# Semantic Energy: Detecting LLM Hallucination Beyond Entropy

arXiv: https://arxiv.org/abs/2508.14496 · HTML: https://mlsanity.com/paper/2508.14496/

## Key facts

- Cited by 18 papers in the map (data through 14 Oct 2026).
- Builds on 36 of its 47 references that are in the map.
- First posted on arXiv 20 Aug 2025.

## Builds on (most cited first, 30 of 36)

- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (2022)
- [TriviaQA: A Large Scale Distantly Supervised Challenge Dataset for Reading Comprehension](https://mlsanity.com/paper/1705.03551/) (2017)
- [Energy-based Out-of-distribution Detection](https://mlsanity.com/paper/2010.03759/) (2020)
- [Can LLMs Express Their Uncertainty? An Empirical Evaluation of Confidence Elicitation in LLMs](https://mlsanity.com/paper/2306.13063/) (2023)
- [Semantic Uncertainty: Linguistic Invariances for Uncertainty Estimation in Natural Language Generation](https://mlsanity.com/paper/2302.09664/) (2023)
- [The Entropy Mechanism of Reinforcement Learning for Reasoning Language Models](https://mlsanity.com/paper/2505.22617/) (2025)
- [Generating with Confidence: Uncertainty Quantification for Black-box Large Language Models](https://mlsanity.com/paper/2305.19187/) (2023)
- [Reasoning with Exploration: An Entropy Perspective](https://mlsanity.com/paper/2506.14758/) (2025)
- [On Hallucination and Predictive Uncertainty in Conditional Language Generation](https://mlsanity.com/paper/2103.15025/) (2021)
- [The Unreasonable Effectiveness of Entropy Minimization in LLM Reasoning](https://mlsanity.com/paper/2505.15134/) (2025)
- [Shifting Attention to Relevance: Towards the Predictive Uncertainty Quantification of Free-Form Large Language Models](https://mlsanity.com/paper/2307.01379/) (2023)
- [Right Question is Already Half the Answer: Fully Unsupervised LLM Reasoning Incentivization](https://mlsanity.com/paper/2504.05812/) (2025)
- [Uncertainty Estimation and Quantification for LLMs: A Simple Supervised Approach](https://mlsanity.com/paper/2404.15993/) (2024)
- [Calibrating Large Language Models with Sample Consistency](https://mlsanity.com/paper/2402.13904/) (2024)
- [SPUQ: Perturbation-Based Uncertainty Quantification for Large Language Models](https://mlsanity.com/paper/2403.02509/) (2024)
- [A Survey of Uncertainty Estimation in LLMs: Theory Meets Practice](https://mlsanity.com/paper/2410.15326/) (2024)
- [First Return, Entropy-Eliciting Explore](https://mlsanity.com/paper/2507.07017/) (2025)
- [Chinese SimpleQA: A Chinese Factuality Evaluation for Large Language Models](https://mlsanity.com/paper/2411.07140/) (2024)
- [Uncertainty-Guided Chain-of-Thought for Code Generation with LLMs](https://mlsanity.com/paper/2503.15341/) (2025)
- [Improving Uncertainty Quantification in Large Language Models via Semantic Embeddings](https://mlsanity.com/paper/2410.22685/) (2024)
- [R2R: Efficiently Navigating Divergent Reasoning Paths with Small-Large Model Token Routing](https://mlsanity.com/paper/2505.21600/) (2025)
- [Estimating LLM Uncertainty with Evidence](https://mlsanity.com/paper/2502.00290/) (2025)
- [TokUR: Token-Level Uncertainty Estimation for Large Language Model Reasoning](https://mlsanity.com/paper/2505.11737/) (2025)
- [Revisiting Uncertainty Estimation and Calibration of Large Language Models](https://mlsanity.com/paper/2505.23854/) (2025)
- [Uncertainty-Aware Step-wise Verification with Generative Reward Models](https://mlsanity.com/paper/2502.11250/) (2025)
- [SLED: Self Logits Evolution Decoding for Improving Factuality in Large Language Models](https://mlsanity.com/paper/2411.02433/) (2024)
- [Empowering GraphRAG with Knowledge Filtering and Integration](https://mlsanity.com/paper/2503.13804/) (2025)
- [Language Model Uncertainty Quantification with Attention Chain](https://mlsanity.com/paper/2503.19168/) (2025)
- [Query-Level Uncertainty in Large Language Models](https://mlsanity.com/paper/2506.09669/) (2025)

