Bayesian Mixture-of-Experts: Towards Making LLMs Know What They Don't Know

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 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 weight-space, the logit-space, and the final 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.