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arXiv · 2605.04054

Endogenous Regime Switching Driven by Scalar-Irreducible Learning Dynamics

Sheng Ran
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Abstract

Achieving endogenous regime switching is crucial for the emergence of autonomous intelligence, yet remains a central challenge for existing machine learning frameworks, where such transitions are typically externally imposed. In this work, we introduce a classification that distinguishes scalar-reducible dynamics, which can be expressed as gradient flows driven by a scalar objective, from scalar-irreducible dynamics that cannot be reduced to such a form. While most existing machine learning systems operate within the scalar-reducible class, we demonstrate that scalar-irreducible dynamics naturally enable internally generated regime switching through feedback between fast dynamical variables and slow structural adaptation. Using a minimal dynamical model, we illustrate how this mechanism produces sustained endogenous regime transitions without external scheduling. Our results suggest a new dynamical paradigm for regime exploration and provide a potential route toward autonomous learning systems whose adaptive behavior is organized internally rather than externally prescribed.

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Sheng Ran. 2026-04-10. Endogenous Regime Switching Driven by Scalar-Irreducible Learning Dynamics. https://doi.org/10.1063/5.0337565

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