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

TL;DR

This work introduces the Refusal Index (RI), a principled, rank-based metric that measures LLMs' knowledge-aware refusal by correlating refusal decisions with incorrectness on factual questions. RI is defined as the Spearman correlation between per-question refusal probability and error probability, and is estimated via a lightweight two-pass evaluation that models the joint refusal–error behavior using a Gaussian copula. Across 16 models and 5 datasets, RI proves robust to varying refusal rates and aligns with calibration signals, while revealing that model family and grounding context substantially influence refusal behavior beyond raw accuracy. The findings argue for incorporating RI into factuality evaluation to capture an essential reliability dimension previously overlooked, with practical implications for safer and more trustworthy LLM deployments.

Abstract

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. However, existing metrics fail to faithfully measure this ability. On the one hand, simple refusal-based metrics are biased by refusal rates and yield inconsistent scores when models exhibit different refusal tendencies. On the other hand, existing calibration metrics are proxy-based, capturing the performance of auxiliary calibration processes rather than the model's actual refusal behavior. In this work, we propose the Refusal Index (RI), a 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. To make RI practically measurable, we design a lightweight two-pass evaluation method that efficiently estimates RI from observed refusal rates across two standard evaluation runs. Extensive experiments across 16 models and 5 datasets demonstrate that RI accurately quantifies a model's intrinsic knowledge-aware refusal capability in factual tasks. Notably, RI remains stable across different refusal rates and provides consistent model rankings independent of a model's overall accuracy and refusal rates. 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. This finding highlights the need to complement traditional accuracy metrics with the Refusal Index for comprehensive factuality evaluation.

Figures (11)

• Figure 1: Illustration of Refusal Index (RI). Refusal Index quantifies a model's internal capability to refuse questions beyond its knowledge by measuring the correlation between refusal decisions and answer incorrectness. Left: Refusal Index models how the correct answer rate drops with increasing refusal rate. Right: Empirical correct answer rates for the same model at different refusal rates align with the Refusal Index.
• Figure 2: Illustration of two-pass evaluation process.
• Figure 3: Comparison of factuality metrics with iso-score accuracy-refusal trade-off curves. C/A, F, and W correspond to Correct / Attempted, F-score, and Weighted score, respectively. Empirical data are from Qwen2.5-72B on SimpleQA.
• Figure 4: Correlation between factuality metrics and AUROC with P(Answering) on SimpleQA. RI shows the highest positive correlation with AUROC while being much cheaper to compute.
• Figure 5: Scatter plot of Refusal Index vs. Correct Answer Rate.

Theorems & Definitions (1)

• Definition 2.1: Refusal Index