# [Tutorial] Understanding and Implementing the Muon Optimizer

> Source: <https://discuss.huggingface.co/t/tutorial-understanding-and-implementing-the-muon-optimizer/167717#post_4>
> Published: 2026-10-25 21:54:21+00:00

**Update: Muon → Muon/Dion3 experiments at scale!**

Since writing this tutorial, I’ve been investigating whether Muon and Dion3 retain their convergence advantages over Adam under practical training conditions, as part of my work for [PyTorch Conference](https://events.linuxfoundation.org/pytorch-conference-north-america/program/schedule/?topic=training) NA 2026.

The work grew into a debugging saga involving learning-rate scheduling, distributed optimizer state, and a silent tensor aliasing bug.

I’ve collected the presentation and my OLMo-core PR in one place:

 **PyTorch Con NA 2026 project materials:**

If you’re interested in how orthogonalized optimizers behave beyond the algorithm itself, come take a look!