Distance Is All You Need: Radial Dispersion for Uncertainty Estimation in Large Language Models

TL;DR

The paper introduces Radial Dispersion Score (RDS), a simple, model-agnostic uncertainty metric for large language models that measures semantic variability via geometric dispersion in embedding space, outperforming existing methods.

Contribution

It proposes RDS, a novel, training-free uncertainty measure based on radial dispersion, which is scalable, effective, and extends to per-sample uncertainty estimation.

Findings

RDS outperforms nine recent state-of-the-art baselines in hallucination detection.

RDS remains robust and scalable across different sample sizes and embedding choices.

Code for RDS is publicly available at https://github.com/manhitv/RDS.

Abstract

Detecting uncertainty in large language models (LLMs) is essential for building reliable systems, yet many existing approaches are overly complex and depend on brittle semantic clustering or access to model internals. We introduce Radial Dispersion Score (RDS), a simple, training-free, fully model-agnostic uncertainty metric that measures the radial dispersion of sampled generations in embedding space. Specifically, given $N$ sampled generations embedded on the unit hypersphere, RDS computes the total l1 distance from the empirical centroid, i.e., the mean embedding, providing a direct geometric signal of semantic variability. A lightweight probability-weighted variant further incorporates the model's own token probabilities when available, outperforming nine recent state-of-the-art baselines. Moreover, RDS naturally extends to effective per-sample uncertainty estimates that complement probability- and consistency-based methods while remaining lightweight for practical use. Across four challenging free-form question-answering datasets and four LLMs, our metrics achieve state-of-the-art hallucination detection performance, while remaining robust and scalable with respect to sample size and embedding choice. These results highlight the practical value of RDS and its contribution toward improving the trustworthiness of LLMs. Code is publicly available at https://github.com/manhitv/RDS.