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Exploiting symmetry in dynamical systems is a powerful way to improve the generalization of deep learning. The model learns to be invariant to transformation and hence is more robust to distribution shift. Data augmentation and equivariant networks are two major approaches to injecting symmetry into learning. However, their exact role in improving generalization is not well understood. In this work, we derive the generalization bounds for data augmentation and equivariant networks,arXiv:2206.09450v1 fatcat:jm3lsuuaxfbdzl24xoklrnilci