Muon optimizer (now used by probably EVERY AI lab)
1. Take the gradient G of a hidden weight matrix W (G = how the loss wants to nudge the weights W).
2. Add momentum: B = mu * B + G (B = a running average of past gradients; mu = momentum decay, about 0.95).
3. Orthogonalize B with 5 Newton-Schulz steps to get O (O = the orthogonalized update: a quintic polynomial applied to B that pushes every singular value of B toward 1).
4. Update the weights: W = W - eta * O (eta = the learning rate; step W against O).
5. Use Muon only for 2D hidden layers - keep AdamW for embeddings, the output head, and biases.
The trick: a momentum update is nearly low-rank - a few directions dominate and drown out the rest. Orthogonalizing flattens all singular values to about 1, so rare-but-useful directions get equal weight. It is steepest descent in spectral norm instead of Euclidean - and it stores one momentum buffer, half of Adam's memory.
Pros:
- about 2x compute efficiency vs AdamW at scale (same loss at 0.519x FLOPs, Moonlight scaling laws).
- half the optimizer memory of Adam (one buffer, not two).
- Newton-Schulz runs in bf16 on GPU - cheap, no SVD.
- already scaled to production (Moonlight 16B MoE / 5.7T tokens, Kimi-K2).
Cons:
- only for 2D hidden layers - embeddings, output head, scalars/biases still need AdamW.
- vanilla Muon lets some weights grow too large over long training; needs added weight decay to fix (Moonshot).
- needs per-parameter update-scale (RMS) matching for stable large-scale training.
- SFT advantage vanishes when pretrain and finetune optimizers differ (authors' own caveat).
- Newton-Schulz only approximates orthogonalization - singular values end up noisy, not exactly 1.
Paper: https://t.co/88Uz99PWI3
Write-up: https://t.co/JGsAYHANGs
Code: https://t.co/MEMqAWOQgO
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Iβm glad you love it brother
This tattoo is going to be with me for the next few months, and honestly I got it because I genuinely believe in $MAD.
And guess Iβm already becoming $MAD too
Either way, Iβll still be carrying $MAD around with me every day, and I think thatβs pretty cool.
My SOL addy hopefully I get justified for making a $MAD tattoo on my body !!
3J3ULRdKqftSaksRZAZdZFFEFEsSKNWKCpDkHMb4nqws
Iβm glad you love it brother
This tattoo is going to be with me for the next few months, and honestly I got it because I genuinely believe in $MAD.
And guess Iβm already becoming $MAD too
Either way, Iβll still be carrying $MAD around with me every day, and I think thatβs pretty cool.
My SOL addy hopefully I get justified for making a $MAD tattoo on my body !!
3J3ULRdKqftSaksRZAZdZFFEFEsSKNWKCpDkHMb4nqws
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@madrichclub_
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A semi-permanent $MAD tattoo.
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One thingβs for sure, Iβll be carrying $MAD with me for life.
@madrichclub_ Iβm glad you love it brother
This tattoo is going to be with me for the next few months, and honestly I got it because I genuinely believe in $MAD.
And guess Iβm already becoming $MAD too
Either way, Iβll still be carrying $MAD around with me every day, and I think thatβs pretty cool.
My SOL addy hopefully I get justified for making a $MAD tattoo on my body !!
3J3ULRdKqftSaksRZAZdZFFEFEsSKNWKCpDkHMb4nqws
@madrichclub_ Iβm glad you love it brother
This tattoo is going to be with me for the next few months, and honestly I got it because I genuinely believe in $MAD.
And guess Iβm already becoming $MAD too
Either way, Iβll still be carrying $MAD around with me every day, and I think thatβs pretty cool.
My SOL addy hopefully I get justified for making a $MAD tattoo on my body !!
3J3ULRdKqftSaksRZAZdZFFEFEsSKNWKCpDkHMb4nqws
@madrichclub_
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Either way, Iβll still be carrying $MAD around with me every day, and I think thatβs pretty cool.
My SOL addy
3J3ULRdKqftSaksRZAZdZFFEFEsSKNWKCpDkHMb4nqws
A semi-permanent $MAD tattoo.
Guess Iβm officially getting $MAD -der.
@madrichclub_ have you ever seen conviction at this level?
If the community loves it, I might just make it permanent.
Letβs go get $MAD
One thingβs for sure, Iβll be carrying $MAD with me for life.
A semi-permanent $MAD tattoo.
Guess Iβm officially getting $MAD -der.
@madrichclub_ have you ever seen conviction at this level?
If the community loves it, I might just make it permanent.
Letβs go get $MAD
One thingβs for sure, Iβll be carrying $MAD with me for life.
A semi-permanent $MAD tattoo.
Guess Iβm officially getting $MAD -der.
@madrichclub_ have you ever seen conviction at this level?
If the community loves it, I might just make it permanent.
Letβs go get $MAD
One thingβs for sure, Iβll be carrying $MAD with me for life.