Muon grok虽快，后grokking会崩到27.59%；冻结embedding/readout就能稳。想用Muon训Transformer的注意。
论文报告，Muon优化器训练Transformer解(a+b) mod 113时，虽比AdamW更快grok，但9种配置均在后grokking阶段失去泛化，5个种子中有4个的AdamW参考准确率跌到27.59%。梯度降到10^-6后，Muon的步长弹性为-0.03，AdamW为+1.5，Muon组每参数移动快8.0倍。冻结嵌入/读出层可消除崩溃：451,400步和5个配对种子中，未冻结组出现137-321次低于阈值评估，冻结组为零。傅里叶滤波显示掩蔽场景下任务对齐族单独达100%，完整模型仅45.85%，重新缩放可恢复99.9%。
Post-Grokking Collapse at the Representation-Readout Interface in Muon-Trained Transformers
Under the standard split, Muon gets hidden matrices and AdamW embeddings/output head. Muon groks modular addition faster, but its solutions do not hold. All nine configurations on $(a+b) \bmod 113$ grok and later lose generalization. Across five seeds the selected AdamW reference falls below threshold on four, reaching 27.59%. Instability persists across two moduli, two widths, two training fractions, subtraction, and depth. The failure arises at the representation-readout interface, identified only jointly up to an invertible map unselected by the loss. After solving the training set, the gradient falls to order $10^{-6}$ and the optimizers respond differently: step-size elasticity is -0.03 for Muon versus +1.5 for AdamW, and the Muon group moves 8.0 times faster per parameter. From bit-identical states, freezing either group prevents failure. Freezing embeddings/readout removes it in five runs over 451,400 post-grokking steps and five paired seeds: unfrozen arms record 137-321 sub-threshold evaluations, frozen arms none. Removing Muon's normalization and orthogonalization is no substitute: it collapses representation from 326 effective conjugate pairs to 4, shows no recurrent collapse, and fails terminally. Fourier filtering separates circuit failure from masking. Across 43 checkpoints over five seeds and three regimes, the task-aligned family reaches exactly 100% alone. In circuit failure it no longer solves the task; in masking it remains perfect while the full model reaches 45.85%, giving a positive margin on every example, including errors, but being outvoted by a near-equal adversarial remainder. Rescaling it restores 99.9%; grokking is the same condition resolving upward. The task selects the family, swapping $(k,k)$ for $(k,-k)$ under subtraction. Across an abrupt collapse, standard Fourier support is unchanged and the power-distribution cosine remains 0.9899.