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

arXiv: https://arxiv.org/abs/2512.04351 · HTML: https://mlsanity.com/paper/2512.04351/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 30 of its 38 references that are in the map.
- First posted on arXiv 4 Dec 2025.

## Builds on (most cited first, 30 of 30)

- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Sentence-BERT: Sentence Embeddings using Siamese BERT-Networks](https://mlsanity.com/paper/1908.10084/) (2019)
- [Efficient Memory Management for Large Language Model Serving with PagedAttention](https://mlsanity.com/paper/2309.06180/) (2023)
- [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (2022)
- [GPQA: A Graduate-Level Google-Proof Q&A Benchmark](https://mlsanity.com/paper/2311.12022/) (2023)
- [Survey of Hallucination in Natural Language Generation](https://mlsanity.com/paper/2202.03629/) (2022)
- [Gemma 2: Improving Open Language Models at a Practical Size](https://mlsanity.com/paper/2408.00118/) (2024)
- [Language Models (Mostly) Know What They Know](https://mlsanity.com/paper/2207.05221/) (2022)
- [A Survey on Hallucination in Large Language Models: Principles, Taxonomy, Challenges, and Open Questions](https://mlsanity.com/paper/2311.05232/) (2023)
- [Gemma: Open Models Based on Gemini Research and Technology](https://mlsanity.com/paper/2403.08295/) (2024)
- [Are NLP Models really able to Solve Simple Math Word Problems?](https://mlsanity.com/paper/2103.07191/) (2021)
- [Semantic Uncertainty: Linguistic Invariances for Uncertainty Estimation in Natural Language Generation](https://mlsanity.com/paper/2302.09664/) (2023)
- [SelfCheckGPT: Zero-Resource Black-Box Hallucination Detection for Generative Large Language Models](https://mlsanity.com/paper/2303.08896/) (2023)
- [Crowdsourcing Multiple Choice Science Questions](https://mlsanity.com/paper/1707.06209/) (2017)
- [The Falcon Series of Open Language Models](https://mlsanity.com/paper/2311.16867/) (2023)
- [INSIDE: LLMs' Internal States Retain the Power of Hallucination Detection](https://mlsanity.com/paper/2402.03744/) (2024)
- [Generating with Confidence: Uncertainty Quantification for Black-box Large Language Models](https://mlsanity.com/paper/2305.19187/) (2023)
- [Universal Self-Consistency for Large Language Model Generation](https://mlsanity.com/paper/2311.17311/) (2023)
- [Scalable Best-of-N Selection for Large Language Models via Self-Certainty](https://mlsanity.com/paper/2502.18581/) (2025)
- [Kernel Language Entropy: Fine-grained Uncertainty Quantification for LLMs from Semantic Similarities](https://mlsanity.com/paper/2405.20003/) (2024)
- [Augmented SBERT: Data Augmentation Method for Improving Bi-Encoders for Pairwise Sentence Scoring Tasks](https://mlsanity.com/paper/2010.08240/) (2020)
- [Decomposing Uncertainty for Large Language Models through Input Clarification Ensembling](https://mlsanity.com/paper/2311.08718/) (2023)
- [Looking for a Needle in a Haystack: A Comprehensive Study of Hallucinations in Neural Machine Translation](https://mlsanity.com/paper/2208.05309/) (2022)
- [Integrate the Essence and Eliminate the Dross: Fine-Grained Self-Consistency for Free-Form Language Generation](https://mlsanity.com/paper/2407.02056/) (2024)
- [Geometric Uncertainty for Detecting and Correcting Hallucinations in LLMs](https://mlsanity.com/paper/2509.13813/) (2025)
- [Understanding Neural Networks with Logarithm Determinant Entropy Estimator](https://mlsanity.com/paper/2105.03705/) (2021)
- [Representation biases in sentence transformers](https://mlsanity.com/paper/2301.13039/) (2023)
- [Simple Yet Effective: An Information-Theoretic Approach to Multi-LLM Uncertainty Quantification](https://mlsanity.com/paper/2507.07236/) (2025)
- [Probabilities Are All You Need: A Probability-Only Approach to Uncertainty Estimation in Large Language Models](https://mlsanity.com/paper/2511.07694/) (2025)

## Built on by (most cited first, 1 of 1)

- [Beyond Majority Voting: Efficient Best-Of-N with Radial Consensus Score](https://mlsanity.com/paper/2604.12196/) (2026)

## Abstract (arXiv)

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.