Commutative Lie Group VAE for Disentanglement Learning

TL;DR

This paper introduces a novel Lie group-based VAE that learns disentangled representations by modeling data variations with groups, offering a more flexible and property-preserving approach than traditional vector space methods.

Contribution

It proposes the Commutative Lie Group VAE, which encodes data variations with Lie groups and derives natural disentanglement constraints, achieving state-of-the-art results without supervision.

Findings

Effectively learns disentangled representations without supervision

Achieves state-of-the-art performance in disentanglement tasks

Models data variations with Lie groups for better property preservation

Abstract

We view disentanglement learning as discovering an underlying structure that equivariantly reflects the factorized variations shown in data. Traditionally, such a structure is fixed to be a vector space with data variations represented by translations along individual latent dimensions. We argue this simple structure is suboptimal since it requires the model to learn to discard the properties (e.g. different scales of changes, different levels of abstractness) of data variations, which is an extra work than equivariance learning. Instead, we propose to encode the data variations with groups, a structure not only can equivariantly represent variations, but can also be adaptively optimized to preserve the properties of data variations. Considering it is hard to conduct training on group structures, we focus on Lie groups and adopt a parameterization using Lie algebra. Based on the parameterization, some disentanglement learning constraints are naturally derived. A simple model named Commutative Lie Group VAE is introduced to realize the group-based disentanglement learning. Experiments show that our model can effectively learn disentangled representations without supervision, and can achieve state-of-the-art performance without extra constraints.