A Stochastic Differential Equation Framework for Multi-Objective LLM Interactions: Dynamical Systems Analysis with Code Generation Applications
This work addresses the challenge of understanding and predicting multi-objective dynamics in LLM interactions, with incremental contributions validated specifically for code generation.
The authors tackled the problem of modeling multi-objective optimization in iterative LLM interactions by introducing a stochastic differential equation framework, which they validated on code generation tasks with 400 sessions showing convergence rates from 0.33 to 1.29 and predictive accuracy of R2 = 0.74.
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.