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

Abstract

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 $\hat{I}¼(x)$ and diffusion $\ddot{I}ƒ(x)$. 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.

Experimental verification and more formal argument for Markov approximation of bias propagation to be released soon. Primarily pushed now to establish novelty and ease of sharing. Please do not cite this work until the forthcoming experimental validation and updated mathematical model are provided