Towards Building A Group-based Unsupervised Representation Disentanglement Framework

TL;DR

This paper introduces a group theory-based framework for unsupervised representation disentanglement, providing theoretical guarantees and improving existing VAE-based models through group-inspired constraints, validated by extensive experiments.

Contribution

It offers a novel theoretical framework for unsupervised disentanglement using group theory and enhances VAE-based models with new constraints derived from this framework.

Findings

Groupified VAEs outperform original VAE-based methods in mean performance.

Theoretical conditions for disentanglement are validated experimentally.

Consistent improvement across five datasets with smaller variances.

Abstract

Disentangled representation learning is one of the major goals of deep learning, and is a key step for achieving explainable and generalizable models. A well-defined theoretical guarantee still lacks for the VAE-based unsupervised methods, which are a set of popular methods to achieve unsupervised disentanglement. The Group Theory based definition of representation disentanglement mathematically connects the data transformations to the representations using the formalism of group. In this paper, built on the group-based definition and inspired by the n-th dihedral group, we first propose a theoretical framework towards achieving unsupervised representation disentanglement. We then propose a model, based on existing VAE-based methods, to tackle the unsupervised learning problem of the framework. In the theoretical framework, we prove three sufficient conditions on model, group structure, and data respectively in an effort to achieve, in an unsupervised way, disentangled representation per group-based definition. With the first two of the conditions satisfied and a necessary condition derived for the third one, we offer additional constraints, from the perspective of the group-based definition, for the existing VAE-based models. Experimentally, we train 1800 models covering the most prominent VAE-based methods on five datasets to verify the effectiveness of our theoretical framework. Compared to the original VAE-based methods, these Groupified VAEs consistently achieve better mean performance with smaller variances.