Endogenous Regime Switching Driven by Scalar-Irreducible Learning Dynamics

• URL: http://arxiv.org/abs/2605.04054v1
• Date: Fri, 10 Apr 2026 02:40:51 GMT
• Title: Endogenous Regime Switching Driven by Scalar-Irreducible Learning Dynamics
• Abstract summary: endogenous regime switching is crucial for the emergence of autonomous intelligence.<n>Most existing machine learning systems operate within the scalar-reducible class.<n>We show that scalar-irreducible dynamics naturally enable internally generated regime switching.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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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