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.

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