Improving the Generation of VAEs with High Dimensional Latent Spaces by the use of Hyperspherical Coordinates

TL;DR

This paper introduces a hyperspherical coordinate-based parameterization for VAEs with high-dimensional latent spaces, improving their generative quality by reducing latent sparsity and enhancing meaningful data reconstruction.

Contribution

The paper presents a novel hyperspherical coordinate approach for VAEs that addresses high-dimensional latent space issues, with a new parameterization method that is computationally efficient.

Findings

Improved data generation quality in high-dimensional VAEs

Reduced latent sparsity through hyperspherical coordinates

Enhanced VAE performance with minimal computational overhead

Abstract

Variational autoencoders (VAE) encode data into lower-dimensional latent vectors before decoding those vectors back to data. Once trained, decoding a random latent vector from the prior usually does not produce meaningful data, at least when the latent space has more than a dozen dimensions. In this paper, we investigate this issue by drawing insight from high dimensional statistics: in these regimes, the latent vectors of a standard VAE are by construction distributed uniformly on a hypersphere. We propose to formulate the latent variables of a VAE using hyperspherical coordinates, which allows compressing the latent vectors towards an island on the hypersphere, thereby reducing the latent sparsity and we show that this improves the generation ability of the VAE. We propose a new parameterization of the latent space with limited computational overhead.