# MoE Mathematics: Top-K Router + Softmax + Noise + Auxiliary Load-Balancing Loss

> Source: https://sukruyusufkaya.com/learn/fine-tuning-cookbook/ftc-moe-mathematics-router-load-balancing
> Updated: 2026-08-20T23:42:06.355Z
> Category: Fine-Tuning Cookbook (Model-by-Model)
> Module: Part V — MoE Internals & Fine-Tuning
**TLDR:** MoE'nin kalbi router. Top-K routing matematiksel derivation (Shazeer 2017, Switch Transformer 2021), token-to-expert assignment, expert capacity factor (overflow vs underutilization), load balancing loss (aux loss), softmax temperature ve top-K=2 vs top-K=1 trade-off. Mixtral 8×7B'nin gerçek router config'i.