Unsupervised Learning of Group Invariant and Equivariant Representations

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Paper "Unsupervised Learning of Group Invariant and Equivariant Representations": https://arxiv.org/abs/2202.07559

Abstract: 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.

Authors: Robin Winter, Marco Bertolini, Tuan Le, Frank Noé, Djork-Arné Clevert

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Chapters

00:00 - Intro
01:45 - Motivation: Symmetry in Data
04:40 - Defining Representations and Equivariance
10:49 - Unsupervised Invariant Representation Learning
26:49 - Q+A
36:04 - Some Practical Examples for Groups
50:59 - Examples and Results for Graphs
55:52 - Results: E(3) and Sn Symmetry
1:00:52 - Q+A