## Built on by (most cited first, 18 of 18)

- [Chain-of-Thought as a Lens: Evaluating Structured Reasoning Alignment between Human Preferences and Large Language Models](https://mlsanity.com/paper/2511.06168/) (2025)
- [Gradient-Stable Attention Heads Signal LLM Correctness](https://mlsanity.com/paper/2602.13699/) (2026)
- [Semantic Reformulation Entropy for Robust Hallucination Detection in QA Tasks](https://mlsanity.com/paper/2509.17445/) (2025)
- [The Alignment Tax: Response Homogenization in Aligned LLMs and Its Implications for Uncertainty Estimation](https://mlsanity.com/paper/2603.24124/) (2026)
- [Sparse Growing Transformer: Training-Time Sparse Depth Allocation via Progressive Attention Looping](https://mlsanity.com/paper/2603.23998/) (2026)
- [Hallucination as Commitment Failure: Larger LLMs Misfire Despite Knowing the Answer](https://mlsanity.com/paper/2605.22007/) (2026)
- [FaithSCAN: Model-Driven Single-Pass Hallucination Detection for Faithful Visual Question Answering](https://mlsanity.com/paper/2601.00269/) (2026)
- ["I May Not Have Articulated Myself Clearly": Diagnosing Dynamic Instability in LLM Reasoning at Inference Time](https://mlsanity.com/paper/2602.02863/) (2026)
- [Self-Calibrating Language Models via Test-Time Discriminative Distillation](https://mlsanity.com/paper/2604.09624/) (2026)
- [False Fixed Points: Kantian Feedback, Stable Miscalibration, and Representational Compression in LLMs](https://mlsanity.com/paper/2510.14925/) (2025)
- [Calibrated Confidence Estimation for Tabular Question Answering](https://mlsanity.com/paper/2604.12491/) (2026)
- [Position: Uncertainty Quantification in LLMs is Just Unsupervised Clustering](https://mlsanity.com/paper/2605.19220/) (2026)
- [Leveraging Visual Signals for Robust Token-Level Uncertainty in Vision-Language Generation](https://mlsanity.com/paper/2605.27136/) (2026)
- [The Role of Ambiguity in Error Prediction via Uncertainty Quantification](https://mlsanity.com/paper/2606.02093/) (2026)
- [Forewarned is Forearmed: When Non-Sequential Embedding Turns Into an Anomaly Detector](https://mlsanity.com/paper/2606.30196/) (2026)
- [Beyond Semantic Equivalence: Logical Graphs for LLM Uncertainty Quantification](https://mlsanity.com/paper/2607.16868/) (2026)
- [LODESTAR: Robust Entropy-Based Answer Selection in Retrieval-Augmented Generation for Question Answering -- Directing Frozen-LLM Entropy with a Reinforcement-Learned Prompt Polarizer under Misleading Passages](https://mlsanity.com/paper/2608.11922/) (2026)
- [From Tokens to Semantics: Leveraging Complementary Signals for Hallucination Detection in Black-Box LLMs](https://mlsanity.com/paper/2609.02679/) (2026)

## Abstract (arXiv)

Large Language Models (LLMs) are being increasingly deployed in real-world applications, but they remain susceptible to hallucinations, which produce fluent yet incorrect responses and lead to erroneous decision-making. Uncertainty estimation is a feasible approach to detect such hallucinations. For example, semantic entropy estimates uncertainty by considering the semantic diversity across multiple sampled responses, thus identifying hallucinations. However, semantic entropy relies on post-softmax probabilities and fails to capture the model's inherent uncertainty, causing it to be ineffective in certain scenarios. To address this issue, we introduce Semantic Energy, a novel uncertainty estimation framework that leverages the inherent confidence of LLMs by operating directly on logits of penultimate layer. By combining semantic clustering with a Boltzmann-inspired energy distribution, our method better captures uncertainty in cases where semantic entropy fails. Experiments across multiple benchmarks show that Semantic Energy significantly improves hallucination detection and uncertainty estimation, offering more reliable signals for downstream applications such as hallucination detection.