Albus Yizhuo Li

Albus Yizhuo Li, Matthew Wicker

Foundation models are increasingly being deployed in contexts where understanding the uncertainty of their outputs is critical to ensuring responsible deployment. While Bayesian methods offer a principled approach to uncertainty quantification, their computational overhead renders their use impractical for training or inference at foundation model scale. State-of-the-art models achieve parameter counts in the trillions through carefully engineered sparsity including Mixture-of-Experts (MoE) layers. In this work, we demonstrate calibrated uncertainty at scale by introducing Variational Mixture-of-Experts Routing (VMoER), a structured Bayesian approach for modelling uncertainty in MoE layers. VMoER confines Bayesian inference to the expert-selection stage which is typically done by a deterministic routing network. We instantiate VMoER using two inference strategies: amortised variational inference over routing logits and inferring a temperature parameter for stochastic expert selection. Across tested foundation models, VMoER improves routing stability under noise by 38\%, reduces calibration error by 94\%, and increases out-of-distribution AUROC by 12\%, while incurring less than 1\% additional FLOPs. These results suggest VMoER offers a scalable path toward robust and uncertainty-aware foundation models.

Albus Yizhuo Li

The Mixture-of-Experts (MoE) architecture has enabled the creation of massive yet efficient Large Language Models (LLMs). However, the standard deterministic routing mechanism presents a significant limitation: its inherent brittleness is a key contributor to model miscalibration and overconfidence, resulting in systems that often do not know what they don't know. This thesis confronts this challenge by proposing a structured \textbf{Bayesian MoE routing framework}. Instead of forcing a single, deterministic expert selection, our approach models a probability distribution over the routing decision itself. We systematically investigate three families of methods that introduce this principled uncertainty at different stages of the routing pipeline: in the \textbf{weight-space}, the \textbf{logit-space}, and the final \textbf{selection-space}. Through a series of controlled experiments on a 3-billion parameter MoE model, we demonstrate that this framework significantly improves routing stability, in-distribution calibration, and out-of-distribution (OoD) detection. The results show that by targeting this core architectural component, we can create a more reliable internal uncertainty signal. This work provides a practical and computationally tractable pathway towards building more robust and self-aware LLMs, taking a crucial step towards making them know what they don't know.