# Gradient-Stable Attention Heads Signal LLM Correctness

arXiv: https://arxiv.org/abs/2602.13699 · HTML: https://mlsanity.com/paper/2602.13699/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 25 of its 38 references that are in the map.
- First posted on arXiv 14 Feb 2026.

## Builds on (most cited first, 25 of 25)

- [A Unified Approach to Interpreting Model Predictions](https://mlsanity.com/paper/1705.07874/) (2017)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [HotpotQA: A Dataset for Diverse, Explainable Multi-hop Question Answering](https://mlsanity.com/paper/1809.09600/) (2018)
- [TriviaQA: A Large Scale Distantly Supervised Challenge Dataset for Reading Comprehension](https://mlsanity.com/paper/1705.03551/) (2017)
- [Language Models (Mostly) Know What They Know](https://mlsanity.com/paper/2207.05221/) (2022)
- [Large Language Models Encode Clinical Knowledge](https://mlsanity.com/paper/2212.13138/) (2022)
- [FEVER: a large-scale dataset for Fact Extraction and VERification](https://mlsanity.com/paper/1803.05355/) (2018)
- [A Gentle Introduction to Conformal Prediction and Distribution-Free Uncertainty Quantification](https://mlsanity.com/paper/2107.07511/) (2021)
- [INSIDE: LLMs' Internal States Retain the Power of Hallucination Detection](https://mlsanity.com/paper/2402.03744/) (2024)
- [Humans or LLMs as the Judge? A Study on Judgement Biases](https://mlsanity.com/paper/2402.10669/) (2024)
- [Semantic Entropy Probes: Robust and Cheap Hallucination Detection in LLMs](https://mlsanity.com/paper/2406.15927/) (2024)
- [A Survey of Confidence Estimation and Calibration in Large Language Models](https://mlsanity.com/paper/2311.08298/) (2023)
- [Judging the Judges: Evaluating Alignment and Vulnerabilities in LLMs-as-Judges](https://mlsanity.com/paper/2406.12624/) (2024)
- [Lookback Lens: Detecting and Mitigating Contextual Hallucinations in Large Language Models Using Only Attention Maps](https://mlsanity.com/paper/2407.07071/) (2024)
- [LLM Internal States Reveal Hallucination Risk Faced With a Query](https://mlsanity.com/paper/2407.03282/) (2024)
- [Calibrating Language Models with Adaptive Temperature Scaling](https://mlsanity.com/paper/2409.19817/) (2024)
- [On Early Detection of Hallucinations in Factual Question Answering](https://mlsanity.com/paper/2312.14183/) (2023)
- [Hallucination Detection in LLMs Using Spectral Features of Attention Maps](https://mlsanity.com/paper/2502.17598/) (2025)
- [No Answer Needed: Predicting LLM Answer Accuracy from Question-Only Linear Probes](https://mlsanity.com/paper/2509.10625/) (2025)
- [ICR Probe: Tracking Hidden State Dynamics for Reliable Hallucination Detection in LLMs](https://mlsanity.com/paper/2507.16488/) (2025)
- [InternalInspector I2: Robust Confidence Estimation in LLMs through Internal States](https://mlsanity.com/paper/2406.12053/) (2024)
- [Semantic Energy: Detecting LLM Hallucination Beyond Entropy](https://mlsanity.com/paper/2508.14496/) (2025)
- [Internal Causal Mechanisms Robustly Predict Language Model Out-of-Distribution Behaviors](https://mlsanity.com/paper/2505.11770/) (2025)
- [Suitability Filter: A Statistical Framework for Classifier Evaluation in Real-World Deployment Settings](https://mlsanity.com/paper/2505.22356/) (2025)
- [AggTruth: Contextual Hallucination Detection using Aggregated Attention Scores in LLMs](https://mlsanity.com/paper/2506.18628/) (2025)

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

- [</think> Doesn't Stop Reasoning: Analysis of Spurious CoT Termination](https://mlsanity.com/paper/2609.03633/) (2026)
- [Predicting Task Difficulty Without Rollouts](https://mlsanity.com/paper/2608.05797/) (2026)
- [No Universal Signal Predicts Sample-Level LLM Regression under Version Updates](https://mlsanity.com/paper/2608.13607/) (2026)
- [LongGuard: Mechanistic Analysis and Training-Free Mitigation of Long-Context Failure in Safety Guardrails](https://mlsanity.com/paper/2608.27580/) (2026)
- [From Saliency to Discriminability: Rank-Preserving Visual Token Pruning for VLM Rerankers](https://mlsanity.com/paper/2609.00667/) (2026)

## Abstract (arXiv)

Large language models (LLMs) often generate plausible yet incorrect answers, posing risks in safety-critical settings such as medicine. Human evaluation is expensive, and LLM-as-judge approaches risk introducing hidden errors. Recent single-pass white-box methods detect contextual hallucinations using linear probes over model internals, but their generalization to out-of-domain, out-of-task, and training-free settings remains poorly understood. We introduce HeadEntropy, a method that predicts answer correctness by measuring how susceptible each attention head's pattern is to modification under further gradient updates. The key insight is that the trace of the softmax Jacobian is a monotonic function of 2-Renyi entropy, linking attention spread to gradient stability during training, even without the reference annotation. With no training, HeadEntropy reaches 0.736 AUROC, outperforms every training-free baseline in paired comparison and matches a hidden-state probe out-of-domain, at under 1% of inference cost. We evaluate broadly across 5 instruction-tuned LLMs and 5 datasets spanning general knowledge, multi-hop reasoning, mathematical reasoning, claim verification, and medicine. The code is available at https://github.com/StanfordMIMI/HeadEntropy.