SeSE: Black-Box Uncertainty Quantification for Large Language Models Based on Structural Information Theory

Xingtao Zhao, Hao Peng, Dingli Su, Xianghua Zeng, Chunyang Liu, Jinzhi Liao, Philip S. Yu
Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence, PMLR 337:8209-8237, 2026.

Abstract

Reliable uncertainty quantification (UQ) is essential for deploying large language models ({LLMs}) in safety-critical scenarios, as it enables them to abstain from responding when uncertain, thereby avoiding hallucinations, i.e., plausible yet factually incorrect responses. However, while current semantic UQ methods have achieved state-of-the-art performance, they inherently overlook latent semantic structural information that could enable more precise uncertainty estimates. In this paper, we propose Semantic Structural Entropy ({SeSE}), a principled black-box UQ framework applicable to both open- and closed-source {LLMs}. To reveal the intrinsic structure of the {LLM} semantic space, {SeSE} constructs its hierarchical abstraction based on the principle of structural entropy minimization. The structural entropy of the resulting optimal hierarchical abstraction thus quantifies the inherent uncertainty within the semantic space after optimal compression. Additionally, unlike existing methods that primarily focus on simple short-form generation, we extend {SeSE} to provide interpretable and granular uncertainty estimation for long-form outputs. We theoretically prove that {SeSE} generalizes semantic entropy, the gold standard for UQ in {LLMs}, and empirically demonstrate its superior performance over baselines across 24 model-dataset combinations.

Cite this Paper

BibTeX
@InProceedings{pmlr-v337-zhao26b, title = {{SeSE}: Black-Box Uncertainty Quantification for Large Language Models Based on Structural Information Theory}, author = {Zhao, Xingtao and Peng, Hao and Su, Dingli and Zeng, Xianghua and Liu, Chunyang and Liao, Jinzhi and Yu, Philip S.}, booktitle = {Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence}, pages = {8209--8237}, year = {2026}, editor = {Perković, Emilija and Malinsky, Daniel}, volume = {337}, series = {Proceedings of Machine Learning Research}, month = {17--21 Aug}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v337/main/assets/zhao26b/zhao26b.pdf}, url = {https://proceedings.mlr.press/v337/zhao26b.html}, abstract = {Reliable uncertainty quantification (UQ) is essential for deploying large language models ({LLMs}) in safety-critical scenarios, as it enables them to abstain from responding when uncertain, thereby avoiding hallucinations, i.e., plausible yet factually incorrect responses. However, while current semantic UQ methods have achieved state-of-the-art performance, they inherently overlook latent semantic structural information that could enable more precise uncertainty estimates. In this paper, we propose Semantic Structural Entropy ({SeSE}), a principled black-box UQ framework applicable to both open- and closed-source {LLMs}. To reveal the intrinsic structure of the {LLM} semantic space, {SeSE} constructs its hierarchical abstraction based on the principle of structural entropy minimization. The structural entropy of the resulting optimal hierarchical abstraction thus quantifies the inherent uncertainty within the semantic space after optimal compression. Additionally, unlike existing methods that primarily focus on simple short-form generation, we extend {SeSE} to provide interpretable and granular uncertainty estimation for long-form outputs. We theoretically prove that {SeSE} generalizes semantic entropy, the gold standard for UQ in {LLMs}, and empirically demonstrate its superior performance over baselines across 24 model-dataset combinations.} }
Endnote
%0 Conference Paper %T SeSE: Black-Box Uncertainty Quantification for Large Language Models Based on Structural Information Theory %A Xingtao Zhao %A Hao Peng %A Dingli Su %A Xianghua Zeng %A Chunyang Liu %A Jinzhi Liao %A Philip S. Yu %B Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence %C Proceedings of Machine Learning Research %D 2026 %E Emilija Perković %E Daniel Malinsky %F pmlr-v337-zhao26b %I PMLR %P 8209--8237 %U https://proceedings.mlr.press/v337/zhao26b.html %V 337 %X Reliable uncertainty quantification (UQ) is essential for deploying large language models ({LLMs}) in safety-critical scenarios, as it enables them to abstain from responding when uncertain, thereby avoiding hallucinations, i.e., plausible yet factually incorrect responses. However, while current semantic UQ methods have achieved state-of-the-art performance, they inherently overlook latent semantic structural information that could enable more precise uncertainty estimates. In this paper, we propose Semantic Structural Entropy ({SeSE}), a principled black-box UQ framework applicable to both open- and closed-source {LLMs}. To reveal the intrinsic structure of the {LLM} semantic space, {SeSE} constructs its hierarchical abstraction based on the principle of structural entropy minimization. The structural entropy of the resulting optimal hierarchical abstraction thus quantifies the inherent uncertainty within the semantic space after optimal compression. Additionally, unlike existing methods that primarily focus on simple short-form generation, we extend {SeSE} to provide interpretable and granular uncertainty estimation for long-form outputs. We theoretically prove that {SeSE} generalizes semantic entropy, the gold standard for UQ in {LLMs}, and empirically demonstrate its superior performance over baselines across 24 model-dataset combinations.
APA
Zhao, X., Peng, H., Su, D., Zeng, X., Liu, C., Liao, J. & Yu, P.S.. (2026). SeSE: Black-Box Uncertainty Quantification for Large Language Models Based on Structural Information Theory. Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research 337:8209-8237 Available from https://proceedings.mlr.press/v337/zhao26b.html.

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