The preceding chapters established the mechanics of individual Mixture of Experts layers. We now address their practical application by incorporating them into modern neural network architectures. The most common use case for MoEs is to increase model capacity without a proportional rise in computational cost, and this is typically achieved by replacing standard feed-forward networks (FFNs) with MoE layers.

This chapter provides a technical guide to this integration process. We will cover:

• The methodology for substituting dense FFN blocks with sparse MoE layers in Transformer models.
• Architectural considerations, including the frequency and depth at which to place MoE layers for optimal performance.
• The adaptation of MoE principles for Vision Transformers (ViT) and multi-modal systems.
• A quantitative analysis of the trade-off between model parameters and computational workload (FLOPs).

A central benefit of MoE is the decoupling of total parameters from the computation required for a single forward pass. An MoE model may contain $N$ experts, but for any given token, the gating network routes it to a small subset of $k$ experts, where $k \ll N$. The total computational cost is therefore a function of $k$, while the model's total parameter count is a function of $N$. This relationship can be expressed as:

$$\text{Total Parameters} \propto N \times \text{Parameters per Expert}$$ $$\text{Computational FLOPs} \propto k \times \text{FLOPs per Expert}$$

The chapter concludes with a hands-on exercise where you will modify a standard Transformer implementation to use sparse MoE layers, putting these architectural principles into practice.