Hey everyone! 
I’m excited to share a comprehensive tutorial I’ve created on understanding and implementing the Muon optimizer - a recent innovation that’s showing impressive performance improvements over traditional optimizers like AdamW and SGD.
What is Muon?
Muon (MomentUm Orthogonalized by Newton-Schulz) was introduced by Keller Jordan in October 2024 and has quickly gained attention in the optimization community. It specifically targets matrix parameters in neural networks, using Newton-Schulz iterations to orthogonalize gradient updates.
What does this tutorial cover?
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The Problem: Why traditional optimizers struggle with skewed singular value distributions
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The Solution: How Muon’s matrix orthogonalization addresses this fundamental issue
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Practical Implementation: A clean, educational implementation in PyTorch
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Performance Analysis: Experimental results showing Muon’s benefits
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Lessons Learned: Practical insights from implementing and using Muon
Key Findings
In my experiments, Muon significantly outperformed traditional optimizers:
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On MNIST, Muon achieved 34% lower loss than AdamW after just 3 epochs
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On CIFAR-10, Muon reached 80.79% accuracy vs. AdamW’s 71.66% after 5 epochs
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All this with minimal computational overhead on modern hardware
Why I created this
While exploring Muon, I found there was a gap between the mathematical description in research papers and practical implementation details. This tutorial aims to bridge that gap, providing both theoretical understanding and a working implementation.
I was particularly struck by how a relatively simple mathematical insight - orthogonalizing gradient updates to better utilize the full parameter space - could lead to such significant performance improvements.
Check it out!
The repository includes a full README explanation and a Colab notebook where you can run all the experiments yourself.
I’d love to hear your thoughts, questions, or experiences if you try Muon in your own projects!