Representation Mechanics: Invariant-Governed Learning Dynamics

Representation Mechanics: Invariant-Governed Learning Dynamics | 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Article Representation Mechanics: Invariant-Governed Learning Dynamics Datorien L. Anderson This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8819134/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 We present Representation Mechanics, a theoretical and empirical framework characterizing learning in invariant-governed domains. We demonstrate that neural networks with set-valued operations (discrete potentials {-W, 0, +W}) and learned selection exhibit sharp phase transitions to generalization without pretraining. The Platonic Spike (Early Phase Transition)—where validation accuracy exceeds training accuracy in early epochs—signals the discovery of structural invariants before instance memorization. We validate these findings on controlled synthetic tasks (spiral classification, closed-world logic, declarative language) to isolate geometric mechanics from natural language statistical confounds. We contrast this Form-First paradigm with diffusion-dominated learning and define the conditions (Basin Preservation and Friction Set tracking) required to maintain these invariants under continual learning pressure. Our results suggest that restricting representational freedom via discrete potentials is not a limitation but a necessary inductive bias for rule-consistent generalization. Artificial Intelligence and Machine Learning Mathematical Physics machine learning inductive bias phase transitions generalization dynamics representation learning neural dynamics discrete optimization. Full Text Additional Declarations The authors declare no competing 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. 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