# Do Language Models Have Bayesian Brains? Distinguishing Stochastic and Deterministic Decision Patterns within Large Language Models

arXiv: https://arxiv.org/abs/2506.10268 · HTML: https://mlsanity.com/paper/2506.10268/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 14 references that are in the map.
- First posted on arXiv 12 Jun 2025.

## Builds on (most cited first, 5 of 5)

- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Gemma 2: Improving Open Language Models at a Practical Size](https://mlsanity.com/paper/2408.00118/) (2024)
- [Eliciting the Priors of Large Language Models using Iterated In-Context Learning](https://mlsanity.com/paper/2406.01860/) (2024)
- [Probing BERT's priors with serial reproduction chains](https://mlsanity.com/paper/2202.12226/) (2022)

## Built on by (most cited first, 2 of 2)

- [Agent Identity Evals: Measuring Agentic Identity](https://mlsanity.com/paper/2507.17257/) (2025)
- [Tractable Asymmetric Verification for Large Language Models via Deterministic Replicability](https://mlsanity.com/paper/2509.11068/) (2025)

## Abstract (arXiv)

Language models are essentially probability distributions over token sequences. Auto-regressive models generate sentences by iteratively computing and sampling from the distribution of the next token. This iterative sampling introduces stochasticity, leading to the assumption that language models make probabilistic decisions, similar to sampling from unknown distributions. Building on this assumption, prior research has used simulated Gibbs sampling, inspired by experiments designed to elicit human priors, to infer the priors of language models. In this paper, we revisit a critical question: Do language models possess Bayesian brains? Our findings show that under certain conditions, language models can exhibit near-deterministic decision-making, such as producing maximum likelihood estimations, even with a non-zero sampling temperature. This challenges the sampling assumption and undermines previous methods for eliciting human-like priors. Furthermore, we demonstrate that without proper scrutiny, a system with deterministic behavior undergoing simulated Gibbs sampling can converge to a "false prior." To address this, we propose a straightforward approach to distinguish between stochastic and deterministic decision patterns in Gibbs sampling, helping to prevent the inference of misleading language model priors. We experiment on a variety of large language models to identify their decision patterns under various circumstances. Our results provide key insights in understanding decision making of large language models.