# Are LLM Belief Updates Consistent with Bayes' Theorem?

arXiv: https://arxiv.org/abs/2507.17951 · HTML: https://mlsanity.com/paper/2507.17951/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 23 references that are in the map.
- First posted on arXiv 23 Jul 2025.

## Builds on (most cited first, 17 of 17)

- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [GPQA: A Graduate-Level Google-Proof Q&A Benchmark](https://mlsanity.com/paper/2311.12022/) (2023)
- [MMLU-Pro: A More Robust and Challenging Multi-Task Language Understanding Benchmark](https://mlsanity.com/paper/2406.01574/) (2024)
- [Challenging BIG-Bench Tasks and Whether Chain-of-Thought Can Solve Them](https://mlsanity.com/paper/2210.09261/) (2022)
- [Pythia: A Suite for Analyzing Large Language Models Across Training and Scaling](https://mlsanity.com/paper/2304.01373/) (2023)
- [Instruction-Following Evaluation for Large Language Models](https://mlsanity.com/paper/2311.07911/) (2023)
- [The Reversal Curse: LLMs trained on "A is B" fail to learn "B is A"](https://mlsanity.com/paper/2309.12288/) (2023)
- [The Illusion of Thinking: Understanding the Strengths and Limitations of Reasoning Models via the Lens of Problem Complexity](https://mlsanity.com/paper/2506.06941/) (2025)
- [Risks from Learned Optimization in Advanced Machine Learning Systems](https://mlsanity.com/paper/1906.01820/) (2019)
- [MuSR: Testing the Limits of Chain-of-thought with Multistep Soft Reasoning](https://mlsanity.com/paper/2310.16049/) (2023)
- [Large Language Models Often Know When They Are Being Evaluated](https://mlsanity.com/paper/2505.23836/) (2025)
- [Utility Engineering: Analyzing and Controlling Emergent Value Systems in AIs](https://mlsanity.com/paper/2502.08640/) (2025)
- [Evaluating Superhuman Models with Consistency Checks](https://mlsanity.com/paper/2306.09983/) (2023)
- [Consistency Checks for Language Model Forecasters](https://mlsanity.com/paper/2412.18544/) (2024)
- [Comment on The Illusion of Thinking: Understanding the Strengths and Limitations of Reasoning Models via the Lens of Problem Complexity](https://mlsanity.com/paper/2506.09250/) (2025)
- [Constrained belief updates explain geometric structures in transformer representations](https://mlsanity.com/paper/2502.01954/) (2025)
- [Evaluation Faking: Unveiling Observer Effects in Safety Evaluation of Frontier AI Systems](https://mlsanity.com/paper/2505.17815/) (2025)

## Built on by (most cited first, 9 of 9)

- [Lying with Truths: Open-Channel Multi-Agent Collusion for Belief Manipulation via Generative Montage](https://mlsanity.com/paper/2601.01685/) (2026)
- [BayesBench: Evaluating LLM Belief Trajectories Under Multi-Turn Evidence Accumulation](https://mlsanity.com/paper/2606.30850/) (2026)
- [Why Do LLMs Struggle in Strategic Play? Broken Links Between Observations, Beliefs, and Actions](https://mlsanity.com/paper/2605.00226/) (2026)
- [Illusions of Confidence? Diagnosing LLM Truthfulness via Neighborhood Consistency](https://mlsanity.com/paper/2601.05905/) (2026)
- [Overcoming State Inertia: Minimally Invasive Temporal Alignment for Evolving Contexts](https://mlsanity.com/paper/2512.03704/) (2025)
- [Assessing mentalization in humans and large language models](https://mlsanity.com/paper/2608.26291/) (2026)
- [Subjective-Graph LLM Agents for Simulating Uncertainty in Classroom Social Perception](https://mlsanity.com/paper/2603.20750/) (2026)
- [MEDLEY-BENCH: Benchmarking Behavioural Metacognition and Belief Revision Under Social Pressure in Large Language Models](https://mlsanity.com/paper/2604.16009/) (2026)
- [Bayesian Intelligence from the Outside](https://mlsanity.com/paper/2609.14724/) (2026)

## Abstract (arXiv)

Do larger and more capable language models learn to update their "beliefs" about propositions more consistently with Bayes' theorem when presented with evidence in-context? To test this, we formulate a Bayesian Coherence Coefficient (BCC) metric and generate a dataset with which to measure the BCC. We measure BCC for multiple pre-trained-only language models across five model families, comparing against the number of model parameters, the amount of training data, and model scores on common benchmarks. Our results provide evidence for our hypothesis that larger and more capable pre-trained language models assign credences that are more coherent with Bayes' theorem. These results have important implications for our understanding and governance of LLMs.