Unsupervised Learning of Group Invariant and Equivariant Representations
This work addresses the challenge of improving training efficiency and generalization in unsupervised learning for researchers in machine learning, though it is incremental as it builds on existing equivariant neural network concepts.
The authors tackled the problem of extending group invariant and equivariant representation learning to unsupervised deep learning by proposing an encoder-decoder framework that separates latent representations into invariant and equivariant components, achieving robust performance across diverse data types and network architectures in experiments.
Equivariant neural networks, whose hidden features transform according to representations of a group G acting on the data, exhibit training efficiency and an improved generalisation performance. In this work, we extend group invariant and equivariant representation learning to the field of unsupervised deep learning. We propose a general learning strategy based on an encoder-decoder framework in which the latent representation is separated in an invariant term and an equivariant group action component. The key idea is that the network learns to encode and decode data to and from a group-invariant representation by additionally learning to predict the appropriate group action to align input and output pose to solve the reconstruction task. We derive the necessary conditions on the equivariant encoder, and we present a construction valid for any G, both discrete and continuous. We describe explicitly our construction for rotations, translations and permutations. We test the validity and the robustness of our approach in a variety of experiments with diverse data types employing different network architectures.