Verbalized Particle Posterior Enables Bayesian LLM Inference

Researchers have introduced the Verbalized Particle Posterior (VPP), a novel framework that applies Bayesian inference to "Verbalized Machine Learning" (VML). VML typically parameterizes models as natural language prompts evaluated by a Large Language Model (LLM), but it suffers from a lack of uncertainty measures and variability across optimization runs. VPP addresses these limitations by treating verbalized learning as a Bayesian problem. It maintains a population of natural-language hypotheses as "particles," which are updated using methods like Metropolis-Hastings or Sequential Monte Carlo. This allows for Bayesian model averaging for predictions. A key advantage is that VPP operates with the LLM as a black box, requiring no access to internal logits or gradients. The framework significantly improves performance over single VML runs, matching or exceeding oracle-best ensembles and eliminating catastrophic failures, while also providing an interpretable posterior of human-readable hypotheses.