arXiv:2510.13103v1 Announce Type: cross Abstract: Uncertainty Quantification (UQ) is a promising approach to improve model reliability, yet quantifying the uncertainty of Large Language Models (LLMs) is non-trivial. In this work, we establish a connection between the uncertainty of LLMs and their invariance under semantic-preserving intervention from a causal perspective. Building on this foundation, we propose a novel grey-box uncertainty quantification method that measures the variation in model outputs before and after the semantic-preserving intervention. Through theoretical justification, we show that our method provides an effective estimate of epistemic uncertainty. Our extensive experiments, conducted across various LLMs and a variety of question-answering (QA) datasets, demonstrate that our method excels not only in terms of effectiveness but also in computational efficiency.