Bayesian Mixture of Experts For Large Language Models

TL;DR

This paper introduces Bayesian-MoE, a method for estimating uncertainty in large language models with Mixture-of-Experts architecture, improving calibration and reliability without retraining the models.

Contribution

It proposes a post-hoc Bayesian inference approach using structured Laplace approximation on existing MoE models, enabling uncertainty estimation without additional training.

Findings

Improves calibration error (ECE) on reasoning benchmarks.

Reduces negative log-likelihood compared to baselines.

Demonstrates scalable uncertainty estimation in large models.

Abstract

We present Bayesian Mixture of Experts (Bayesian-MoE), a post-hoc uncertainty estimation framework for fine-tuned large language models (LLMs) based on Mixture-of-Experts architectures. Our method applies a structured Laplace approximation to the second linear layer of each expert, enabling calibrated uncertainty estimation without modifying the original training procedure or introducing new parameters. Unlike prior approaches, which apply Bayesian inference to added adapter modules, Bayesian-MoE directly targets the expert pathways already present in MoE models, leveraging their modular design for tractable block-wise posterior estimation. We use Kronecker-factored low-rank approximations to model curvature and derive scalable estimates of predictive uncertainty and marginal likelihood. Experiments on common-sense reasoning benchmarks with Qwen1.5-MoE and DeepSeek-MoE demonstrate that Bayesian-MoE improves both expected calibration error (ECE) and negative log-likelihood (NLL) over baselines, confirming its effectiveness for reliable downstream decision-making.