Meet Muon - the optimizer quietly powering some of the most advanced AI models in the world. It’s not just another theoretical breakthrough; it’s the secret sauce behind Kimi-K2, Moonshot AI’s trillion-parameter language MoE model that’s now outperforming even GPT-4 in some benchmarks.
So, what makes Muon special?
Traditional optimizers treat all parameters the same, but Muon is smarter. It understands that weight matrices have unique geometric structures. By tuning them with this insight, Muon speeds up training by 35% and cuts down token usage by 15%, all without sacrificing performance.
In short, Muon is helping push the boundaries of what’s possible in AI and it’s doing it faster and leaner than ever before.
Muon Optimizer Process Flow
The algorithm might seem overwhelming at first, but through this blog, I will explain everything that you will need to understand how it works, why it is better and what’s the catch.
Onwards!
When training neural networks, we're essentially solving a massive optimization problem - adjusting millions or billions of parameters to minimize errors. Imagine trying to tune a classical piano with a million strings simultaneously. Traditional optimizers like AdamW treat each parameter independently, like tuning each string without considering how they work together.
This approach creates a fundamental problem: the parameter updates become ill-conditioned. In simple terms, this means the optimizer heavily favors certain directions for improvement while neglecting others that might be equally important. It's like having a gardener who waters some plants too much while others barely get any water.
When we examine the gradient matrices that traditional optimizers produce, we find they often have very high condition numbers. Here's what this means in practical terms:
Muon (MomentUm Orthogonalized by Newton-Schulz) solves this problem through a elegant mathematical insight: instead of applying raw momentum updates, it orthogonalizes them to create more balanced parameter changes.