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

arXiv:2611.07065v1 Announce Type: new 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.

The paper presents a technical development in AI models without discussing societal implications.

The paper presents advanced theoretical frameworks for understanding generative AI, including LLMs and their networks, which improves foundational knowledge and may inform mitigation of biases. However, it also highlights structural biases and persistent effects, which could reinforce societal inequalities. The implications are complex and balanced, with moderate confidence based on the technical and analytical nature of the work.

This is foundational mathematical theory, not a deployed system or empirical societal finding. The glass-ceiling bias result is an abstract mean-field property, not demonstrated in real LLM deployments, so implications for human flourishing are highly indirect and speculative.

This paper is a highly technical academic work focused on developing mathematical frameworks for understanding and modeling generative AI, including LLMs and neural SDEs. It describes theoretical formulations and dynamics rather than discussing societal implications or real-world applications. The mention of 'persistent structural biases' and 'glass-ceiling effects' is purely within the context of model dynamics, not human societal impact.

The paper presents technical advances in generative AI models. It discusses improved understanding and training methods, which could lead to better AI performance. There is no substantive claim about AI's effect on society.

SOURCE     arXiv cs.LG (Machine Learning) (tier 1)
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DOCUMENT   0378ec83-8cbe-415b-9b94-d60259912799
           https://arxiv.org/abs/2611.07065
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EVIDENCE   3 extracted excerpts
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MODEL RUN  5 runs, methodology 1.0.1
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SCORE      -16  (Mixed or uncertain)
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CONFIDENCE 70%