Apple study finds large language models update beliefs inconsistently with Bayesian principles

Apple’s Machine Learning Research team published a paper arguing that large language models do not consistently update their probabilistic beliefs in line with Bayesian principles, which are foundational to rational belief updating under uncertainty. The study introduces a novel technique to evaluate LLMs as information processing systems, using a metric called the information processing gap. This gap quantifies deviations from Bayes updates when LLMs incorporate new evidence into their beliefs.

The researchers conducted extensive experiments comparing multiple approaches for how LLMs can integrate evidence. They found that some methods produce nearly Bayesian updates, which represent optimal information processing, while others rely on learned heuristics. Surprisingly, the non-Bayesian heuristic updates often outperformed exact Bayesian updates in terms of downstream task performance. The authors interpret this as evidence that the LLMs’ internal probabilistic models of the world may be misspecified, meaning they do not accurately represent uncertainty.

The study also demonstrates how the proposed measure can serve as a diagnostic tool to identify issues in LLM-powered inferential systems. By quantifying inconsistencies in belief updating, the method could help developers assess and improve the reliability of LLMs in domains where rational belief updating is critical, such as medicine, science, and law.

The paper is authored by Chacha Chen, Matthew Jörke, Adam Goliński, Masha Fedzechkina, Guillermo Sapiro, Sinead Williamson, and Nicholas Foti, with affiliations including Apple and Stanford University. The work was published in August 2026.