标题： 一种随机动力学理论的LLM自对抗性：将严重性漂移建模为临界过程 显示英文标题

标题： A Stochastic Dynamical Theory of LLM Self-Adversariality: Modeling Severity Drift as a Critical Process

摘要： 本文介绍了一个连续时间随机动力学框架，用于理解大型语言模型（LLMs）如何通过自身的思维链推理自我放大潜在偏见或有害性。 该模型假设一个瞬时“严重性”变量$x(t) \in [0,1]$在带有漂移项$\mu(x)$和扩散$\sigma(x)$的随机微分方程（SDE）下演化。 关键的是，如果每个增量步骤在严重性空间中几乎具有马尔可夫性，那么这种过程可以通过福克-普朗克方法进行一致分析。 分析研究了临界现象，表明某些参数范围会导致从亚临界（自我纠正）到超临界（失控严重性）的相变。 本文推导了稳态分布、达到有害阈值的第一穿越时间以及临界点附近的标度定律。 最后，它强调了对智能体和扩展的LLM推理模型的含义：原则上，这些方程可能作为形式验证的基础，以确定模型在重复推理过程中是否保持稳定或传播偏见。 显示英文摘要

摘要： This paper introduces a continuous-time stochastic dynamical framework for understanding how large language models (LLMs) may self-amplify latent biases or toxicity through their own chain-of-thought reasoning. The model posits an instantaneous "severity" variable $x(t) \in [0,1]$ evolving under a stochastic differential equation (SDE) with a drift term $\mu(x)$ and diffusion $\sigma(x)$. Crucially, such a process can be consistently analyzed via the Fokker--Planck approach if each incremental step behaves nearly Markovian in severity space. The analysis investigates critical phenomena, showing that certain parameter regimes create phase transitions from subcritical (self-correcting) to supercritical (runaway severity). The paper derives stationary distributions, first-passage times to harmful thresholds, and scaling laws near critical points. Finally, it highlights implications for agents and extended LLM reasoning models: in principle, these equations might serve as a basis for formal verification of whether a model remains stable or propagates bias over repeated inferences.