Increasing Expressivity of a Hyperspherical VAE

Tim R. Davidson; Jakub M. Tomczak; Efstratios Gavves

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arXiv · 1910.02912

Increasing Expressivity of a Hyperspherical VAE

Tim R. Davidson·Jakub M. Tomczak·Efstratios Gavves

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Abstract

Learning suitable latent representations for observed, high-dimensional data is an important research topic underlying many recent advances in machine learning. While traditionally the Gaussian normal distribution has been the go-to latent parameterization, recently a variety of works have successfully proposed the use of manifold-valued latents. In one such work (Davidson et al., 2018), the authors empirically show the potential benefits of using a hyperspherical von Mises-Fisher (vMF) distribution in low dimensionality. However, due to the unique distributional form of the vMF, expressivity in higher dimensional space is limited as a result of its scalar concentration parameter leading to a 'hyperspherical bottleneck'. In this work we propose to extend the usability of hyperspherical parameterizations to higher dimensions using a product-space instead, showing improved results on a selection of image datasets.

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BibTeX RIS

Tim R. Davidson, Jakub M. Tomczak, Efstratios Gavves. 2019-10-07. Increasing Expressivity of a Hyperspherical VAE. https://arxiv.org/abs/1910.02912

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