Illusions of Confidence? Diagnosing LLM Truthfulness via Neighborhood Consistency
Authors: name: Haoming Xu, name: Ningyuan Zhao, name: Yunzhi Yao, name: Weihong Xu, name: Hongru Wang, name: Xinle Deng, name: Shumin Deng, name: Jeff Z. Pan, name: Huajun Chen, name: Ningyu Zhang
Organization: Zhejiang University

As Large Language Models (LLMs) are increasingly deployed in real-world settings, correctness alone is insufficient. Reliable deployment requires maintaining truthful beliefs under contextual perturbations. Existing evaluations largely rely on point-wise confidence like Self-Consistency, which can mask brittle belief. We show that even facts answered with perfect self-consistency can rapidly collapse under mild contextual interference. To address this gap, we propose Neighbor-Consistency Belief (NCB), a structural measure of belief robustness that evaluates response coherence across a conceptual neighborhood. To validate the efficiency of NCB, we introduce a new cognitive stress-testing protocol that probes outputs stability under contextual interference. Experiments across multiple LLMs show that the performance of high-NCB data is relatively more resistant to interference. Finally, we present Structure-Aware Training (SAT), which optimizes context-invariant belief structure and reduces long-tail knowledge brittleness by approximately 30%. Code will be available at https://github.com/zjunlp/belief.