From Parallel to Sequential: Small-Batch Noise Restores Simplicity Bias of Muon
Simplicity bias, which can arise from sequential feature learning during training, has been proposed as a general explanation for the success of deep learning. An important driver of this phenomenon is saddle-to-saddle behavior, in which the gradient flow trajectory remains close to a sequence of saddle manifolds while learning one feature at a time. However, Muon, a state-of-the-art optimizer based on spectral descent, does not exhibit such dynamics in the full-batch setting and instead learns features in parallel. How is it then that Muon is so successful in deep learning settings? We show that stochastic gradient noise fundamentally changes this behavior: small-batch noise restores seq...
| Authors | Tom Jacobs, Rebekka Burkholz |
|---|---|
| Primary category | cs.LG |
| Published | 12 October 2026 |
| Last updated at source | 12 October 2026 |
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