BayesAgent: Bayesian Agentic Reasoning Under Uncertainty via Verbalized Probabilistic Graphical Modeling

Human cognition excels at transcending sensory input and forming latent representations that structure our understanding of the world. While Large Language Model (LLM) agents demonstrate emergent reasoning and decision-making abilities, they lack a principled framework for capturing latent structures and modeling uncertainty. In this work, we explore for the first time how to bridge LLM agents with probabilistic graphical models (PGMs) to address agentic reasoning under uncertainty. To this end, we introduce Verbalized Probabilistic Graphical Modeling (vPGM), a Bayesian agentic framework that (i) guides LLM agents in following key principles of PGMs through natural language and (ii) refines the resulting posterior distributions via numerical Bayesian inference. Unlike many traditional probabilistic methods requiring substantial domain expertise, vPGM bypasses expert-driven model design, making it well-suited for scenarios with limited assumptions. We evaluated our model on several agentic reasoning tasks, both close-ended and open-ended. Our results indicate that the model effectively enhances confidence calibration and text generation quality.

💡 Research Summary

The paper introduces Verbalized Probabilistic Graphical Modeling (vPGM), a framework that equips large language model (LLM) agents with the ability to perform Bayesian reasoning using natural‑language prompts. Traditional LLM agents excel at chain‑of‑thought prompting and tool use, yet they lack a principled way to represent latent variables, capture dependencies, and quantify uncertainty. vPGM bridges this gap by having the LLM simulate the three core components of a probabilistic graphical model (PGM): (1) Graphical Structure Discovery, where a specially crafted meta‑prompt asks the LLM to identify hidden variables and their conditional relationships from a few input‑output examples, domain background, and explicit constraints (e.g., maximum number of variables). The output is a directed acyclic graph (DAG) of latent nodes Z={Z₁,…,Zₙ} together with natural‑language descriptions of each conditional probability distribution (CPD). (2) Prompting‑Based Inference, in which another prompt instructs the LLM to compute posterior distributions P(Zᵢ | Pa(Zᵢ), X) for a new observation X. The LLM leverages its internal soft‑max probabilities and the previously discovered CPDs to generate textual and numeric estimates of these posteriors, effectively performing a Bayesian update without explicit parameter estimation. (3) Predictions under Uncertainty, where the posterior over latent variables P(Z | X) is used to obtain a predictive distribution for the target Y. The expectation E_{P(Z|X)}