@inproceedings{zhang-etal-2026-sampling,
title = "Sampling Less, Knowing More: Contradiction-aware Adaptive Spectral and Entropic Uncertainty Quantification for {LLM}s",
author = "Zhang, Jiaming and
Lu, Heng-yang and
Chen, Xinan and
Zheng, Junyuan and
Jiang, Yuncheng and
Zhu, Ying and
Fan, Chenyou",
editor = "Lee, Hung-Yi and
Dev, Sunipa and
Li, Jessy and
Elliott, Desmond",
booktitle = "Proceedings of the 2026 Conference on Empirical Methods in Natural Language Processing",
month = oct,
year = "2026",
address = "Budapest, Hungary",
publisher = "Association for Computational Linguistics",
url = "https://aclanthology.org/2026.emnlp-main.1093/",
pages = "25092--25106",
ISBN = "979-8-89176-459-0",
abstract = "Uncertainty quantification (UQ) is essential for improving the reliability of large language models (LLMs). However, multi-sample UQ methods typically employ a fixed sampling budget for all queries, leading to computational redundancy. In addition, multi-sample UQ methods often fail in the presence of consistent errors. To address these limitations, we propose CASE (Contradiction-aware Adaptive Spectral and Entropic UQ), a UQ framework that jointly models semantic disagreement and token-level uncertainty under an adaptive sampling paradigm. Specifically, CASE constructs a contradiction graph over sampled responses and quantifies semantic disagreement using normalized spectral norms of the graph representation. The resulting uncertainty signals are further leveraged for adaptive sampling, enabling query-dependent budget allocation while reducing redundant computation. In addition, CASE incorporates token-level predictive entropy as a complementary uncertainty signal to mitigate the failure of graph structures under consistent errors. Experimental results demonstrate that CASE outperforms existing multi-sample UQ methods across factual question answering datasets while reducing sampling costs by over 30{\%} on average."
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<abstract>Uncertainty quantification (UQ) is essential for improving the reliability of large language models (LLMs). However, multi-sample UQ methods typically employ a fixed sampling budget for all queries, leading to computational redundancy. In addition, multi-sample UQ methods often fail in the presence of consistent errors. To address these limitations, we propose CASE (Contradiction-aware Adaptive Spectral and Entropic UQ), a UQ framework that jointly models semantic disagreement and token-level uncertainty under an adaptive sampling paradigm. Specifically, CASE constructs a contradiction graph over sampled responses and quantifies semantic disagreement using normalized spectral norms of the graph representation. The resulting uncertainty signals are further leveraged for adaptive sampling, enabling query-dependent budget allocation while reducing redundant computation. In addition, CASE incorporates token-level predictive entropy as a complementary uncertainty signal to mitigate the failure of graph structures under consistent errors. Experimental results demonstrate that CASE outperforms existing multi-sample UQ methods across factual question answering datasets while reducing sampling costs by over 30% on average.</abstract>
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%0 Conference Proceedings
%T Sampling Less, Knowing More: Contradiction-aware Adaptive Spectral and Entropic Uncertainty Quantification for LLMs
%A Zhang, Jiaming
%A Lu, Heng-yang
%A Chen, Xinan
%A Zheng, Junyuan
%A Jiang, Yuncheng
%A Zhu, Ying
%A Fan, Chenyou
%Y Lee, Hung-Yi
%Y Dev, Sunipa
%Y Li, Jessy
%Y Elliott, Desmond
%S Proceedings of the 2026 Conference on Empirical Methods in Natural Language Processing
%D 2026
%8 October
%I Association for Computational Linguistics
%C Budapest, Hungary
%@ 979-8-89176-459-0
%F zhang-etal-2026-sampling
%X Uncertainty quantification (UQ) is essential for improving the reliability of large language models (LLMs). However, multi-sample UQ methods typically employ a fixed sampling budget for all queries, leading to computational redundancy. In addition, multi-sample UQ methods often fail in the presence of consistent errors. To address these limitations, we propose CASE (Contradiction-aware Adaptive Spectral and Entropic UQ), a UQ framework that jointly models semantic disagreement and token-level uncertainty under an adaptive sampling paradigm. Specifically, CASE constructs a contradiction graph over sampled responses and quantifies semantic disagreement using normalized spectral norms of the graph representation. The resulting uncertainty signals are further leveraged for adaptive sampling, enabling query-dependent budget allocation while reducing redundant computation. In addition, CASE incorporates token-level predictive entropy as a complementary uncertainty signal to mitigate the failure of graph structures under consistent errors. Experimental results demonstrate that CASE outperforms existing multi-sample UQ methods across factual question answering datasets while reducing sampling costs by over 30% on average.
%U https://aclanthology.org/2026.emnlp-main.1093/
%P 25092-25106
Markdown (Informal)
[Sampling Less, Knowing More: Contradiction-aware Adaptive Spectral and Entropic Uncertainty Quantification for LLMs](https://aclanthology.org/2026.emnlp-main.1093/) (Zhang et al., EMNLP 2026)
ACL
- Jiaming Zhang, Heng-yang Lu, Xinan Chen, Junyuan Zheng, Yuncheng Jiang, Ying Zhu, and Chenyou Fan. 2026. Sampling Less, Knowing More: Contradiction-aware Adaptive Spectral and Entropic Uncertainty Quantification for LLMs. In Proceedings of the 2026 Conference on Empirical Methods in Natural Language Processing, pages 25092–25106, Budapest, Hungary. Association for Computational Linguistics.