The performance of a Mixture of Experts model depends heavily on its routing mechanism. This component is responsible for directing each input token to a small subset of experts. The quality of this routing decision has a direct impact on model performance, training stability, and computational efficiency. While a standard top-k router is a functional starting point, it can lead to problems like load imbalance, where some experts are consistently over-selected while others remain under-utilized.

This chapter covers a set of advanced routing mechanisms designed to address the limitations of basic gating. We will examine the trade-offs between different routing algorithms, considering their computational cost, effect on load balancing, and impact on expert specialization.

Throughout this chapter, you will learn to implement and analyze several key routing strategies:

• Noisy Top-k Gating: A technique that introduces noise into the gating logits, $h(x)$, to improve load distribution during training.
• Switch Transformers: An architecture that simplifies routing by sending each token to only one expert ($k=1$), reducing communication overhead.
• Hash-based Routing: A deterministic method that uses a hash function for token assignment, removing the need for a learned gating network.
• Soft MoE: A fully differentiable approach that computes a weighted average of all experts, creating a "soft" assignment instead of a hard, discrete selection.

We will also cover techniques for analyzing router decisions to understand how specialization forms. The chapter concludes with a hands-on section where you will implement these different routers to gain a practical understanding of their mechanics and performance characteristics.