Stochastic Dynamics of Generative AI: From Autoregressive Models to Interacting LLM Networks and Neural SDEs

Vikram Krishnamurthy, Yiming Zhang, Luke Snow

This paper develops a stochastic dynamical-systems perspective on three classes of generative AI models. First, we formulate large language models (LLMs) as high-dimensional nonlinear autoregressive models with attention-based dependencies. This formulation connects pretraining by conditional maximum likelihood to sequential token generation and provides a probabilistic interpretation of LLM operation. Second, we consider networks of interacting LLMs and characterize their collective behavior through mean-field ordinary differential equations. These dynamics provide a framework for understanding emergent preferential attachment and persistent structural biases, including type-dependent glass-ceiling effects. Third, we consider neural stochastic differential equations (SDEs) as continuous-time generative models for stochastic trajectories, including those observed at irregular time intervals. We discuss their training with particular emphasis on Wiener-space cubature methods based on rough-path analysis as an efficient alternative to Monte Carlo estimation. Together, the three settings address probabilistic prediction, information exchange and emergent behavior in interacting…