这篇论文提出用LLM做MCMC采样，比直接生成更鲁棒，适合复杂推理场景，值得做概率建模的人看看。
Large Language Gibbs 是一种利用大型语言模型条件分布进行结构化概率推理的MCMC方案。该方法通过迭代重采样单个变量避免单次自回归生成的顺序偏差，产生的平稳分布反映所有局部条件之间的折中。在合成分布采样、一致性推理和贝叶斯结构学习任务上验证了有效性。结果表明LLM条件作为MCMC转移算子可替代单次生成进行结构化推理。
Structured Inference with Large Language Gibbs
The knowledge encoded in large language models (LLMs) can serve as a substrate for structured reasoning over variables describing a complex world, but accessing this knowledge in a probabilistically coherent manner poses a difficult inference problem. We propose Large Language Gibbs, a scheme for structured probabilistic inference that uses conditional distributions of an LLM as transition operators. Rather than sampling structured objects through single-pass autoregressive generation, we iteratively resample individual variables conditioned on others using an LLM's next-token conditionals. This approach avoids order-dependent biases and produces a stationary distribution that reflects a compromise between all local conditionals. We apply this approach to sampling from synthetic distributions, consistent reasoning tasks, and Bayesian structure learning. The results suggest that the use of LLM conditionals in MCMC is a practical alternative to one-pass generation for structured probabilistic inference under a world prior accessible through noisy LLM conditionals.