Pith. sign in

REVIEW 1 cited by

Diffusion Variational Autoencoders

Not yet reviewed by Pith; the record is open.

This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.

SPECIMEN: schema-true, not a live event

T0 review · schema-true

One-sentence machine reading of the paper's core claim.

pith:XXXXXXXX · record.json · timestamp

arxiv 1901.08991 v2 pith:4EI4VLCB submitted 2019-01-25 cs.LG stat.ML

classification cs.LGstat.ML
keywords topologicalvariationaldiffusionpropertiesautoencoderlatentautoencodersbrownian
verification ladder T0 review T1 audit T2 compute T3 formal
0 comments
read the original 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 with arbitrary 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 Diffusion Variational Autoencoder is capable of capturing topological properties of synthetic datasets. Additionally, we train MNIST on spheres, tori, projective spaces, SO(3), and a torus embedded in R3. Although a natural dataset like MNIST does not have latent variables with a clear-cut topological structure, training it on a manifold can still highlight topological and geometrical properties.

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Characterizing Neural Manifolds' Properties and Curvatures using Normalizing Flows

    q-bio.NC 2025-06 conditional novelty 6.0 of 10

    A normalizing flow with a mixture-of-Gaussians latent space and a quadratic post-hoc approximation yields higher-order correlations and curvature estimates for neural manifolds in macaque visual cortex.

Pith tools