Information bottleneck through variational glasses

TL;DR

This paper explores the information bottleneck framework for generative models, providing a variational decomposition that unifies and interprets various VAE and GAN-based methods, enhancing understanding and potential applications.

Contribution

It introduces a variational decomposition of mutual information within the IB framework, offering a new interpretation of VAE and related models, and connecting them through a common structure.

Findings

Unified variational decomposition of mutual information for generative models

Connections established between VAE, beta-VAE, AAE, InfoVAE, and VAE/GAN

Enhanced interpretability and potential for improved generative model analysis

Abstract

Information bottleneck (IB) principle [1] has become an important element in information-theoretic analysis of deep models. Many state-of-the-art generative models of both Variational Autoencoder (VAE) [2; 3] and Generative Adversarial Networks (GAN) [4] families use various bounds on mutual information terms to introduce certain regularization constraints [5; 6; 7; 8; 9; 10]. Accordingly, the main difference between these models consists in add regularization constraints and targeted objectives. In this work, we will consider the IB framework for three classes of models that include supervised, unsupervised and adversarial generative models. We will apply a variational decomposition leading a common structure and allowing easily establish connections between these models and analyze underlying assumptions. Based on these results, we focus our analysis on unsupervised setup and reconsider the VAE family. In particular, we present a new interpretation of VAE family based on the IB framework using a direct decomposition of mutual information terms and show some interesting connections to existing methods such as VAE [2; 3], beta-VAE [11], AAE [12], InfoVAE [5] and VAE/GAN [13]. Instead of adding regularization constraints to an evidence lower bound (ELBO) [2; 3], which itself is a lower bound, we show that many known methods can be considered as a product of variational decomposition of mutual information terms in the IB framework. The proposed decomposition might also contribute to the interpretability of generative models of both VAE and GAN families and create a new insights to a generative compression [14; 15; 16; 17]. It can also be of interest for the analysis of novelty detection based on one-class classifiers [18] with the IB based discriminators.