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

arXiv: https://arxiv.org/abs/2604.19162 · HTML: https://mlsanity.com/paper/2604.19162/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 26 of its 38 references that are in the map.
- First posted on arXiv 21 Apr 2026.

## Builds on (most cited first, 26 of 26)

- [SQuAD: 100,000+ Questions for Machine Comprehension of Text](https://mlsanity.com/paper/1606.05250/) (2016)
- [HotpotQA: A Dataset for Diverse, Explainable Multi-hop Question Answering](https://mlsanity.com/paper/1809.09600/) (2018)
- [OPT: Open Pre-trained Transformer Language Models](https://mlsanity.com/paper/2205.01068/) (2022)
- [TriviaQA: A Large Scale Distantly Supervised Challenge Dataset for Reading Comprehension](https://mlsanity.com/paper/1705.03551/) (2017)
- [Survey of Hallucination in Natural Language Generation](https://mlsanity.com/paper/2202.03629/) (2022)
- [Phi-3 Technical Report: A Highly Capable Language Model Locally on Your Phone](https://mlsanity.com/paper/2404.14219/) (2024)
- [DeBERTaV3: Improving DeBERTa using ELECTRA-Style Pre-Training with Gradient-Disentangled Embedding Sharing](https://mlsanity.com/paper/2111.09543/) (2021)
- [Semantic Uncertainty: Linguistic Invariances for Uncertainty Estimation in Natural Language Generation](https://mlsanity.com/paper/2302.09664/) (2023)
- [CoQA: A Conversational Question Answering Challenge](https://mlsanity.com/paper/1808.07042/) (2018)
- [A Survey of Hallucination in Large Foundation Models](https://mlsanity.com/paper/2309.05922/) (2023)
- [INSIDE: LLMs' Internal States Retain the Power of Hallucination Detection](https://mlsanity.com/paper/2402.03744/) (2024)
- [Semantic Entropy Probes: Robust and Cheap Hallucination Detection in LLMs](https://mlsanity.com/paper/2406.15927/) (2024)
- [Graph Random Neural Network for Semi-Supervised Learning on Graphs](https://mlsanity.com/paper/2005.11079/) (2020)
- [Kernel Language Entropy: Fine-grained Uncertainty Quantification for LLMs from Semantic Similarities](https://mlsanity.com/paper/2405.20003/) (2024)
- [A Survey on Uncertainty Quantification of Large Language Models: Taxonomy, Open Research Challenges, and Future Directions](https://mlsanity.com/paper/2412.05563/) (2024)
- [Quantifying Uncertainty in Answers from any Language Model and Enhancing their Trustworthiness](https://mlsanity.com/paper/2308.16175/) (2023)
- [Uncertainty Quantification and Confidence Calibration in Large Language Models: A Survey](https://mlsanity.com/paper/2503.15850/) (2025)
- [Beyond Semantic Entropy: Boosting LLM Uncertainty Quantification with Pairwise Semantic Similarity](https://mlsanity.com/paper/2506.00245/) (2025)
- [Verify when Uncertain: Beyond Self-Consistency in Black Box Hallucination Detection](https://mlsanity.com/paper/2502.15845/) (2025)
- [Superpixel-based and Spatially-regularized Diffusion Learning for Unsupervised Hyperspectral Image Clustering](https://mlsanity.com/paper/2312.15447/) (2023)
- [Uncertainty Estimation by Flexible Evidential Deep Learning](https://mlsanity.com/paper/2510.18322/) (2025)
- [Estimating Semantic Alphabet Size for LLM Uncertainty Quantification](https://mlsanity.com/paper/2509.14478/) (2025)
- [Learning Where to Embed: Noise-Aware Positional Embedding for Query Retrieval in Small-Object Detection](https://mlsanity.com/paper/2604.15065/) (2026)
- [Bilateral Signal Warping for Left Ventricular Hypertrophy Diagnosis](https://mlsanity.com/paper/2411.08819/) (2024)
- [On the Effectiveness of Random Weights in Graph Neural Networks](https://mlsanity.com/paper/2502.00190/) (2025)
- [Efficient Hallucination Detection: Adaptive Bayesian Estimation of Semantic Entropy with Guided Semantic Exploration](https://mlsanity.com/paper/2603.22812/) (2026)

## Abstract (arXiv)

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.