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

TL;DR

This paper develops a stochastic dynamical model to analyze how large language models might self-amplify biases or toxicity, revealing phase transitions and critical phenomena that influence model stability and bias propagation.

Contribution

It introduces a novel continuous-time stochastic framework for modeling LLM severity drift, enabling analysis of critical thresholds and stability conditions.

Findings

Identifies phase transitions between self-correcting and runaway bias regimes.

Derives stationary distributions and first-passage times for harmful thresholds.

Provides scaling laws near critical points for bias amplification.

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 $\mu(x)$ 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.