用随机微分方程建模多目标大模型交互，揭示目标间干扰机制。
A Stochastic Differential Equation Framework for Multi-Objective LLM Interactions: Dynamical Systems Analysis with Code Generation Applications
- 引入随机微分方程框架，显式建模大模型响应的随机性。
- 400次代码生成实验显示策略依赖的收敛速率（0.33~1.29）与0.74的预测精度。
- 为多目标大模型交互提供动力学分析新范式，适合研究优化策略者参考。
我们提出一种通用的随机微分方程框架，用于建模迭代式大语言模型（LLM）交互中的多目标优化动态。该框架通过显式的扩散项捕捉大模型响应的固有随机性，并借助干扰矩阵形式揭示竞争目标间的系统性干扰模式。我们以迭代代码生成为例进行验证，分析了400次会话中安全、效率和功能性的多目标表现。结果表明，不同策略导致的收敛行为存在差异，收敛速率范围在0.33至1.29之间，且平衡策略的预测准确率可达R² = 0.74。本工作证明了动力学系统分析在多目标大模型交互中的可行性，代码生成作为初步验证领域具有代表性。
原文摘要 · Abstract (English)
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.
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