improve the time series prediction performance of ESN, yet the reasons for this improvement have not been quantitatively explained in terms of reservoir dynamics characteristics. Therefore, we hypothesized that the performance enhancement brought about by time-history terms could be explained by delay capacity, a recently proposed metric for assessing the memory performance of reservoirs. To test this hypothesis, we conducted comparative experiments using ESN models with time-history terms, namely Leaky-Integrator ESNs (LI-ESN) and chaotic echo state networks (ChESN). The results suggest that, compared to ESNs without time-history terms, the reservoir dynamics of LI-ESN and ChESN can maintain diversity and stability while possessing higher delay capacity, leading to their superior performance. Explaining ESN performance through dynamical metrics are crucial for evaluating the numerous ESN architectures recently proposed from a general perspective and for the development of more sophisticated architectures, and this study contributes to such efforts. Physical sciences/Mathematics and computing/Applied mathematics Physical sciences/Physics/Statistical physics thermodynamics and nonlinear dynamics/Nonlinear phenomena Biological sciences/Neuroscience/Computational neuroscience/Dynamical systems Leaky-Integrator ESN echo state network reservoir computing time-series prediction time-history terms Full Text Additional Declarations No competing interests reported. Supplementary Files ebatosupplemental20231216.pdf Cite Share Download PDF Status: Published Journal Publication published 15 Apr, 2024 Read the published version in Scientific Reports → Version 1 posted Editorial decision: Revision requested 25 Feb, 2024 Reviews received at journal 23 Feb, 2024 Reviewers agreed at journal 16 Feb, 2024 Reviews received at journal 27 Jan, 2024 Reviewers agreed at journal 17 Jan, 2024 Reviewers agreed at journal 17 Jan, 2024 Reviewers invited by journal 17 Jan, 2024 Editor assigned by journal 17 Jan, 2024 Editor invited by journal 06 Jan, 2024 Submission checks completed at journal 06 Jan, 2024 First submitted to journal 04 Jan, 2024 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-3834443","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":265728465,"identity":"93545e84-ccd6-42e0-8e08-7085a62fc4e1","order_by":0,"name":"Yudai 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This model, utilizing the response of a recurrent neural network called a reservoir to input signals, achieves high training efficiency. Introducing time-history terms into the neuron model of the reservoir is known to improve the time series prediction performance of ESN, yet the reasons for this improvement have not been quantitatively explained in terms of reservoir dynamics characteristics. Therefore, we hypothesized that the performance enhancement brought about by time-history terms could be explained by delay capacity, a recently proposed metric for assessing the memory performance of reservoirs. To test this hypothesis, we conducted comparative experiments using ESN models with time-history terms, namely Leaky-Integrator ESNs (LI-ESN) and chaotic echo state networks (ChESN). 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Explaining ESN performance through dynamical metrics are crucial for evaluating the numerous ESN architectures recently proposed from a general perspective and for the development of more sophisticated architectures, and this study contributes to such efforts.","manuscriptTitle":"Impact of Time-History Terms on Reservoir Dynamics and Prediction Accuracy in Echo State Networks","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2024-01-09 04:11:53","doi":"10.21203/rs.3.rs-3834443/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Revision requested","date":"2024-02-25T06:32:51+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2024-02-23T16:13:28+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"2467920f-9acf-4713-9941-81f7aa8fb7d4","date":"2024-02-16T12:18:51+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2024-01-27T06:04:21+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"ed165ac0-5f07-4712-bc84-17aa92e94095","date":"2024-01-18T02:33:22+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"3260cd6e-83d4-43f6-867a-be95bf1ef2bc","date":"2024-01-17T08:48:55+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2024-01-17T07:54:20+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2024-01-17T07:49:22+00:00","index":"","fulltext":""},{"type":"editorInvited","content":"","date":"2024-01-06T08:19:24+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2024-01-06T08:02:42+00:00","index":"","fulltext":""},{"type":"submitted","content":"Scientific Reports","date":"2024-01-04T11:37:50+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"scientific-reports","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"scirep","sideBox":"Learn more about [Scientific Reports](http://www.nature.com/srep/)","snPcode":"","submissionUrl":"","title":"Scientific Reports","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Scientific Reports","inReviewEnabled":true,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"296c178c-c50e-4a8c-98a4-ebea26735e82","owner":[],"postedDate":"January 9th, 2024","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"published-in-journal","subjectAreas":[{"id":27994706,"name":"Physical sciences/Mathematics and computing/Applied mathematics"},{"id":27994707,"name":"Physical sciences/Physics/Statistical physics thermodynamics and nonlinear dynamics/Nonlinear phenomena"},{"id":27994708,"name":"Biological sciences/Neuroscience/Computational neuroscience/Dynamical systems"}],"tags":[],"updatedAt":"2024-04-17T09:45:30+00:00","versionOfRecord":{"articleIdentity":"rs-3834443","link":"https://doi.org/10.1038/s41598-024-59143-y","journal":{"identity":"scientific-reports","isVorOnly":false,"title":"Scientific Reports"},"publishedOn":"2024-04-15 09:45:30","publishedOnDateReadable":"April 15th, 2024"},"versionCreatedAt":"2024-01-09 04:11:53","video":"","vorDoi":"10.1038/s41598-024-59143-y","vorDoiUrl":"https://doi.org/10.1038/s41598-024-59143-y","workflowStages":[]},"version":"v1","identity":"rs-3834443","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-3834443","identity":"rs-3834443","version":["v1"]},"buildId":"qtupq5eGEP_6zYnWcrvyt","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}