Muon Optimizer vs AdamW: What a NanoGPT Test Reveals About the Future of AI Training

Every large language model you have ever talked to was trained by a piece of software most people never think about: the optimizer. It is the quiet workhorse of machine learning. It looks at how wrong the model is, and then nudges billions of numbers in the right direction, over and over, until the model starts producing sensible text. Get the optimizer right and you save millions of dollars in computing power. Get it wrong and your training run crawls, or collapses entirely.

For years, one optimizer has ruled them all: AdamW. It is reliable, well understood, and baked into nearly every training pipeline on the planet. But a new challenger called Muon has been getting serious attention, and a fresh hands-on test against AdamW inside NanoGPT gives us a clear, honest look at what is actually different, and what it might mean for the next wave of AI models.

The Optimizer Problem, in Plain Terms

Imagine you are trying to find the lowest point in a vast, foggy valley while blindfolded. You can only feel the slope under your feet. Your strategy for deciding which direction to step, and how big a step to take, is your optimizer.

AdamW is a smart, adaptive strategy. It remembers which directions have been useful in the past and gives those directions bigger steps. It also keeps a per-parameter running average of how noisy the ground feels, so it does not overreact to a single bump. That combination has made it the default choice for training transformers and almost everything else.

The downside is memory and bookkeeping. AdamW has to store several extra numbers for every single parameter in the model. On a model with billions of parameters, that is a huge amount of extra memory and extra work on every step. As models get bigger, that overhead becomes a real financial and engineering problem.

What Muon Does Differently

Muon takes a different angle. Its name stands for MomentUm Orthogonalized by Newton-Schulz, and that name is actually a pretty good summary of the idea.

Instead of tracking a separate adaptive learning rate for every individual weight, Muon collects the momentum, the smoothed-out direction of recent updates, and then reshapes it. It pushes that update toward being orthogonal, meaning the different directions of change are made as independent from one another as possible. The Newton-Schulz part is just the fast, iterative math trick used to do that reshaping cheaply without a heavy matrix decomposition.

Why would that help? Because in a big neural network, many weight updates end up pointing in similar directions and stepping on each other's toes. When updates overlap, you waste effort. If you force them to spread out and act independently, each step can carry more useful information. You are essentially making every stride count.

In practice, Muon is usually applied only to the big two-dimensional weight matrices inside the model, the layers where most of the parameters live. The embeddings, the output layer, and the small one-dimensional settings still typically use AdamW. So the real-world comparison is not "Muon instead of AdamW" but "Muon plus a little AdamW."

Why NanoGPT Is the Right Test Lab

NanoGPT is the perfect place to run this comparison, and that is the most important practical lesson in the whole exercise.

NanoGPT is a deliberately small, readable implementation of a GPT-style language model. It trains on character-level text on a single machine, and the whole codebase is short enough to read in an afternoon. That makes it a laboratory rather than a production system. You can swap one optimizer for another, hold everything else constant, and see what changes.

This matters because optimizer claims are notoriously hard to evaluate. A new method can look brilliant on a paper benchmark and then fall apart when you bolt it onto a real training run with a different learning rate schedule, a different batch size, or a different model shape. Small, faithful test setups like NanoGPT are how the field separates genuine improvements from lucky configurations.

Testing Muon against AdamW in NanoGPT means both optimizers get the same data, the same model, the same schedule, and the same hardware. Whatever gap shows up comes from the optimizer itself, not from a hidden advantage somewhere else in the pipeline.

Reading the Results Without Overreading Them

Here is where discipline matters. A win in a small-scale test is a signal, not a verdict. There are several honest caveats anyone should keep in mind.

• Scale changes everything. Optimizers that shine at small scale do not automatically shine at large scale. The dynamics of training a model with billions of parameters are genuinely different from training a small one.
• Hyperparameters are fragile. Muon may want a different learning rate or a different schedule than AdamW. Comparing them with identical settings is fair, but it may understate what either one can do when properly tuned.
• Engineering support matters. AdamW is optimized to the metal. Every major framework, chip vendor, and distributed training library has spent years making AdamW fast. Muon is younger, and its real-world speed depends on whether the orthogonalization step is implemented efficiently on your hardware.
• Stability at scale is unproven in a lab. Long training runs can hit loss spikes and instabilities that simply do not appear in short experiments.

