[Submitted on 4 Nov 2026]
Title:Stochastic Dynamics of Generative AI: From Autoregressive Models to Interacting LLM Networks and Neural SDEs
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Abstract: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 networks, and path-space generative modeling.
Subjects:
Machine Learning (cs.LG); Signal Processing (eess.SP); Systems and Control (eess.SY)
Cite as: arXiv:2611.07065 [cs.LG]
(or arXiv:2611.07065v1 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2611.07065
arXiv-issued DOI via DataCite
Submission history
From: Vikram Krishnamurthy [view email] [v1] Wed, 4 Nov 2026 19:23:13 UTC (604 KB)
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