Implicit Learning as Phase Transition: Integrating Free Energy Minimization with Stuart-Landau Dynamics
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| Format: | Recurso digital |
| Language: | English |
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2025
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| _version_ | 1866901038999535616 |
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| author | Ishibashi, Ryuhei |
| author_facet | Ishibashi, Ryuhei |
| contents | <p>The Free Energy Principle (FEP) provides a powerful framework for perception, action, and learning, yet it lacks mechanisms for representing the implicit-to-explicit knowledge transition and temporal accumulation dynamics. We address these limitations by coupling FEP with Stuart-Landau bifurcation dynamics—a framework developed for biological emergence by Shimizu (1972) but largely overlooked in cognitive science. In our model, FEP specifies why the system changes (free energy minimization), while Stuart-Landau dynamics specify how qualitative change occurs (Hopf bifurcation).<br>The bifurcation parameter μ is defined as accumulated model evidence: μ(t) = ∫[λ − F(τ)]dτ. When prediction error reduction through practice drives μ across the critical threshold, a phase transition transforms transient neural patterns into self-sustaining cognitive structures. This bifurcation point corresponds to Boundary B in the four-term model of knowledge transformation—the threshold between embodied knowledge and linguistic meaning.<br>The framework unifies implicit learning, automatic motivation, and motor skill acquisition as three perspectives on a single process: pre-bifurcation neural adaptation. Combined with a companion paper addressing oscillatory order parameters in predictive processing (Ishibashi, 2025c), this work suggests that Stuart-Landau dynamics operate at multiple timescales of neural computation, from millisecond-scale prediction error integration to the slower accumulation underlying skill formation.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_18103106 |
| institution | Zenodo |
| language | eng |
| publishDate | 2025 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Implicit Learning as Phase Transition: Integrating Free Energy Minimization with Stuart-Landau Dynamics Ishibashi, Ryuhei Free Energy Principle active inference implicit learning neural adaptation dynamic systems Stuart-Landau Hopf bifurcation embodied cognition automatic motivation phase transition spike-timing-dependent plasticity <p>The Free Energy Principle (FEP) provides a powerful framework for perception, action, and learning, yet it lacks mechanisms for representing the implicit-to-explicit knowledge transition and temporal accumulation dynamics. We address these limitations by coupling FEP with Stuart-Landau bifurcation dynamics—a framework developed for biological emergence by Shimizu (1972) but largely overlooked in cognitive science. In our model, FEP specifies why the system changes (free energy minimization), while Stuart-Landau dynamics specify how qualitative change occurs (Hopf bifurcation).<br>The bifurcation parameter μ is defined as accumulated model evidence: μ(t) = ∫[λ − F(τ)]dτ. When prediction error reduction through practice drives μ across the critical threshold, a phase transition transforms transient neural patterns into self-sustaining cognitive structures. This bifurcation point corresponds to Boundary B in the four-term model of knowledge transformation—the threshold between embodied knowledge and linguistic meaning.<br>The framework unifies implicit learning, automatic motivation, and motor skill acquisition as three perspectives on a single process: pre-bifurcation neural adaptation. Combined with a companion paper addressing oscillatory order parameters in predictive processing (Ishibashi, 2025c), this work suggests that Stuart-Landau dynamics operate at multiple timescales of neural computation, from millisecond-scale prediction error integration to the slower accumulation underlying skill formation.</p> |
| title | Implicit Learning as Phase Transition: Integrating Free Energy Minimization with Stuart-Landau Dynamics |
| topic | Free Energy Principle active inference implicit learning neural adaptation dynamic systems Stuart-Landau Hopf bifurcation embodied cognition automatic motivation phase transition spike-timing-dependent plasticity |
| url | https://doi.org/10.5281/zenodo.18103106 |