
Geometry of Deep Generative Models for Disentangled Representations
Deep generative models like variational autoencoders approximate the int...
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Adversarial Autoencoders with ConstantCurvature Latent Manifolds
Constantcurvature Riemannian manifolds (CCMs) have been shown to be ide...
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Switch Spaces: Learning Product Spaces with Sparse Gating
Learning embedding spaces of suitable geometry is critical for represent...
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Linear Classifiers in Mixed Constant Curvature Spaces
Embedding methods for mixedcurvature spaces are powerful techniques for...
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ChannelRecurrent Variational Autoencoders
Variational Autoencoder (VAE) is an efficient framework in modeling natu...
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Variational Autoencoders with Riemannian Brownian Motion Priors
Variational Autoencoders (VAEs) represent the given data in a lowdimens...
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A curvature and densitybased generative representation of shapes
This paper introduces a generative model for 3D surfaces based on a repr...
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Mixedcurvature Variational Autoencoders
It has been shown that using geometric spaces with nonzero curvature instead of plain Euclidean spaces with zero curvature improves performance on a range of Machine Learning tasks for learning representations. Recent work has leveraged these geometries to learn latent variable models like Variational Autoencoders (VAEs) in spherical and hyperbolic spaces with constant curvature. While these approaches work well on particular kinds of data that they were designed for e.g. treelike data for a hyperbolic VAE, there exists no generic approach unifying all three models. We develop a Mixedcurvature Variational Autoencoder, an efficient way to train a VAE whose latent space is a product of constant curvature Riemannian manifolds, where the percomponent curvature can be learned. This generalizes the Euclidean VAE to curved latent spaces, as the model essentially reduces to the Euclidean VAE if curvatures of all latent space components go to 0.
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