Expert Choice Mixture of Experts (MoE)

Frontier AI Drawings: 1 of 13

Frontier AI Drawings: the series

1. "Expert Choice" Mixture of Experts (MoE)

2. MHA, MQA, GQA, MoE-A: More Attention!

3. New GPT-OSS Trick to Ignore Tokens

4. MXFP4, FP4, FP8

5. LoRA, Fine-Tune, Pre-Train

6. QLoRA, DoRA, BitFit, NF4 vs INT4

7. KV Cache, Prefill, Decode

8. EmbeddingGemma, MRL, InfoNCE, Embed vs. Decode

9. Inference Batching, Request-vs-Token Level

10. MLP Parallelism: Data, Context, Row, Column, Pipeline

11. RoPE vs PE in QKV Self-Attention

12. RMS, Group, Layer, Batch Norm, Tensor Parallelism

13. Qwen 3

Mixture of Experts (MoE) is one of the most important architectural ideas in frontier AI today. Models like Mistral, DeepSeek, and Qwen all use it. The core idea: instead of running every parameter on every token, you route each token to a small subset of "experts" and activate only those.

Summary

Q: Why Expert Choice routing?

A: Because traditional MoE (Token Choice) suffers from load imbalance: some experts get overloaded with tokens while others stay idle, wasting capacity.

Q: How does Expert Choice fix this?

A: By letting experts select their top tokens, it prevents any expert from being overloaded and keeps computation balanced.

Q: Who invented Expert Choice routing?

A: Researchers at Google.

In Token Choice routing, each token picks its favorite expert. The problem is popularity: some experts attract too many tokens and get swamped, while others receive none and sit idle. Expert Choice flips the direction. Each expert selects its top K tokens. Because every expert selects the same number of tokens, load is perfectly balanced and no capacity is wasted.

Drawings

1. Token Choice vs Expert Choice (overview): side-by-side diagram showing how the routing direction differs between the two approaches.

2. Token Choice: full numerical example: 5 experts, 6 tokens. Walks through the expert embeddings, affinity scores, softmax, sorted gating matrix, and routing table step by step.

3. Expert Choice: per-expert FFN computation (part 1): Experts 1 and 2 each select their top 2 tokens and run them through W1, ReLU, W2, and gating.

4. Expert Choice: routing setup (5 experts, Top 2): token vectors, expert embeddings, affinity matrix A, sorted gating matrix, and sorted token index matrix.

5. Expert Choice: full computation and aggregation (5 experts, Top 2): all 5 experts compute in parallel, results are summed and combined into the final output tokens.

6. Expert Choice: routing setup (3 experts, Top 2): same walkthrough scaled down, useful for tracing the math by hand.

7. Expert Choice: full computation (3 experts, Top 2): per-expert FFN for all three experts, with final aggregation.

8. Expert Choice: routing setup (5 experts, Top 3): shows what changes when each expert selects more tokens.

9. Expert Choice: full computation (5 experts, Top 3): all five experts each pick three tokens, demonstrating how Top K controls capacity and compute.

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