FONDUE: an algorithm to automatically find the dimensionality of the latent representations of variational autoencoders
Abstract: When training a variational autoencoder (VAE) on a given dataset, determining the number of latent variables requires human supervision and to fully train one or more VAEs. In this paper, we explore ways to simplify this time-consuming process through the lens of the polarised regime. Specifically, we show that the discrepancies between the variance of the mean and sampled representations of a VAE reveal the presence of passive variables in the latent space, which, in well-behaved VAEs, indicates a superfluous number of dimensions.
After formally demonstrating this phenomenon, we use it to propose FONDUE: an unsupervised algorithm which efficiently finds a suitable number of latent dimensions without fully training any models. We additionally show that FONDUE can be extended in a number of ways, providing a principled and unified method for selecting the number of latent dimensions for VAEs and deterministic autoencoders.
Submission Length: Long submission (more than 12 pages of main content)
Previous TMLR Submission Url: https://openreview.net/forum?id=zPA3KzOA7i
Changes Since Last Submission: The previous submission was desk rejected for the following reason:
> The submission doesn't follow TMLR's stylefile format (notably the font isn't the right one). Please fix the format and compare with an existing submission before resubmitting.
We have now ensured that the submission follows TMLR's stylefile format.
Assigned Action Editor: ~Alexander_A_Alemi1
Submission Number: 1249
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