Knowledge Fitness Criterion: Measure-Theoretic Knowledge Assessment via Manifolds for Multi-Agent LLM Systems

Qianqi Zhang, xu zl, Hongyan Liu, Caichun Cen, Yuntao Zou

Keywords: Large language models, Knowledge Adaptability Score, measure theory, statistical manifolds, multi-agent systems, autonomous driving, safety-critical applications

Abstract: Evaluating the intrinsic compatibility between activated knowledge and task objectives is a fundamental challenge in LLM-based multi-agent systems. Existing methods, however, often rely on indirect, task-specific outcome metrics, lacking a unified framework for direct quantification. To address this, we introduce the Knowledge Fitness Criterion (KFC), a general evaluation paradigm grounded in measure theory. KFC models knowledge states as measure spaces and establishes a chain of measurable mappings—from knowledge to features, features to indicators, and indicators to normalized scores—enabling direct, quantitative assessment of knowledge-task alignment. Theoretically, we establish the Knowledge Goal Quantified-Quality (KGQQ) Theorem, which provides a rigorous guarantee linking scoring stability to feature manifold density. Empirically, we validate KFC across three diverse domains: autonomous driving (nuScenes), social role simulation (CAMEL), and collaborative software development (ChatDev). Results demonstrate that KFC consistently outperforms supervised baselines, achieving MSE reductions of 22.5\% (Driving), 20.0\% (Social), and 21.1\% (Coding), along with significant improvements in Pearson correlation (up to 15.3\%). Furthermore, our framework exhibits strong cross-domain robustness ($r=0.82$) and data efficiency, effectively utilizing 80\% unlabeled data through contrastive manifold learning. By offering a model-agnostic measurement instrument, KFC provides a universal, quantifiable foundation for optimizing knowledge in complex multi-agent collaboration.

Primary Area: foundation or frontier models, including LLMs

Submission Number: 6187