Invariant-equivariant representation learning for multi-class data

TL;DR

This paper proposes a probabilistic deep learning framework that disentangles class-invariant features from symmetry-related variations, improving interpretability and performance across various data types.

Contribution

It introduces a novel invariant-equivariant representation learning approach that explicitly models class information and symmetry transformations separately.

Findings

Qualitative analysis shows clear separation of invariant and equivariant features.

Achieves competitive or superior performance in supervised and semi-supervised tasks.

Method is easy to implement and broadly applicable across data types.

Abstract

Representations learnt through deep neural networks tend to be highly informative, but opaque in terms of what information they learn to encode. We introduce an approach to probabilistic modelling that learns to represent data with two separate deep representations: an invariant representation that encodes the information of the class from which the data belongs, and an equivariant representation that encodes the symmetry transformation defining the particular data point within the class manifold (equivariant in the sense that the representation varies naturally with symmetry transformations). This approach is based primarily on the strategic routing of data through the two latent variables, and thus is conceptually transparent, easy to implement, and in-principle generally applicable to any data comprised of discrete classes of continuous distributions (e.g. objects in images, topics in language, individuals in behavioural data). We demonstrate qualitatively compelling representation learning and competitive quantitative performance, in both supervised and semi-supervised settings, versus comparable modelling approaches in the literature with little fine tuning.