Understanding Variational Autoencoders with Intrinsic Dimension and Information Imbalance

TL;DR

This paper analyzes how Variational Autoencoders process information by examining intrinsic dimension and information imbalance, revealing phase transitions and providing insights into architecture design and model behavior.

Contribution

It introduces the use of Intrinsic Dimension and Information Imbalance to analyze VAE representations, uncovering phase transitions and training dynamics.

Findings

VAEs exhibit a double hunchback ID profile when bottleneck exceeds data ID

Two training phases identified: rapid fitting and slower generalization

II and ID are useful for architecture search and diagnosing underfitting

Abstract

This work presents an analysis of the hidden representations of Variational Autoencoders (VAEs) using the Intrinsic Dimension (ID) and the Information Imbalance (II). We show that VAEs undergo a transition in behaviour once the bottleneck size is larger than the ID of the data, manifesting in a double hunchback ID profile and a qualitative shift in information processing as captured by the II. Our results also highlight two distinct training phases for architectures with sufficiently large bottleneck sizes, consisting of a rapid fit and a slower generalisation, as assessed by a differentiated behaviour of ID, II, and KL loss. These insights demonstrate that II and ID could be valuable tools for aiding architecture search, for diagnosing underfitting in VAEs, and, more broadly, they contribute to advancing a unified understanding of deep generative models through geometric analysis.