Can LLMs Refuse Questions They Do Not Know? Measuring Knowledge-Aware Refusal in Factual Tasks

Large Language Models (LLMs) should refuse to answer questions beyond their knowledge. This capability, which we term knowledge-aware refusal, is crucial for factual reliability, while existing metrics fail to capture this ability. In this work, we propose the Refusal Index (RI), a novel and principled metric that measures how accurately LLMs refuse questions they do not know. We define RI as Spearman's rank correlation between refusal probability and error probability. RI is practically measurable with a lightweight two-pass evaluation method which only require observed refusal rates across two standard evaluation runs. Extensive experiments across 16 models and 5 datasets demonstrate that RI accurately quantifies a model's knowledge-aware refusal capability. Notably, RI remains stable across different refusal rates and provides consistent model rankings independent of a model's overall accuracy and refusal rates. These properties suggest RI captures a stable, intrinsic aspect of model knowledge calibration. More importantly, RI provides insight into an important but previously overlooked aspect of LLM factuality: while LLMs achieve high accuracy on factual tasks, their refusal behavior can be unreliable and fragile.