Mind the Gap: Catching Hallucinations via Evidence Drop on the Reasoning Manifold

Qunjie Chen, Yufei Chen, Xiaodong Yue, Linye Li
Proceedings of the 43rd International Conference on Machine Learning, PMLR 306:13782-13806, 2026.

Abstract

Large Language Models (LLMs) show strong reasoning abilities, yet their reliability is hindered by hallucinations, where fluent reasoning becomes factually or logically incorrect. Most existing uncertainty-based detectors rely on sequence-level averaging, which ignores the step-wise dynamics of reasoning and often misclassifies hard-but-correct or easy-but-wrong samples. We propose a dynamic perspective that models reasoning as a trajectory on a latent Evidence Manifold, where each step is supported by local evidence. Hallucinations are characterized as Evidence Drops, i.e., sudden declines in local evidence support that indicate topological deviations from this manifold. Based on this insight, we design a training-free and model-agnostic detector that identifies hallucinations via the worst-case Evidence Drop and enables step-level error localization. Experiments on GSM8K, MATH, and ProcessBench show consistent improvements over sequence-level uncertainty baselines in selective accuracy and risk–coverage trade-offs.

Cite this Paper

BibTeX
@InProceedings{pmlr-v306-chen26n, title = {Mind the Gap: Catching Hallucinations via Evidence Drop on the Reasoning Manifold}, author = {Chen, Qunjie and Chen, Yufei and Yue, Xiaodong and Li, Linye}, booktitle = {Proceedings of the 43rd International Conference on Machine Learning}, pages = {13782--13806}, year = {2026}, editor = {Zhang, Tong and Dudik, Miroslav and Jaggi, Martin and Agarwal, Alekh and Li, Sharon and Schuurmans, Dale and Zhu, Jerry and Berkenkamp, Felix and Dong, Hanze and Bietti, Alberto}, volume = {306}, series = {Proceedings of Machine Learning Research}, month = {06--11 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v306/main/assets/chen26n/chen26n.pdf}, url = {https://proceedings.mlr.press/v306/chen26n.html}, abstract = {Large Language Models (LLMs) show strong reasoning abilities, yet their reliability is hindered by hallucinations, where fluent reasoning becomes factually or logically incorrect. Most existing uncertainty-based detectors rely on sequence-level averaging, which ignores the step-wise dynamics of reasoning and often misclassifies hard-but-correct or easy-but-wrong samples. We propose a dynamic perspective that models reasoning as a trajectory on a latent Evidence Manifold, where each step is supported by local evidence. Hallucinations are characterized as Evidence Drops, i.e., sudden declines in local evidence support that indicate topological deviations from this manifold. Based on this insight, we design a training-free and model-agnostic detector that identifies hallucinations via the worst-case Evidence Drop and enables step-level error localization. Experiments on GSM8K, MATH, and ProcessBench show consistent improvements over sequence-level uncertainty baselines in selective accuracy and risk–coverage trade-offs.} }
Endnote
%0 Conference Paper %T Mind the Gap: Catching Hallucinations via Evidence Drop on the Reasoning Manifold %A Qunjie Chen %A Yufei Chen %A Xiaodong Yue %A Linye Li %B Proceedings of the 43rd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2026 %E Tong Zhang %E Miroslav Dudik %E Martin Jaggi %E Alekh Agarwal %E Sharon Li %E Dale Schuurmans %E Jerry Zhu %E Felix Berkenkamp %E Hanze Dong %E Alberto Bietti %F pmlr-v306-chen26n %I PMLR %P 13782--13806 %U https://proceedings.mlr.press/v306/chen26n.html %V 306 %X Large Language Models (LLMs) show strong reasoning abilities, yet their reliability is hindered by hallucinations, where fluent reasoning becomes factually or logically incorrect. Most existing uncertainty-based detectors rely on sequence-level averaging, which ignores the step-wise dynamics of reasoning and often misclassifies hard-but-correct or easy-but-wrong samples. We propose a dynamic perspective that models reasoning as a trajectory on a latent Evidence Manifold, where each step is supported by local evidence. Hallucinations are characterized as Evidence Drops, i.e., sudden declines in local evidence support that indicate topological deviations from this manifold. Based on this insight, we design a training-free and model-agnostic detector that identifies hallucinations via the worst-case Evidence Drop and enables step-level error localization. Experiments on GSM8K, MATH, and ProcessBench show consistent improvements over sequence-level uncertainty baselines in selective accuracy and risk–coverage trade-offs.
APA
Chen, Q., Chen, Y., Yue, X. & Li, L.. (2026). Mind the Gap: Catching Hallucinations via Evidence Drop on the Reasoning Manifold. Proceedings of the 43rd International Conference on Machine Learning, in Proceedings of Machine Learning Research 306:13782-13806 Available from https://proceedings.mlr.press/v306/chen26n.html.

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