FONDUE: an algorithm to find the optimal dimensionality of the latent representations of variational autoencoders

TL;DR

FONDUE is a novel algorithm that efficiently determines the optimal latent dimensionality of VAEs by analyzing intrinsic dimension discrepancies, reducing reliance on costly grid searches.

Contribution

The paper introduces FONDUE, a new method leveraging intrinsic dimension estimation to automatically select the appropriate number of latent variables in VAEs.

Findings

FONDUE accurately identifies the optimal latent dimension.

It reduces computational costs compared to grid search.

The method detects passive variables in latent space.

Abstract

When training a variational autoencoder (VAE) on a given dataset, determining the optimal number of latent variables is mostly done by grid search: a costly process in terms of computational time and carbon footprint. In this paper, we explore the intrinsic dimension estimation (IDE) of the data and latent representations learned by VAEs. We show that the discrepancies between the IDE of the mean and sampled representations of a VAE after only a few steps of training reveal the presence of passive variables in the latent space, which, in well-behaved VAEs, indicates a superfluous number of dimensions. Using this property, we propose FONDUE: an algorithm which quickly finds the number of latent dimensions after which the mean and sampled representations start to diverge (i.e., when passive variables are introduced), providing a principled method for selecting the number of latent dimensions for VAEs and autoencoders.