Structured Disentangled Representations

TL;DR

This paper introduces a hierarchical objective for deep latent-variable models that enhances disentanglement of both discrete and continuous factors, improving generalization and representation quality.

Contribution

It proposes a novel hierarchical objective that generalizes the evidence lower bound to better disentangle discrete and continuous variables in unsupervised learning.

Findings

Successfully disentangles discrete variables.

Improves disentanglement of other variables.

Enhances generalization to unseen factor combinations.

Abstract

Deep latent-variable models learn representations of high-dimensional data in an unsupervised manner. A number of recent efforts have focused on learning representations that disentangle statistically independent axes of variation by introducing modifications to the standard objective function. These approaches generally assume a simple diagonal Gaussian prior and as a result are not able to reliably disentangle discrete factors of variation. We propose a two-level hierarchical objective to control relative degree of statistical independence between blocks of variables and individual variables within blocks. We derive this objective as a generalization of the evidence lower bound, which allows us to explicitly represent the trade-offs between mutual information between data and representation, KL divergence between representation and prior, and coverage of the support of the empirical data distribution. Experiments on a variety of datasets demonstrate that our objective can not only disentangle discrete variables, but that doing so also improves disentanglement of other variables and, importantly, generalization even to unseen combinations of factors.