Symmetry-Aware Feature Learning: A Polynomial Separation for Multi-Index Models

תקציר מקורי באנגליתarXiv:2610.08420v1 Announce Type: new Abstract: We establish a polynomial sample complexity separation between symmetry-aware and symmetry-agnostic feature learning. We study growing-rank multi-index models with high-dimensional Gaussian covariates in $\mathbb{R}^d$ and $r=\Theta(d^\delta)$ teacher directions forming a cyclic symmetry orbit, where $0<\delta<1/2$. We compare three ways of exploiting this structure: architectural weight sharing, data augmentation over the full symmetry group, and learning without access to the symmetry. In particular, we analyze a symmetry-tied convolutional network, an untied network, and the same untied network trained with full-group data augmentation, using spherical online SGD with correlation loss. For a class of polynomial links with information expon