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

2025/08/28 by Lin Sun, Zhu, Yongfu, Sun, Lin +6
Computer Science · #Artificial Intelligence (cs.AI) #FOS: Computer and information sciences #Natural Language Processing Techniques #Semantic Web and Ontologies #Topic Modeling

paper · pdf · doi:10.48550/arxiv.2508.20384

openalex publication_date 2025/08/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

Citations

• Evaluation is All You Need: Strategic Overclaiming of LLM Reasoning Capabilities Through Evaluation Design
• A Sober Look at Progress in Language Model Reasoning: Pitfalls and Paths to Reproducibility
• Do LLMs estimate uncertainty well in instruction-following?
• SWIFT:A Scalable lightWeight Infrastructure for Fine-Tuning
• Uncertainty Estimation and Quantification for LLMs: A Simple Supervised Approach
• Just Ask for Calibration: Strategies for Eliciting Calibrated Confidence Scores from Language Models Fine-Tuned with Human Feedback
• Unsupervised Quality Estimation for Neural Machine Translation
• How Can We Know What Language Models Know?

Related

• When an LLM is apprehensive about its answers -- and when its uncertainty is justified
• Measuring Reasoning Utility in LLMs via Conditional Entropy Reduction
• Probabilities Are All You Need: A Probability-Only Approach to Uncertainty Estimation in Large Language Models
• Beyond Semantic Equivalence: Logical Graphs for LLM Uncertainty Quantification
• Kernel Language Entropy: Fine-grained Uncertainty Quantification for LLMs from Semantic Similarities