Meta-Learning Symmetries by Reparameterization

Abstract: Many successful deep learning architectures are equivariant to certain transformations in order to conserve parameters and improve generalization: most famously, convolution layers are equivariant to shifts of the input. This approach only works when practitioners know a-priori symmetries of the task and can manually construct an architecture with the corresponding equivariances. Our goal is a general approach for learning equivariances from data, without needing prior knowledge of a task's symmetries or custom task-specific architectures. We present a method for learning and encoding equivariances into networks by learning corresponding parameter sharing patterns from data. Our method can provably encode equivariance-inducing parameter sharing for any finite group of symmetry transformations, and we find experimentally that it can automatically learn a variety of equivariances from symmetries in data. We provide our experiment code and pre-trained models at https://github.com/AllanYangZhou/metalearning-symmetries.