Textual Bayes: Quantifying Uncertainty in LLM-Based Systems
This work addresses the critical need for reliable uncertainty estimation in LLM systems, particularly for high-stakes applications, by integrating Bayesian methods, though it is incremental in applying existing statistical techniques to a new context.
The paper tackles the problem of quantifying uncertainty in LLM-based systems, which limits their use in high-stakes domains, by introducing a Bayesian approach that interprets prompts as textual parameters and uses a novel MCMC algorithm (MHLP) for inference, resulting in improvements in predictive accuracy and uncertainty quantification on benchmarks.
Although large language models (LLMs) are becoming increasingly capable of solving challenging real-world tasks, accurately quantifying their uncertainty remains a critical open problem, which limits their applicability in high-stakes domains. This challenge is further compounded by the closed-source, black-box nature of many state-of-the-art LLMs. Moreover, LLM-based systems can be highly sensitive to the prompts that bind them together, which often require significant manual tuning (i.e., prompt engineering). In this work, we address these challenges by viewing LLM-based systems through a Bayesian lens. We interpret prompts as textual parameters in a statistical model, allowing us to use a small training dataset to perform Bayesian inference over these prompts. This novel perspective enables principled uncertainty quantification over both the model's textual parameters and its downstream predictions, while also incorporating prior beliefs about these parameters expressed in free-form text. To perform Bayesian inference, a difficult problem even for well-studied data modalities, we introduce Metropolis-Hastings through LLM Proposals (MHLP), a novel Markov chain Monte Carlo (MCMC) algorithm that combines prompt optimization techniques with standard MCMC methods. MHLP is a turnkey modification to existing LLM pipelines, including those that rely exclusively on closed-source models. Empirically, we demonstrate that our method yields improvements in both predictive accuracy and uncertainty quantification (UQ) on a range of LLM benchmarks and UQ tasks. More broadly, our work demonstrates a viable path for incorporating methods from the rich Bayesian literature into the era of LLMs, paving the way for more reliable and calibrated LLM-based systems.