None of that weakens the case for Muon. It just means the right takeaway is "worth testing on your own workload," not "throw out AdamW tomorrow."

The Bigger Trend: Everyone Is Chasing Training Efficiency

Step back and the Muon story fits into a much larger shift in AI. The industry's center of gravity has moved from "can we build a bigger model?" to "can we train a model of the same quality with less compute, less memory, and less energy?"

That shift shows up everywhere. Researchers are rethinking data quality, model architecture, quantization, and, crucially, the low-level math of training itself. The optimizer is one of the last places where a relatively small change can produce a large, compounding payoff, because it touches every single training step. A one-percent improvement in step efficiency across a multi-week training run is not a rounding error; it is a meaningful chunk of a compute budget.

Muon is attractive precisely because it attacks the problem from a different angle than AdamW. AdamW's memory overhead scales with the number of parameters. Muon's approach to momentum is structurally leaner in the parts of the model where most parameters live. If that advantage holds up at scale, it changes the economics of training.

What This Means for the Future of AI

If Muon-style optimizers prove themselves on large models, the effects ripple outward in three ways.

1. Cheaper training means more experimentation

When each training run costs less, more teams can afford to run more experiments. That tends to accelerate progress, because the field's breakthroughs often come from many small attempts rather than one giant one. It also democratizes access: labs and startups without hyperscaler budgets get to play in a game that has felt increasingly closed.

2. Memory becomes the new battleground

Optimizer state is a major consumer of GPU memory. Any method that shrinks it means you can fit a larger model, or a larger batch, on the same hardware. That is the difference between needing a bigger cluster and not needing one at all.

3. The default stops being obvious

For years, "just use AdamW" was the safe answer and nobody questioned it. Once credible alternatives exist, teams have to actually measure. That is healthier for the field, even if it means more work.

Practical Implications for Businesses

Most companies are not training foundation models from scratch. But almost every company is now fine-tuning, distilling, or serving models, and that is exactly where optimizer choices show up as real money.

For teams fine-tuning models: a leaner optimizer can mean fitting a larger fine-tune onto the GPUs you already own, or cutting the cost of a training job. Even modest improvements compound across many runs.

For teams running many experiments: faster steps mean more iterations per week, which means faster time to a working model. Speed of iteration is often a bigger competitive advantage than raw quality.

For teams with strict energy or cost targets: training efficiency translates directly into lower electricity use and lower cloud bills. That is increasingly a board-level number, not just an engineering detail.

For procurement and infrastructure planning: if optimizer-level efficiency keeps improving, the hardware you need for a given workload may drop. Locking into long, expensive commitments without testing newer methods is a risk worth re-examining.

Actionable Insights

• Run your own A/B test. Take a small, faithful version of your actual training setup, the way NanoGPT is a small, faithful GPT, and swap the optimizer. Do not trust a general benchmark over your own data.
• Keep AdamW for the edges. If you try Muon, use it on the large 2D weight matrices and leave embeddings, the output layer, and 1-D parameters on AdamW. That is the standard, pragmatic split.
• Re-tune the learning rate. A new optimizer with old hyperparameters is a false comparison. Budget time to find the right settings before you judge.
• Measure wall-clock time, not just step count. A mathematically cheaper update can be slower in practice if the implementation is not optimized for your hardware.
• Watch for instability over long runs. Short tests look great; multi-day runs reveal whether a method is robust.
• Track memory, not just loss. Optimizer state is a large hidden cost. Halving it can change what hardware you need entirely.
• Keep a baseline. Always retain an AdamW run as your reference point so you never lose track of what "normal" looks like for your workload.

The Road Ahead

The most interesting thing about the Muon-versus-AdamW comparison is not that one wins. It is that the question is being asked seriously at all. For years the optimizer layer felt settled, a solved problem buried under the more glamorous work of architecture and data. That is no longer true.

As model training costs climb and the returns on simply adding more compute start to flatten, the field is being forced to get smarter about the fundamentals. Small, careful experiments in tools like NanoGPT are how that happens. They let anyone, a solo developer, a research lab, a corporate ML team, test an idea in an afternoon instead of a quarter.

The likely future is not a world where one optimizer replaces another overnight. It is a world with a richer toolkit: AdamW where it is proven and reliable, Muon-style methods where the math pays off, and a culture of measuring instead of assuming. That is a healthier, cheaper, and faster-moving AI industry, and it starts with tests exactly like this one.