On the Implicit Bias of Linear Equivariant Steerable Networks

Part of Advances in Neural Information Processing Systems 36 (NeurIPS 2023) Main Conference Track

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Ziyu Chen, Wei Zhu


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.