On the Implicit Bias of Linear Equivariant Steerable Networks

Ziyu Chen, Wei Zhu

Keywords: implicit bias, equivariant steerable networks, data augmentation, margin, generalization bound

TL;DR: We analyze the implicit bias of gradient flow on linear equivariant steerable networks and demonstrate their implications in margin and generalization.

Abstract: We study the implicit bias of gradient flow on linear equivariant steerable networks in group-invariant binary classification. Our findings reveal that the parameterized predictor converges in direction to the unique group-invariant classifier with a maximum margin defined by the input group action. Under a unitary assumption on the input representation, we establish the equivalence between steerable networks and data augmentation. Furthermore, we demonstrate the improved margin and generalization bound of steerable networks over their non-invariant counterparts.

Submission Number: 1659