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.
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/Territory | Japan |
City | Yokohama |
Period | 11/07/20 → 17/07/20 |
Internet address |
Keywords
- Brownian Movement
- Topology
- Deep learning