arXiv:2605.16325cs.LGcs.AI2026-05

用双场框架统一解释深度学习与非平衡化学中的相变现象

Phase Transitions in Driven Informational Systems: A Two-Field Perspective on Learning Theory and Non-Equilibrium Chemistry

  • 提出熵产生率与信息势能双重梯度驱动的理论模型
  • 发现对抗崩溃阈值与自指耦合阈值共同决定相变行为
  • 适用于理解大模型对齐、自省能力等新兴现象

深度学习中的相变现象(如涌现能力、上下文切换下的本体重构)已通过表征压缩、奇异学习理论和信息论进展指标等视角研究。独立地,非平衡统计物理在前生命选择的驱动化学反应网络中识别出相变,其经验特征难以用单一场梯度模型再现。本文提出将两类现象统一为受驱信息系统的描述:由熵产生率Σ与信息准势能Φ_I := -ln p*(p*为稳态密度)共同主导的随机过程。在此框架下引入两个候选序参数:对抗性崩溃阈值α_†与自指耦合阈值κ_c。两者的联合标度定义了一个候选普适类,具有指数(γ₁, γ₂)。本文阐明该框架的几何结构,提出可检验的预测以区分单场模型,并展示其与2024–2026年最新实证结果的一致性,包括对齐相变、对抗崩溃标度及大语言模型的部分内省行为。

原文摘要 · Abstract (English)

Phase-transition phenomena in deep learning (grokking, emergent capabilities, and ontological reorganization under context shift) have been studied through several lenses, including representational compression, singular learning theory, and information-theoretic progress measures. Independently, non-equilibrium statistical physics has identified phase transitions in driven chemical reaction networks underlying prebiotic selection, with empirical signatures that are difficult to reproduce within single-field gradient accounts. We propose a perspective in which both classes of phenomena admit a common description as driven informational systems: stochastic processes governed by two gradient fields, an entropy production rate Sigma and an information quasi-potential Phi_I := -ln p*, where p* is the stationary density. Within this framework we introduce two candidate order parameters: an adversarial breakdown threshold alpha_dagger and a self-referential coupling threshold kappa_c. The joint scaling of (alpha_dagger, kappa_c) defines a candidate universality class with exponents (gamma_1, gamma_2). We outline the geometric structure of this framework, identify falsifiable predictions distinguishing it from single-field alternatives, and show consistency with recent empirical findings (2024--2026) on alignment transitions, adversarial breakdown scaling, and partial introspection in large language models.

相变信息理论深度学习非平衡系统

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