Learning Nonlinear Heterogeneity in Physical Kolmogorov-Arnold Networks

Learning Nonlinear Heterogeneity in Physical Kolmogorov-Arnold 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 Learning Nonlinear Heterogeneity in Physical Kolmogorov-Arnold Networks Jack Gartside, Fabiana Taglietti, Andrea Pulici, Maxwell Roxburgh, and 9 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8911576/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract Physical neural networks typically train linear synaptic weights while treating device nonlinearities as fixed. We show the opposite - by training the synaptic nonlinearity itself, as in Kolmogorov-Arnold Network (KAN) architectures, we yield markedly higher task performance per physical resource and improved performance-parameter scaling than conventional linear weightbased networks, demonstrating ability of KAN topologies to exploit reconfigurable nonlinear physical dynamics. We experimentally realise physical KANs in silicon-on-insulator devices we term ‘Synaptic Nonlinear Elements’ (SYNEs), operating at room temperature, microampere currents, 2 MHz speeds and ∼750 fJ per nonlinear operation, with no observed degradation over 10^13 measurements and months-long timescales. We demonstrate nonlinear function regression, classification, and prediction of Li-Ion battery dynamics from noisy real-world multi-sensor data. Physical KANs outperform equivalently-parameterised software multilayer perceptron networks across all tasks, with up to two orders of magnitude fewer parameters, and two orders of magnitude fewer devices than linear weight based physical networks. These results establish learned physical nonlinearity as a hardware-native computational primitive for compact and efficient learning systems, and SYNE devices as effective substrates for heterogeneous nonlinear computing. Physical sciences/Nanoscience and technology/Nanoscale devices/Electronic devices Physical sciences/Mathematics and computing/Computer science Physical sciences/Physics/Electronics, photonics and device physics/Electronic and spintronic devices Physical sciences/Materials science/Materials for devices/Electronic devices Full Text Additional Declarations There is NO Competing Interest. Cite Share Download PDF Status: Posted Version 1 posted 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. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. 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-8911576","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":604141220,"identity":"b2d29cbd-916d-4c44-b960-57a809949a49","order_by":0,"name":"Jack Gartside","email":"data:image/png;base64,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","orcid":"https://orcid.org/0000-0002-7044-7399","institution":"Imperial College London","correspondingAuthor":true,"prefix":"","firstName":"Jack","middleName":"","lastName":"Gartside","suffix":""},{"id":604141221,"identity":"23ec68b3-1d47-462a-88fe-f595c1886001","order_by":1,"name":"Fabiana Taglietti","email":"","orcid":"https://orcid.org/0000-0002-0354-4463","institution":"Department of Materials Science, University of Milano-Bicocca, 20125 Milan, Italy.","correspondingAuthor":false,"prefix":"","firstName":"Fabiana","middleName":"","lastName":"Taglietti","suffix":""},{"id":604141222,"identity":"8b11f48b-9198-4f65-a9ff-59cde7946ad5","order_by":2,"name":"Andrea Pulici","email":"","orcid":"","institution":"National Research Council (CNR) - Institute for Microelectronics and Microsystems (IMM), Unit of Agrate Brianza, Via C. 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We show the opposite - by training the synaptic nonlinearity itself, as in Kolmogorov-Arnold Network (KAN) architectures, we yield markedly higher task performance per physical resource and improved performance-parameter scaling than conventional linear weightbased\r\nnetworks, demonstrating ability of KAN topologies to exploit reconfigurable nonlinear physical dynamics.\r\n\r\nWe experimentally realise physical KANs in silicon-on-insulator devices we term ‘Synaptic Nonlinear Elements’ (SYNEs), operating at room temperature, microampere currents, 2 MHz speeds and ∼750 fJ per nonlinear operation, with no observed degradation over 10^13 measurements and months-long timescales. We demonstrate nonlinear function regression, classification, and prediction of Li-Ion battery dynamics from noisy real-world multi-sensor data. Physical KANs outperform equivalently-parameterised software multilayer perceptron networks across all tasks, with up to two orders of magnitude fewer parameters, and two orders of magnitude fewer devices than linear weight\r\nbased physical networks. 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