A Stochastic Differential Equation Framework for Multi-Objective LLM Interactions: Dynamical Systems Analysis with Code Generation Applications

Fuente: arXiv
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Autores principales: Shukla, Shivani, Joshi, Himanshu
Formato: Preprint
Publicado: 2025
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author Shukla, Shivani
Joshi, Himanshu
author_facet Shukla, Shivani
Joshi, Himanshu
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2510_10739
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle A Stochastic Differential Equation Framework for Multi-Objective LLM Interactions: Dynamical Systems Analysis with Code Generation Applications
Shukla, Shivani
Joshi, Himanshu
Machine Learning
Artificial Intelligence
Software Engineering
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.
title A Stochastic Differential Equation Framework for Multi-Objective LLM Interactions: Dynamical Systems Analysis with Code Generation Applications
topic Machine Learning
Artificial Intelligence
Software Engineering
url https://arxiv.org/abs/2510.10739