Data Augmentation vs. Equivariant Networks: A Theoretical Study of Generalizability on Dynamics Forecasting

Exploiting symmetry in structured data is a powerful way to improve the learning and generalization ability of deep learning models. Data augmentation and equivariant neural nets are two of the main approaches for enabling neural nets to preserve symmetries. Since real-world data is rarely strictly symmetric, recently, several approximately equivariant networks have also been introduced. In this work, we theoretically compare the generalizability of data augmentation techniques, strictly equivariant networks, and approximately equivariant networks.Unlike most prior theoretical works on symmetry that are based on the i.i.d assumption, we instead focus on generalizability of these three approaches on the task of non-stationary dynamics forecasting.