Equivariance Breaks the Learning Rate

תקציר מקורי באנגליתarXiv:2609.08381v2 Announce Type: replace Abstract: Equivariant networks are commonly trained with Adam, yet recent work reports that matrix structured optimizers such as Muon can perform better, with the reasons for these gains only partly understood. We identify one source of this difference inside equivariant layers. An equivariant layer learns one channel mixing matrix $W_l$ per degree $l$, which we call an irrep block, and shares it across the $2l+1$ components, giving the expanded map $W_l \otimes I_{2l+1}$. This sharing sums gradient contributions across components and can produce different update scales under SGD. Adam's entrywise normalization reduces sensitivity to gradient scale, but neither optimizer directly controls the effective step size of each block. A single learning rat