Diffusion Variational Autoencoders

Luis A. Perez Rey; V. Menkovski; Jacobus W. Portegies

Diffusion Variational Autoencoders

Luis A. Perez Rey, V. Menkovski, Jacobus W. Portegies

Research output: Contribution to conference › Paper › Academic

Abstract

A standard Variational Autoencoder, with a Euclidean latent space, is structurally incapable of capturing topological properties of certain datasets. To remove topological obstructions, we introduce Diffusion Variational Autoencoders DeltaVAE with arbitrary (closed) manifolds as a latent space. A Diffusion Variational Autoencoder uses transition kernels of Brownian motion on the manifold. In particular, it uses properties of the Brownian motion to implement the reparametrization trick and fast approximations to the KL divergence.
We show that the DeltaVAE is indeed capable of capturing topological properties for datasets with a known underlying latent structure derived from generative processes such as rotations and translations.

Original language	English
Publication status	Accepted/In press - 11 Jul 2020
Event	29th International Joint Conference on Artificial Intelligence - 17th Pacific Rim International Conference on Artificial Intelligence. - Pacifico Convention Plaza Yokohama, Yokohama, Japan Duration: 11 Jul 2020 → 17 Jul 2020 Conference number: 29 https://ijcai20.org/

Conference

Conference	29th International Joint Conference on Artificial Intelligence - 17th Pacific Rim International Conference on Artificial Intelligence.
Abbreviated title	IJCAI-PRICAI 2020
Country	Japan
City	Yokohama
Period	11/07/20 → 17/07/20
Internet address	https://ijcai20.org/

Keywords

Brownian Movement
Topology
Deep learning

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@conference{6fb709abdcaa4998a3edd2097789eaf3,

title = "Diffusion Variational Autoencoders",

abstract = "A standard Variational Autoencoder, with a Euclidean latent space, is structurally incapable of capturing topological properties of certain datasets. To remove topological obstructions, we introduce Diffusion Variational Autoencoders DeltaVAE with arbitrary (closed) manifolds as a latent space. A Diffusion Variational Autoencoder uses transition kernels of Brownian motion on the manifold. In particular, it uses properties of the Brownian motion to implement the reparametrization trick and fast approximations to the KL divergence. We show that the DeltaVAE is indeed capable of capturing topological properties for datasets with a known underlying latent structure derived from generative processes such as rotations and translations.",

keywords = "Brownian Movement, Topology, Deep learning",

author = "{Perez Rey}, {Luis A.} and V. Menkovski and Portegies, {Jacobus W.}",

year = "2020",

month = jul,

day = "11",

language = "English",

note = "29th International Joint Conference on Artificial Intelligence - 17th Pacific Rim International Conference on Artificial Intelligence., IJCAI-PRICAI 2020 ; Conference date: 11-07-2020 Through 17-07-2020",

url = "https://ijcai20.org/",

}

TY - CONF

T1 - Diffusion Variational Autoencoders

AU - Perez Rey, Luis A.

AU - Menkovski, V.

AU - Portegies, Jacobus W.

N1 - Conference code: 29

PY - 2020/7/11

Y1 - 2020/7/11

N2 - A standard Variational Autoencoder, with a Euclidean latent space, is structurally incapable of capturing topological properties of certain datasets. To remove topological obstructions, we introduce Diffusion Variational Autoencoders DeltaVAE with arbitrary (closed) manifolds as a latent space. A Diffusion Variational Autoencoder uses transition kernels of Brownian motion on the manifold. In particular, it uses properties of the Brownian motion to implement the reparametrization trick and fast approximations to the KL divergence. We show that the DeltaVAE is indeed capable of capturing topological properties for datasets with a known underlying latent structure derived from generative processes such as rotations and translations.

AB - A standard Variational Autoencoder, with a Euclidean latent space, is structurally incapable of capturing topological properties of certain datasets. To remove topological obstructions, we introduce Diffusion Variational Autoencoders DeltaVAE with arbitrary (closed) manifolds as a latent space. A Diffusion Variational Autoencoder uses transition kernels of Brownian motion on the manifold. In particular, it uses properties of the Brownian motion to implement the reparametrization trick and fast approximations to the KL divergence. We show that the DeltaVAE is indeed capable of capturing topological properties for datasets with a known underlying latent structure derived from generative processes such as rotations and translations.

KW - Brownian Movement

KW - Topology

KW - Deep learning

M3 - Paper

T2 - 29th International Joint Conference on Artificial Intelligence - 17th Pacific Rim International Conference on Artificial Intelligence.

Y2 - 11 July 2020 through 17 July 2020

ER -