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Exploiting symmetry in dynamical systems is a powerful way to improve thegeneralization of deep learning. The model learns to be invariant totransformation and hence is more robust to distribution shift. Dataaugmentation and equivariant networks are two major approaches to injectingsymmetry into learning. However, their exact role in improving generalizationis not well understood. In this work, we derive the generalization bounds fordata augmentation and equivariant networks, characterizing their effect onlearning in a unified framework. Unlike most prior theories for the i.i.d.setting, we focus on non-stationary dynamics forecasting with complex temporaldependencies.

Data Augmentation vs. Equivariant Networks: A Theory of Generalization on Dynamics Forecasting