Hierarchical Automaticity Emerges from Prediction-Error-Triggered Learning in Continuous Wave Fields Trained by Equilibrium Propagation

Hierarchical Automaticity Emerges from Prediction-Error-Triggered Learning in Continuous Wave Fields Trained by Equilibrium Propagation | 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 Research Article Hierarchical Automaticity Emerges from Prediction-Error-Triggered Learning in Continuous Wave Fields Trained by Equilibrium Propagation Jeremy Slater, Gardar Thorvardsson This is a preprint; it has not been peer reviewed by a journal.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-9465047/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 The transition from effortful to automatic processing is a defining feature of skill acquisition, and converging evidence implicates theta-gamma phase-amplitude coupling as the neural signature of this transition. The Chrono-Resonant Field Model (CRFM) formalizes this observation into a computational theory: hierarchical automaticity should manifest as a measurable change in the phase organization of cortical field dynamics, and top-down predictions from higher levels should accelerate this transition at lower levels. Testing this prediction requires a physical substrate that generates phase-rich dynamics and a local learning rule that does not rely on backpropagation. We implement such a system using continuous Landau-Ginzburg wave fields trained by Equilibrium Propagation, constructing a three-layer architecture that processes speech at progressively longer timescales: phonemes (40 classes), words (501 classes), and sentence types (3 classes) from the TIMIT corpus. The architecture uses no neurons; field settling dynamics, spatial coarse-graining, holographic matched-filter readout, threshold-gated parameter updates, and top-down boundary conditions on lower-layer settling dynamics are the complete set of computational primitives. We report four principal findings. First, single-layer automaticity manifests as contraction of the Temporal Binding Index distribution rather than a rise in its mean, with Layer 1 converging to a stable phase-response attractor across samples. Second, top-down predictions from Layer 3 drive Layer 2's Temporal Binding Index from 0.349 to 0.510 over 20 training epochs, closing 92% of the gap to Layer 1's frozen value. Third, classification and prediction transmission dissociate: Layer 3 classifies equally well with or without coherent phase dynamics, but only coherent dynamics produce top-down signals capable of driving the cascade. Fourth, a multi-time-point readout exploits the underdamped regime to raise single-layer accuracy by nearly three percentage points over endpoint-only reading. These results provide a physically realizable, backpropagation-free proof-of-concept for CRFM-predicted hierarchical automaticity. Computational Neuroscience Artificial Intelligence and Machine Learning Soft Condensed-matter Physics Equilibrium Propagation Landau-Ginzburg wave field holographic readout hierarchical predictive coding backpropagation-free learning theta-gamma phase-amplitude coupling Chrono-Resonant Field Model hierarchical automaticity predictive processing Kuramoto order parameter continuous wave field computing underdamped settling dynamics photonic neural networks neuromorphic computing TIMIT speech recognition Full Text Additional Declarations The authors declare potential competing interests as follows: Competing Interests JDS is Chief Medical Officer at Stratus Neuro, a remote neurophysiology company, and Principal Investigator at MERLN LLC, a private research entity. GT is affiliated with Kvikna Medical ehf., a medical device company in the neurophysiology space. Neither Stratus Neuro nor Kvikna Medical had any role in the conception, design, execution, analysis, or reporting of the work described in this manuscript, and neither company provided financial support for this study. The authors declare no other competing financial or non-financial interests. 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-9465047","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":625850641,"identity":"f3d0d6b2-3864-47c5-aacd-2049f100e74c","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":"MERLN LLC","correspondingAuthor":true,"prefix":"","firstName":"Jeremy","middleName":"","lastName":"Slater","suffix":""},{"id":625850642,"identity":"180edf41-4cf3-448e-8c1e-52af580d8b0f","order_by":1,"name":"Gardar Thorvardsson","email":"","orcid":"","institution":"Kvikna Medical","correspondingAuthor":false,"prefix":"","firstName":"Gardar","middleName":"","lastName":"Thorvardsson","suffix":""}],"badges":[],"createdAt":"2026-04-19 22:57:21","currentVersionCode":1,"declarations":{"humanSubjects":false,"vertebrateSubjects":false,"conflictsOfInterestStatement":true,"humanSubjectEthicalGuidelines":false,"humanSubjectConsent":false,"humanSubjectClinicalTrial":false,"humanSubjectCaseReport":false,"vertebrateSubjectEthicalGuidelines":false},"doi":"10.21203/rs.3.rs-9465047/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-9465047/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":107453156,"identity":"6216e30b-1250-40ba-859a-d9cd8efcbdd3","added_by":"auto","created_at":"2026-04-21 15:31:26","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":490771,"visible":true,"origin":"","legend":"","description":"","filename":"FICUCRFMManuscript1.pdf","url":"https://assets-eu.researchsquare.com/files/rs-9465047/v1_covered_21740ab5-eac3-4bfb-9d62-e063e25ffb4a.pdf"}],"financialInterests":"The authors declare potential competing interests as follows: Competing Interests\nJDS is Chief Medical Officer at Stratus Neuro, a remote neurophysiology company, and Principal Investigator at MERLN LLC, a private research entity. 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