Are LLM Belief Updates Consistent with Bayes' Theorem?

Abstract: Do larger and more capable LLMs 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 LLMs 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 LLMs assign credences that are more coherent with Bayes' theorem. These results have important implications for our understanding and governance of LLMs.