Phase Structure in Continuous Wave Fields Enables Speech Classification Without Backpropagation

Phase Structure in Continuous Wave Fields Enables Speech Classification Without Backpropagation | 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 Phase Structure in Continuous Wave Fields Enables Speech Classification Without Backpropagation Jeremy Slater, Gardar Thorvardsson This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-9205518/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 promise energy-efficient computation by exploiting the intrinsic dynamics of physical substrates, but existing implementations rely on discrete elements or restrict learning to digital readout layers. Here we demonstrate that a continuous Landau-Ginzburg wave field, operating in the underdamped regime, generates phase structure sufficient for classifying spoken words at 74.1% accuracy on a 10-class spoken command recognition task (Google Speech Commands V2) — using only a linear readout and no backpropagation through the physical dynamics. Systematic ablation across ten conditions reveals a three-tier hierarchy of contributions. First, operating in the underdamped regime accounts for ~20 percentage points (pp): a from-scratch baseline trained with EP but initialized in the overdamped regime (γ/ω = 1.0) reaches only 53%, while theoretically-motivated underdamped initialization (γ/ω < 0.05) yields 74.1% (EP fine-tuning contributed an additional 0.81 pp; ablation 7). Second, within the architecture, readout design is decisive: explicit phase extraction — cosine and sine of the phase angle, amplitude, and amplitude gradient — contributes 7.8 points over implicit complex-component encoding, revealing that linear readouts cannot exploit phase information unless it is explicitly projected into trigonometric form. Third, individual physics components — cross-phase modulation, spatial parameter grids, evanescent coupling, and EP fine-tuning of material parameters — each contribute less than 1 percentage point individually, indicating that the underdamped LG regime is robust to specific parameter choices once the architecture is correctly designed. Notably, Equilibrium Propagation drives the lateral inhibition strength toward opposite optima depending on the readout — higher under amplitude measurement (D → 0.27), lower under phase-sensitive measurement (D → 0.025) — demonstrating that EP co-adapts the physical substrate to the measurement apparatus. Every learned parameter in principle maps directly to fabrication specifications for photonic or acoustic hardware. Physical sciences/Physics/Electronics, photonics and device physics/Photonic devices Biological sciences/Neuroscience/Cognitive neuroscience Physical sciences/Mathematics and computing/Computer science Physical sciences/Engineering physical neural networks Landau-Ginzburg dynamics equilibrium propagation wave computing phase readout keyword spotting mel spectrogram Full Text Additional Declarations Yes there is potential Competing Interest. J.D.S. is Chief Medical Officer of Stratus Neuro, the Chief Innovation Officer for MERLN LLC, and founder of Medscrios LLC. G.T. is the managing director of Kvikna Medical. 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. 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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-9205518","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":614681453,"identity":"8c8a1fc2-aab3-4eea-a6b6-8e54f4af7dc5","order_by":0,"name":"Jeremy Slater","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAABA0lEQVRIie3RsWrDMBCA4TMBZwnJViTc2q9wQtBS6MNIFDIZunoIRKLgMbNMBr+CH8FQcBbROcUdEjpkdRdPIdTZ7TbZOugHwQ33gYQAXK7/WNmd3XkYq2uIAASYlF6H8BpCxIVkWpejRiyO4UN2OHwli6PM169VkCQQzW7KXkLfhU9Ehfy2jpm2Fcris5pTa4Fla9FL0IIPwkdpgtjTqhsKEt9TnYLAepB0Fzvh0tDNXqsTyty8tH8RIDJFQQgwrVOUahv7vxJqvZTIFWdmErNMrzgvtnP+qCwZfMvUjt6apg0jMt7svlUb3uXmef+hkqdoFvQTgPNv9EQG1l0ul8t1ST9k/l9ysveVFgAAAABJRU5ErkJggg==","orcid":"https://orcid.org/0000-0002-2656-1354","institution":"Stratus","correspondingAuthor":true,"prefix":"","firstName":"Jeremy","middleName":"","lastName":"Slater","suffix":""},{"id":614681454,"identity":"bb989806-ec73-465d-ad6d-87224dfcc267","order_by":1,"name":"Gardar Thorvardsson","email":"","orcid":"","institution":"Kvikna Medical ehf","correspondingAuthor":false,"prefix":"","firstName":"Gardar","middleName":"","lastName":"Thorvardsson","suffix":""}],"badges":[],"createdAt":"2026-03-24 02:00:15","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-9205518/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-9205518/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":106092931,"identity":"32eebb0b-3b58-4a6b-953c-493df0541ddc","added_by":"auto","created_at":"2026-04-03 11:30:51","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":596572,"visible":true,"origin":"","legend":"","description":"","filename":"FICUNatCommsfinal.pdf","url":"https://assets-eu.researchsquare.com/files/rs-9205518/v1_covered_e21e24aa-f772-4337-ba11-d79d4d33b241.pdf"}],"financialInterests":"\u003cb\u003eYes\u003c/b\u003e there is potential Competing Interest.\nJ.D.S. is Chief Medical Officer of Stratus Neuro, the Chief Innovation Officer for MERLN LLC, and founder of Medscrios LLC. 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Here we demonstrate that a continuous Landau-Ginzburg wave field, operating in the underdamped regime, generates phase structure sufficient for classifying spoken words at 74.1% accuracy on a 10-class spoken command recognition task (Google Speech Commands V2) — using only a linear readout and no backpropagation through the physical dynamics. Systematic ablation across ten conditions reveals a three-tier hierarchy of contributions. First, operating in the underdamped regime accounts for ~20 percentage points (pp): a from-scratch baseline trained with EP but initialized in the overdamped regime (γ/ω = 1.0) reaches only 53%, while theoretically-motivated underdamped initialization (γ/ω \u003c 0.05) yields 74.1% (EP fine-tuning contributed an additional 0.81 pp; ablation 7). Second, within the architecture, readout design is decisive: explicit phase extraction — cosine and sine of the phase angle, amplitude, and amplitude gradient — contributes 7.8 points over implicit complex-component encoding, revealing that linear readouts cannot exploit phase information unless it is explicitly projected into trigonometric form. Third, individual physics components — cross-phase modulation, spatial parameter grids, evanescent coupling, and EP fine-tuning of material parameters — each contribute less than 1 percentage point individually, indicating that the underdamped LG regime is robust to specific parameter choices once the architecture is correctly designed. Notably, Equilibrium Propagation drives the lateral inhibition strength toward opposite optima depending on the readout — higher under amplitude measurement (D → 0.27), lower under phase-sensitive measurement (D → 0.025) — demonstrating that EP co-adapts the physical substrate to the measurement apparatus. 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