# Training-Free Halving of Activated Experts in Fine-Grained Mixture-of-Experts Models

arXiv: https://arxiv.org/abs/2609.04575 · HTML: https://mlsanity.com/paper/2609.04575/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in MoE theory and gating functions, one of 12 directions in Mixture-of-experts.
- Builds on 19 of its 24 references that are in the map.
- First posted on arXiv 4 Sep 2026.

## Placed in

- Mixture-of-experts / [MoE theory and gating functions](https://mlsanity.com/moe/moe-theory-and-gating-functions/)

## Builds on (most cited first, 19 of 19)

- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Outrageously Large Neural Networks: The Sparsely-Gated Mixture-of-Experts Layer](https://mlsanity.com/paper/1701.06538/) (2017)
- [Pointer Sentinel Mixture Models](https://mlsanity.com/paper/1609.07843/) (2016)
- [Switch Transformers: Scaling to Trillion Parameter Models with Simple and Efficient Sparsity](https://mlsanity.com/paper/2101.03961/) (2021)
- [GPTQ: Accurate Post-Training Quantization for Generative Pre-trained Transformers](https://mlsanity.com/paper/2210.17323/) (2022)
- [GShard: Scaling Giant Models with Conditional Computation and Automatic Sharding](https://mlsanity.com/paper/2006.16668/) (2020)
- [AWQ: Activation-aware Weight Quantization for LLM Compression and Acceleration](https://mlsanity.com/paper/2306.00978/) (2023)
- [DeepSeekMoE: Towards Ultimate Expert Specialization in Mixture-of-Experts Language Models](https://mlsanity.com/paper/2401.06066/) (2024)
- [C-Eval: A Multi-Level Multi-Discipline Chinese Evaluation Suite for Foundation Models](https://mlsanity.com/paper/2305.08322/) (2023)
- [Mixture-of-Experts with Expert Choice Routing](https://mlsanity.com/paper/2202.09368/) (2022)
- [ST-MoE: Designing Stable and Transferable Sparse Expert Models](https://mlsanity.com/paper/2202.08906/) (2022)
- [OpenMoE: An Early Effort on Open Mixture-of-Experts Language Models](https://mlsanity.com/paper/2402.01739/) (2024)
- [Merge, Then Compress: Demystify Efficient SMoE with Hints from Its Routing Policy](https://mlsanity.com/paper/2310.01334/) (2023)
- [Compressing LLMs: The Truth is Rarely Pure and Never Simple](https://mlsanity.com/paper/2310.01382/) (2023)
- [AdaMoE: Token-Adaptive Routing with Null Experts for Mixture-of-Experts Language Models](https://mlsanity.com/paper/2406.13233/) (2024)
- [REAP the Experts: Why Pruning Prevails for One-Shot MoE compression](https://mlsanity.com/paper/2510.13999/) (2025)
- [Elastic MoE: Unlocking the Inference-Time Scalability of Mixture-of-Experts](https://mlsanity.com/paper/2509.21892/) (2025)
- [Training Matryoshka Mixture-of-Experts for Elastic Inference-Time Expert Utilization](https://mlsanity.com/paper/2509.26520/) (2025)
- [Post-Trained MoE Can Skip Half Experts via Self-Distillation](https://mlsanity.com/paper/2605.18643/) (2026)

## Abstract (arXiv)

Modern fine-grained Mixture-of-Experts (MoE) models route each token to a small number of experts and renormalize their router probabilities. We show that this renormalization implicitly calibrates expert output gain to the training top-k: reducing k at inference changes not only which experts are used but also the strength of the expert branch. We separate these effects by activating the top k1 experts while normalizing by the probability mass of the top k2 experts, introducing one integer with no parameters, training, or measurable compute overhead. On Qwen3.6-35B-A3B, reducing from 8 to 4 experts causes a 4.65-point MMLU drop under standard renormalization but only 0.35 points with k2=16, while halving routed-expert compute. The result replicates on the 11× larger Qwen3.5-397B-A17B, where reducing from 10 to 5 experts loses only 0.55 points with an appropriate reference set. Removing renormalization entirely is catastrophic, showing that preserving a suitable reference mass is crucial. We further find that perplexity and downstream accuracy favor different k2, cautioning against selecting MoE compression settings using unlabeled text alone. Analyses also show that expert identity matters substantially more than expert weighting, while balanced and domain-specialized routing leaves limited room for expert pruning.