Calibrating Verbal Uncertainty as a Linear Feature to Reduce Hallucinations

TL;DR

This paper tackles the problem of overconfident hallucinations in large language models by introducing Verbal Uncertainty Feature (VUF), a single linear direction in the model's representation space that governs verbal uncertainty (VU). It shows that VU and semantic uncertainty (SU) can be miscalibrated, and that detecting hallucinations benefits from jointly considering SU and VU. The authors propose Mechanistic Uncertainty Calibration (MUC), an inference-time intervention that steers activations along VUF directions to align VU with SU, substantially reducing confident hallucinations (≈29.6–30%) while improving SU–VU calibration. Crucially, VUFs are shown to generalize across datasets and model sizes, enabling non-tuning, universal calibration that enhances the reliability and nuance of LLM outputs in short-form QA tasks.

Abstract

LLMs often adopt an assertive language style also when making false claims. Such ``overconfident hallucinations'' mislead users and erode trust. Achieving the ability to express in language the actual degree of uncertainty around a claim is therefore of great importance. We find that ``verbal uncertainty'' is governed by a single linear feature in the representation space of LLMs, and show that this has only moderate correlation with the actual ``semantic uncertainty'' of the model. We apply this insight and show that (1) the mismatch between semantic and verbal uncertainty is a better predictor of hallucinations than semantic uncertainty alone and (2) we can intervene on verbal uncertainty at inference time and reduce confident hallucinations on short-form answers, achieving an average relative reduction of ~30%.

Figures (13)

• Figure 1: Illustration of our framework. We discover a linear verbal uncertainty feature (VUF) that controls model expression of uncertainty, and apply this insight to: (1) detect hallucinations arising from the miscalibration between high semantic uncertainty (SU) and low verbal uncertainty (VU); (2) mitigate hallucinations by intervening on activations along the VUF direction at inference time to make VU more aligned with model's SU. For example, when asked "What is the 29th largest city in England?", the model initially responds with "It's Bournemouth", exhibiting high SU and VU. By applying the VUF to intervention, we improve the VU to better align with the SU and the response becomes "Hmm, maybe Bournemouth?" -- demonstrating a nuanced expression of uncertainty.
• Figure 2: Evidence of verbal-semantic uncertainty miscalibration. This plot presents the Kernel Density Estimation (KDE) for samples from TriviaQA, categorized into four classes. These classes are based on the correctness of the answers generated by Llama3.1 and the consistency in abstaining. Miscalibration is indicated by high Semantic Entropy (proxy for SU) & low VU in hallucinated answers (red), and low SU & high VU in consistently abstained answers (blue).
• Figure 3: Visualization of verbalized certain (blue) vs. uncertain (pink) query representations exacted from selected layers of (a) Llama-3.1-8B-Instruct, (b) Mistral-7B-Instruct-v0.3, and (c) Qwen2.5-7B-Instruct on three datasets (TriviaQA, NQ-Open, PopQA). Please refer to Appendix \ref{['app:vuf']} for the visualization of representations exacted from all layers.
• Figure 4: Compare VUFs exacted from different datasets from Llama-3.1-8B-Instruct, Mistral-7B-Instruct-v0.3, and Qwen2.5-7B-Instruct
• Figure 5: Mean model-generated answer verbal uncertainty on three QA datasets with varying degrees of inference-time VUF intervention (modulated by the intervention intensity $\alpha$).