From Drift to Coherence: Stabilizing Beliefs in LLMs

Songeun Kim, Seungyoo Lee, Edwin Fong, Hyungi Lee, Juho Lee
Proceedings of the 43rd International Conference on Machine Learning, PMLR 306:58079-58105, 2026.

Abstract

Large language models (LLMs) are often hypothesized to perform implicit Bayesian inference, yet a key coherence condition—the martingale property of predictive beliefs—has been shown to fail in controlled synthetic in-context learning settings. We revisit this question in a more typical usage regime: generic multiple-choice question answering. Exploiting the discrete answer space, we compute exact predictive distributions and study belief dynamics induced by autoregressive answer resampling. We introduce prompted predictive resampling (PPR), where an LLM generates a sequence of answers to the same question. Empirically, PPR reveals early-stage belief drift, indicating martingale violations. However, after sufficient resampling steps, the belief process self-stabilizes and converges to a coherent predictive distribution. Based on this observation, we further propose (i) a seed-answer prompting strategy to accelerate stabilization, and (ii) a self-consistency loss that amortizes early-stage drift into the model via fine-tuning. Experiments on multiple-choice QA benchmarks show that our methods substantially reduce belief drift and improve predictive coherence without sacrificing accuracy.

Cite this Paper

BibTeX
@InProceedings{pmlr-v306-kim26ah, title = {From Drift to Coherence: Stabilizing Beliefs in {LLM}s}, author = {Kim, Songeun and Lee, Seungyoo and Fong, Edwin and Lee, Hyungi and Lee, Juho}, booktitle = {Proceedings of the 43rd International Conference on Machine Learning}, pages = {58079--58105}, 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/kim26ah/kim26ah.pdf}, url = {https://proceedings.mlr.press/v306/kim26ah.html}, abstract = {Large language models (LLMs) are often hypothesized to perform implicit Bayesian inference, yet a key coherence condition—the martingale property of predictive beliefs—has been shown to fail in controlled synthetic in-context learning settings. We revisit this question in a more typical usage regime: generic multiple-choice question answering. Exploiting the discrete answer space, we compute exact predictive distributions and study belief dynamics induced by autoregressive answer resampling. We introduce prompted predictive resampling (PPR), where an LLM generates a sequence of answers to the same question. Empirically, PPR reveals early-stage belief drift, indicating martingale violations. However, after sufficient resampling steps, the belief process self-stabilizes and converges to a coherent predictive distribution. Based on this observation, we further propose (i) a seed-answer prompting strategy to accelerate stabilization, and (ii) a self-consistency loss that amortizes early-stage drift into the model via fine-tuning. Experiments on multiple-choice QA benchmarks show that our methods substantially reduce belief drift and improve predictive coherence without sacrificing accuracy.} }
Endnote
%0 Conference Paper %T From Drift to Coherence: Stabilizing Beliefs in LLMs %A Songeun Kim %A Seungyoo Lee %A Edwin Fong %A Hyungi Lee %A Juho Lee %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-kim26ah %I PMLR %P 58079--58105 %U https://proceedings.mlr.press/v306/kim26ah.html %V 306 %X Large language models (LLMs) are often hypothesized to perform implicit Bayesian inference, yet a key coherence condition—the martingale property of predictive beliefs—has been shown to fail in controlled synthetic in-context learning settings. We revisit this question in a more typical usage regime: generic multiple-choice question answering. Exploiting the discrete answer space, we compute exact predictive distributions and study belief dynamics induced by autoregressive answer resampling. We introduce prompted predictive resampling (PPR), where an LLM generates a sequence of answers to the same question. Empirically, PPR reveals early-stage belief drift, indicating martingale violations. However, after sufficient resampling steps, the belief process self-stabilizes and converges to a coherent predictive distribution. Based on this observation, we further propose (i) a seed-answer prompting strategy to accelerate stabilization, and (ii) a self-consistency loss that amortizes early-stage drift into the model via fine-tuning. Experiments on multiple-choice QA benchmarks show that our methods substantially reduce belief drift and improve predictive coherence without sacrificing accuracy.
APA
Kim, S., Lee, S., Fong, E., Lee, H. & Lee, J.. (2026). From Drift to Coherence: Stabilizing Beliefs in LLMs. Proceedings of the 43rd International Conference on Machine Learning, in Proceedings of Machine Learning Research 306:58079-58105 Available from https://proceedings.mlr.press/v306/kim26ah.html.

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