# ExpertMuon-Compass: Alignment-Guided Step Sizes for Mixture-of-Experts Training

arXiv: https://arxiv.org/abs/2610.04140 · HTML: https://mlsanity.com/paper/2610.04140/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in MoE large language models, one of 12 directions in Mixture-of-experts.
- Builds on 13 of its 21 references that are in the map.
- First posted on arXiv 2 Oct 2026.

## Placed in

- Mixture-of-experts / [MoE large language models](https://mlsanity.com/moe/moe-large-language-models/)

## Builds on (most cited first, 13 of 13)

- [Outrageously Large Neural Networks: The Sparsely-Gated Mixture-of-Experts Layer](https://mlsanity.com/paper/1701.06538/) (2017)
- [Switch Transformers: Scaling to Trillion Parameter Models with Simple and Efficient Sparsity](https://mlsanity.com/paper/2101.03961/) (2021)
- [DataComp-LM: In search of the next generation of training sets for language models](https://mlsanity.com/paper/2406.11794/) (2024)
- [OLMoE: Open Mixture-of-Experts Language Models](https://mlsanity.com/paper/2409.02060/) (2024)
- [Auxiliary-Loss-Free Load Balancing Strategy for Mixture-of-Experts](https://mlsanity.com/paper/2408.15664/) (2024)
- [SOAP: Improving and Stabilizing Shampoo using Adam](https://mlsanity.com/paper/2409.11321/) (2024)
- [FineWeb2: One Pipeline to Scale Them All -- Adapting Pre-Training Data Processing to Every Language](https://mlsanity.com/paper/2506.20920/) (2025)
- [JetMoE: Reaching Llama2 Performance with 0.1M Dollars](https://mlsanity.com/paper/2404.07413/) (2024)
- [Cautious Optimizers: Improving Training with One Line of Code](https://mlsanity.com/paper/2411.16085/) (2024)
- [Convergence of Muon with Newton-Schulz](https://mlsanity.com/paper/2601.19156/) (2026)
- [Diversifying the Mixture-of-Experts Representation for Language Models with Orthogonal Optimizer](https://mlsanity.com/paper/2310.09762/) (2023)
- [Beyond the Ideal: Analyzing the Inexact Muon Update](https://mlsanity.com/paper/2510.19933/) (2025)
- [On Surprising Effectiveness of Masking Updates in Adaptive Optimizers](https://mlsanity.com/paper/2602.15322/) (2026)

## Abstract (arXiv)

Mixture-of-experts (MoE) language models send each token to a few experts, so each expert is trained on a different part of the data, and this part changes during training. With a shared learning rate, Muon applies updates of roughly the same size to expert matrices of the same shape, even when an expert's update is poorly aligned with its current gradient. We here propose ExpertMuon-Compass (Compass), which multiplies the Muon step of each expert by two factors. A family factor compares the cosine between the expert's orthogonalized update and its gradient with the same cosine for the other experts in its layer. A scalar radius aggregates the alignment between corresponding rows of the update and gradient into one step-length multiplier. Compass keeps the update direction and the momentum buffer of Muon. In pretraining on FineWeb-Edu, Compass with Nesterov momentum on all matrices performs as well as or better than Muon, NorMuon, and other optimizers, with weight decay matched to NorMuon in the longer runs. Adding its factors to NorMuon gives the same or a lower loss than NorMuon. Compass is the most effective when the data seen by each expert varies during training, for example, as when the languages of a multilingual corpus arrive in separate blocks. With Compass, the expert load stays balanced, and the router assigns tokens to experts more decisively. We also prove a perturbation bound for the two factors.