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

• URL: http://arxiv.org/abs/2501.16783v1
• Date: Tue, 28 Jan 2025 08:08:25 GMT
• Title: A Stochastic Dynamical Theory of LLM Self-Adversariality: Modeling Severity Drift as a Critical Process
• Authors: Jack David Carson,
• Abstract summary: This paper introduces a continuous-time 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 differential equation (SDE) with a drift term $mu(x)$ and diffusion $sigma(x)$.
• Score: 0.0
• License:
• 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.

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