Mind the Unseen Mass: Unmasking LLM Hallucinations via Soft-Hybrid Alphabet Estimation

• URL: http://arxiv.org/abs/2604.19162v1
• Date: Tue, 21 Apr 2026 07:16:05 GMT
• Title: Mind the Unseen Mass: Unmasking LLM Hallucinations via Soft-Hybrid Alphabet Estimation
• Abstract summary: This paper studies uncertainty quantification for large language models under black-box access.<n> estimating the effective semantic alphabet size--that is, the number of distinct meanings expressed in the sampled responses--provides a useful proxy for downstream risk.<n>We propose SHADE, a simple and interpretable estimator that combines Good-Turing coverage with a heat- kernel trace of the normalized Laplacian.
• Score: 1.1230191950153754
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: This paper studies uncertainty quantification for large language models (LLMs) under black-box access, where only a small number of responses can be sampled for each query. In this setting, estimating the effective semantic alphabet size--that is, the number of distinct meanings expressed in the sampled responses--provides a useful proxy for downstream risk. However, frequency-based estimators tend to undercount rare semantic modes when the sample size is small, while graph-spectral quantities alone are not designed to estimate semantic occupancy accurately. To address this issue, we propose SHADE (Soft-Hybrid Alphabet Dynamic Estimator), a simple and interpretable estimator that combines Generalized Good-Turing coverage with a heat-kernel trace of the normalized Laplacian constructed from an entailment-weighted graph over sampled responses. The estimated coverage adaptively determines the fusion rule: under high coverage, SHADE uses a convex combination of the two signals, while under low coverage it applies a LogSumExp fusion to emphasize missing or weakly observed semantic modes. A finite-sample correction is then introduced to stabilize the resulting cardinality estimate before converting it into a coverage-adjusted semantic entropy score. Experiments on pooled semantic alphabet-size estimation against large-sample references and on QA incorrectness detection show that SHADE achieves the strongest improvements in the most sample-limited regime, while the performance gap narrows as the number of samples increases. These results suggest that hybrid semantic occupancy estimation is particularly beneficial when black-box uncertainty quantification must operate under tight sampling budgets.

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