Learning unfolded networks with a cyclic group structure

Deep neural networks lack straightforward ways to incorporate domain knowledge and are notoriously treated as black boxes. Prior works attempted to inject domain knowledge into architectures implicitly through data augmentation. Building on recent advances on equivariant neural networks, we propose networks that explicitly encode domain knowledge, specifically equivariance with respect to rotations. By using unfolded architectures, a rich framework that originated from sparse coding and has theoretical guarantees, we present interpretable networks with sparse activations. The equivariant unfolded networks compete favorably with baselines, with only a fraction of their parameters, as showcased on (rotated) MNIST and CIFAR-10.