# Directional Concentration Uncertainty: A representational approach to uncertainty quantification for generative models

arXiv: https://arxiv.org/abs/2602.13264 · HTML: https://mlsanity.com/paper/2602.13264/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 18 of its 25 references that are in the map.
- First posted on arXiv 4 Feb 2026.

## Builds on (most cited first, 18 of 18)

- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [SQuAD: 100,000+ Questions for Machine Comprehension of Text](https://mlsanity.com/paper/1606.05250/) (2016)
- [TriviaQA: A Large Scale Distantly Supervised Challenge Dataset for Reading Comprehension](https://mlsanity.com/paper/1705.03551/) (2017)
- [Learn to Explain: Multimodal Reasoning via Thought Chains for Science Question Answering](https://mlsanity.com/paper/2209.09513/) (2022)
- [Semantic Uncertainty: Linguistic Invariances for Uncertainty Estimation in Natural Language Generation](https://mlsanity.com/paper/2302.09664/) (2023)
- [Generating with Confidence: Uncertainty Quantification for Black-box Large Language Models](https://mlsanity.com/paper/2305.19187/) (2023)
- [Conformal Language Modeling](https://mlsanity.com/paper/2306.10193/) (2023)
- [Benchmarking LLMs via Uncertainty Quantification](https://mlsanity.com/paper/2401.12794/) (2024)
- [Uncertainty Quantification with Pre-trained Language Models: A Large-Scale Empirical Analysis](https://mlsanity.com/paper/2210.04714/) (2022)
- [Uncertainty Quantification and Confidence Calibration in Large Language Models: A Survey](https://mlsanity.com/paper/2503.15850/) (2025)
- [Can Knowledge Graphs Reduce Hallucinations in LLMs? : A Survey](https://mlsanity.com/paper/2311.07914/) (2023)
- [SPUQ: Perturbation-Based Uncertainty Quantification for Large Language Models](https://mlsanity.com/paper/2403.02509/) (2024)
- [Uncertainty Quantification for In-Context Learning of Large Language Models](https://mlsanity.com/paper/2402.10189/) (2024)
- [UProp: Investigating the Uncertainty Propagation of LLMs in Multi-Step Agentic Decision-Making](https://mlsanity.com/paper/2506.17419/) (2025)
- [Mechanistic Understanding and Mitigation of Language Model Non-Factual Hallucinations](https://mlsanity.com/paper/2403.18167/) (2024)
- [Can Knowledge Graphs Make Large Language Models More Trustworthy? An Empirical Study Over Open-ended Question Answering](https://mlsanity.com/paper/2410.08085/) (2024)
- [Non-Exchangeable Conformal Language Generation with Nearest Neighbors](https://mlsanity.com/paper/2402.00707/) (2024)
- [Towards Transparent AI: A Survey on Explainable Language Models](https://mlsanity.com/paper/2509.21631/) (2025)

## Abstract (arXiv)

In the critical task of making generative models trustworthy and robust, methods for Uncertainty Quantification (UQ) have begun to show encouraging potential. However, many of these methods rely on rigid heuristics that fail to generalize across tasks and modalities. Here, we propose a novel framework for UQ that is highly flexible and approaches or surpasses the performance of prior heuristic methods. We introduce Directional Concentration Uncertainty (DCU), a novel statistical procedure for quantifying the concentration of embeddings based on the von Mises-Fisher (vMF) distribution. Our method captures uncertainty by measuring the geometric dispersion of multiple generated outputs from a language model using continuous embeddings of the generated outputs without any task specific heuristics. In our experiments, we show that DCU matches or exceeds calibration levels of prior works like semantic entropy (Kuhn et al., 2023) and also generalizes well to more complex tasks in multi-modal domains. We present a framework for the wider potential of DCU and its implications for integration into UQ for multi-modal and agentic frameworks.