FONDUE: an algorithm to find the optimal dimensionality of the latent representations of variational autoencoders
This addresses a computational bottleneck for researchers and practitioners training VAEs, offering a more efficient method for model selection, though it is incremental as it builds on existing intrinsic dimension estimation techniques.
The paper tackles the problem of determining the optimal number of latent dimensions in variational autoencoders (VAEs) without costly grid search, by proposing FONDUE, an algorithm that uses intrinsic dimension estimation to identify passive variables and quickly find the optimal dimensionality.
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.