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

arXiv: https://arxiv.org/abs/2501.16783 · HTML: https://mlsanity.com/paper/2501.16783/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Placed in Test-time compute and efficient thinking, one of 17 directions in LLM reasoning.
- First posted on arXiv 28 Jan 2025.

## Placed in

- LLM reasoning / [Test-time compute and efficient thinking](https://mlsanity.com/lr/test-time-compute-and-efficient-thinking/)

## Built on by (most cited first, 2 of 2)

- [Limited Reasoning Space: The cage of long-horizon reasoning in LLMs](https://mlsanity.com/paper/2602.19281/) (2026)
- [On the Structural Limits of Machine Learning Decision Systems: An Information-Theoretic, Interaction-Based, and Stochastic-Dynamical Perspective](https://mlsanity.com/paper/2608.13510/) (2026)

## Abstract (arXiv)

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) ∈ [0,1] evolving under a stochastic differential equation (SDE) with a drift term μ(x) and diffusion σ(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.