Endogenous Regime Switching Driven by Scalar-Irreducible Learning Dynamics
This work proposes a new dynamical paradigm for autonomous learning systems, addressing the challenge of internally generated regime switching for AI researchers.
The paper introduces a classification of learning dynamics into scalar-reducible and scalar-irreducible types, showing that scalar-irreducible dynamics enable endogenous regime switching without external scheduling. Using a minimal model, they demonstrate sustained regime transitions driven by internal feedback.
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.