Endogenous Regime Switching Driven by Scalar-Irreducible Learning Dynamics

TL;DR

This paper introduces a new dynamical framework distinguishing scalar-irreducible dynamics that enable autonomous, internally driven regime switching, advancing the development of self-organizing adaptive learning systems.

Contribution

It identifies scalar-irreducible dynamics as a key to endogenous regime switching, providing a minimal model demonstrating autonomous internal transitions.

Findings

Scalar-irreducible dynamics facilitate sustained endogenous regime transitions.

Most existing systems operate within scalar-reducible dynamics, which lack internal switching.

The proposed model shows how feedback mechanisms produce autonomous regime changes.

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.