A Stochastic Differential Equation Framework for Multi-Objective LLM Interactions: Dynamical Systems Analysis with Code Generation Applications
Abstract
We introduce a general stochastic differential equation framework for modelling multiobjective optimization dynamics in iterative Large Language Model (LLM) interactions. Our framework captures the inherent stochasticity of LLM responses through explicit diffusion terms and reveals systematic interference patterns between competing objectives via an interference matrix formulation. We validate our theoretical framework using iterative code generation as a proof-of-concept application, analyzing 400 sessions across security, efficiency, and functionality objectives. Our results demonstrate strategy-dependent convergence behaviors with rates ranging from 0.33 to 1.29, and predictive accuracy achieving R2 = 0.74 for balanced approaches. This work proposes the feasibility of dynamical systems analysis for multi-objective LLM interactions, with code generation serving as an initial validation domain.
Cite
@article{arxiv.2510.10739,
title = {A Stochastic Differential Equation Framework for Multi-Objective LLM Interactions: Dynamical Systems Analysis with Code Generation Applications},
author = {Shivani Shukla and Himanshu Joshi},
journal= {arXiv preprint arXiv:2510.10739},
year = {2025}
}
Comments
Peer-reviewed and accepted to the 39th Conference on Neural Information Processing Systems (NeurIPS 2025) DynaFront 2025 Workshop (https://sites.google.com/view/dynafrontneurips25)