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Entropy Distribution as a Fingerprint for Hallucinations in Generative Models

NeurIPS 2026 · Large language models › Language, safety and interpretability · approach: Data and hallucination detection · 0 citations (OpenAlex)

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Proposes Calibrated Entropy Score (CES), a single-pass black-box hallucination detector that combines mean and max token entropy through a calibrated reference CDF, with a random-length DKW bound and exponential power guarantees.

Problem

Hallucination detection in LLMs typically needs multiple samples or model internals, while single-pass entropy heuristics (perplexity, length-normalised entropy) collapse the token-entropy signal to a single scalar and discard distributional information.

Approach

Treat hallucination detection as a hypothesis test: compare a generation's token-entropy sequence against a reference CDF estimated from oracle-labelled non-hallucinated data, scoring it with the geometric mean of the CDF evaluated at the mean and max entropy; supported by a random-length DKW inequality and exponential power bounds.

Key results

• CES (unsupervised) wins 66.8% of pairwise comparisons against the 16 benchmark methods and is in the top Nemenyi clique with average rank 6.29.
• 72 of 80 model-dataset experiments show significant two-sample KS separation of faithful vs hallucinated token entropies (median d_KS 0.100); 80/80 remain significant after mean-centring.
• On Meta-Llama-3-8B-Instruct, CES (unsup) reaches AUROC 0.685 on GSM8K, the best single-run score, while multi-sample KLE and SelfCheckGPT are competitive or better on some datasets.

Surprising findings

• Mean-centred entropy sequences still differ significantly between faithful and hallucinated generations in all 80 experiments, indicating shape signal beyond mean shift.
• Embedding Regression outperforms CES on several datasets for GPT-4o-mini, e.g. CoQA, NQ-Open, SVAMP and TriviaQA, contrary to the claim of overall dominance.

Limitations

• Power degrades for short generations (fewer than 10 tokens) and the conditional i.i.d. assumption is not strictly true.
• Evaluation uses in-sample ECDF construction and in-sample AUROC on the same 500 samples, with no held-out split.
• Requires next-token or top-k logit access unavailable from some API providers; quality bounded by oracle labels; only greedy short-answer QA tested.

Experimental setup

Datasets: BioASQ CoQA DROP GSM8K NQ-Open SQuAD SVAMP TriviaQA

Benchmarks: BioASQ CoQA DROP GSM8K NQ-Open SQuAD SVAMP TriviaQA

Metrics: AUROC pairwise win rate average rank (Friedman/Nemenyi) KS distance

Baselines: Semantic Entropy Discrete Semantic Entropy KLE KLE-full Eigenscore Effective Rank SelfCheckGPT Embedding Regression P(True) FAVA Length-Normalised Entropy Perplexity

Builds on: Semantic Entropy Kernel Language Entropy SelfCheckGPT Dvoretzky-Kiefer-Wolfowitz inequality

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