提出内生切换机制，让模型自主改变学习模式。
Endogenous Regime Switching Driven by Scalar-Irreducible Learning Dynamics
- 区分可简化为标量梯度流与不可简化的动力学类型
- 在最小模型中实现无需外部调度的持续内生切换
- 适合研究自主智能与自适应系统构建的学者
实现内生的模式切换是自主智能涌现的关键，但现有机器学习框架多依赖外部设定。本文提出分类：将可表示为标量目标驱动梯度流的动力学称为标量可约，反之为标量不可约。多数现有系统属于前者，而我们证明标量不可约动力学通过快速变量与缓慢结构适应之间的反馈，自然产生内生的模式切换。通过一个极简动力学模型，展示了该机制可在无外部调度条件下实现持续的内生模式转换。结果揭示了一种新的动态范式，为实现内部组织的自适应学习系统提供了可能路径。
原文摘要 · Abstract (English)
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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