# Uncertainty Under the Curve: A Sequence-Level Entropy Area Metric for Reasoning LLM

arXiv: https://arxiv.org/abs/2508.20384 · HTML: https://mlsanity.com/paper/2508.20384/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Placed in Test-time compute and efficient thinking, one of 17 directions in LLM reasoning.
- Builds on 11 of its 21 references that are in the map.
- First posted on arXiv 28 Aug 2025.

## Placed in

- LLM reasoning / [Test-time compute and efficient thinking](https://mlsanity.com/lr/test-time-compute-and-efficient-thinking/)

## Builds on (most cited first, 11 of 11)

- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [Language Models (Mostly) Know What They Know](https://mlsanity.com/paper/2207.05221/) (2022)
- [Teaching Models to Express Their Uncertainty in Words](https://mlsanity.com/paper/2205.14334/) (2022)
- [Kimi K2: Open Agentic Intelligence](https://mlsanity.com/paper/2507.20534/) (2025)
- [SWIFT:A Scalable lightWeight Infrastructure for Fine-Tuning](https://mlsanity.com/paper/2408.05517/) (2024)
- [Light-R1: Curriculum SFT, DPO and RL for Long COT from Scratch and Beyond](https://mlsanity.com/paper/2503.10460/) (2025)
- [A Sober Look at Progress in Language Model Reasoning: Pitfalls and Paths to Reproducibility](https://mlsanity.com/paper/2504.07086/) (2025)
- [Uncertainty Estimation and Quantification for LLMs: A Simple Supervised Approach](https://mlsanity.com/paper/2404.15993/) (2024)
- [Exploring the Limit of Outcome Reward for Learning Mathematical Reasoning](https://mlsanity.com/paper/2502.06781/) (2025)
- [Do LLMs estimate uncertainty well in instruction-following?](https://mlsanity.com/paper/2410.14582/) (2024)
- [Evaluation is All You Need: Strategic Overclaiming of LLM Reasoning Capabilities Through Evaluation Design](https://mlsanity.com/paper/2506.04734/) (2025)

## Built on by (most cited first, 5 of 5)

- [From Efficiency to Adaptivity: A Deeper Look at Adaptive Reasoning in Large Language Models](https://mlsanity.com/paper/2511.10788/) (2025)
- [The Alignment Tax: Response Homogenization in Aligned LLMs and Its Implications for Uncertainty Estimation](https://mlsanity.com/paper/2603.24124/) (2026)
- [InstructDiff: Domain-Adaptive Data Selection via Differential Entropy for Efficient LLM Fine-Tuning](https://mlsanity.com/paper/2601.23006/) (2026)
- [InfoDensity: Rewarding Information-Dense Traces for Efficient Reasoning](https://mlsanity.com/paper/2603.17310/) (2026)
- [From Tokens to Semantics: Leveraging Complementary Signals for Hallucination Detection in Black-Box LLMs](https://mlsanity.com/paper/2609.02679/) (2026)

## Abstract (arXiv)

In this work, we introduce Entropy Area Score (EAS), a simple yet effective metric to quantify uncertainty in the answer generation process of reasoning large language models (LLMs). EAS requires neither external models nor repeated sampling, it integrates token-level predictive entropy from the model itself to capture the evolution of uncertainty during generation. Empirical results show that EAS is strongly correlated with answer entropy across models and datasets. In training data selection, EAS identifies high-potential samples and consistently outperforms Pass Rate filtering under equal sample budgets, improving student model accuracy on math benchmarks. EAS is both efficient and interpretable, offering a practical tool for uncertainty modeling and data quality assessment in LLM training.