Multi-Dimensional Constraint Integration Method for Large Language Models via Lyapunov Stability Theory

Qianqi Zhang, xu zl, Jieping Xu, Yuntao Zou

Keywords: Large language model agents, multi-constraint environments, Lyapunov stability theory, constraint-aware decoding, environmental modeling, constraint satisfaction, discrete language generation, convergence optimization

Abstract: Large language model agents face a fundamental challenge of environmental understanding deficiency in multi-constraint environments: they rely on textual pattern matching rather than deep environmental modeling, leading to decisions that are disconnected from environmental requirements. The root cause lies in the general pre-training paradigm's lack of constraint-structured annotations, causing models to treat multiple constraints as independent fragments without capturing inter-constraint dependencies and environmental dynamic characteristics. This paper proposes a Lyapunov-guided multi-constraint aware decoding framework that innovatively adapts Lyapunov stability theory to discrete language generation processes. By constructing a multi-constraint Lyapunov modeling system, constraint deviations are quantified as Lyapunov functions, enabling agents to quantitatively assess constraint satisfaction distances and obtain optimal convergence directions. Experimental validation demonstrates that this method significantly improves constraint satisfaction rates while maintaining generation quality.

Primary Area: foundation or frontier models, including LLMs

Submission Number: 6192