A Stochastic Dynamical Theory of LLM Self-Adversariality: Modeling Severity Drift as a Critical Process
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866912207037530112 |
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| author | Carson, Jack David |
| author_facet | Carson, Jack David |
| contents | 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 $μ(x)$ 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_16783 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Stochastic Dynamical Theory of LLM Self-Adversariality: Modeling Severity Drift as a Critical Process Carson, Jack David Computation and Language Artificial Intelligence Adaptation and Self-Organizing Systems 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 $μ(x)$ 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. |
| title | A Stochastic Dynamical Theory of LLM Self-Adversariality: Modeling Severity Drift as a Critical Process |
| topic | Computation and Language Artificial Intelligence Adaptation and Self-Organizing Systems |
| url | https://arxiv.org/abs/2501.16783 |