Revisiting Factorizing Aggregated Posterior in Learning Disentangled Representations

TL;DR

This paper reveals a theoretical gap in current disentangled representation learning methods that penalize total correlation, showing that low sampled total correlation does not ensure low mean total correlation, and proposes a solution to address this issue.

Contribution

It provides a theoretical analysis of the disparity between sampled and mean representations in disentanglement, and introduces a method to reduce mean total correlation.

Findings

Low total correlation of samples does not guarantee low total correlation of means.

The proposed method effectively reduces mean total correlation, leading to more factorized representations.

The paper discusses limitations of current approaches, highlighting the issue of factor disintegration.

Abstract

In the problem of learning disentangled representations, one of the promising methods is to factorize aggregated posterior by penalizing the total correlation of sampled latent variables. However, this well-motivated strategy has a blind spot: there is a disparity between the sampled latent representation and its corresponding mean representation. In this paper, we provide a theoretical explanation that low total correlation of sampled representation cannot guarantee low total correlation of the mean representation. Indeed, we prove that for the multivariate normal distributions, the mean representation with arbitrarily high total correlation can have a corresponding sampled representation with bounded total correlation. We also propose a method to eliminate this disparity. Experiments show that our model can learn a mean representation with much lower total correlation, hence a factorized mean representation. Moreover, we offer a detailed explanation of the limitations of factorizing aggregated posterior: factor disintegration. Our work indicates a potential direction for future research of disentangled learning.