  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, characterizing their effect on
learning in a unified framework. Unlike most prior theories for the i.i.d.
setting, we focus on non-stationary dynamics forecasting with complex temporal
dependencies.
