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We study the implicit bias of gradient flow on linear equivariant steerablenetworks in group-invariant binary classification. Our findings reveal that theparameterized predictor converges in direction to the unique group-invariantclassifier with a maximum margin defined by the input group action. Under aunitary assumption on the input representation, we establish the equivalencebetween steerable networks and data augmentation. Furthermore, we demonstratethe improved margin and generalization bound of steerable networks over theirnon-invariant counterparts.

On the Implicit Bias of Linear Equivariant Steerable Networks