The Variational Autoencoder (VAE) is a powerful architecture capable of
representation learning and generative modeling. When it comes to learning
interpretable (disentangled) representations, VAE and its variants show
unparalleled performance. However, the reasons for this are unclear, since a
very particular alignment of the latent embedding is needed but the design of
the VAE does not encourage it in any explicit way. We address this matter and
offer the following explanation: the diagonal approximation in the encoder
together with the inherent stochasticity force local orthogonality of the
decoder. The local behavior of promoting both reconstruction and orthogonality
matches closely how the PCA embedding is chosen. Alongside providing an
intuitive understanding, we justify the statement with full theoretical
analysis as well as with experiments.
%0 Journal Article
%1 rolinek2018variational
%A Rolinek, Michal
%A Zietlow, Dominik
%A Martius, Georg
%D 2018
%K bayesian optimization
%T Variational Autoencoders Pursue PCA Directions (by Accident)
%U http://arxiv.org/abs/1812.06775
%X The Variational Autoencoder (VAE) is a powerful architecture capable of
representation learning and generative modeling. When it comes to learning
interpretable (disentangled) representations, VAE and its variants show
unparalleled performance. However, the reasons for this are unclear, since a
very particular alignment of the latent embedding is needed but the design of
the VAE does not encourage it in any explicit way. We address this matter and
offer the following explanation: the diagonal approximation in the encoder
together with the inherent stochasticity force local orthogonality of the
decoder. The local behavior of promoting both reconstruction and orthogonality
matches closely how the PCA embedding is chosen. Alongside providing an
intuitive understanding, we justify the statement with full theoretical
analysis as well as with experiments.
@article{rolinek2018variational,
abstract = {The Variational Autoencoder (VAE) is a powerful architecture capable of
representation learning and generative modeling. When it comes to learning
interpretable (disentangled) representations, VAE and its variants show
unparalleled performance. However, the reasons for this are unclear, since a
very particular alignment of the latent embedding is needed but the design of
the VAE does not encourage it in any explicit way. We address this matter and
offer the following explanation: the diagonal approximation in the encoder
together with the inherent stochasticity force local orthogonality of the
decoder. The local behavior of promoting both reconstruction and orthogonality
matches closely how the PCA embedding is chosen. Alongside providing an
intuitive understanding, we justify the statement with full theoretical
analysis as well as with experiments.},
added-at = {2019-03-06T13:41:06.000+0100},
author = {Rolinek, Michal and Zietlow, Dominik and Martius, Georg},
biburl = {https://www.bibsonomy.org/bibtex/210890fcca03f65fafe838f64de9bca3f/kirk86},
description = {[1812.06775] Variational Autoencoders Pursue PCA Directions (by Accident)},
interhash = {6fad97eab629243dbf8e4afc84ef7b4a},
intrahash = {10890fcca03f65fafe838f64de9bca3f},
keywords = {bayesian optimization},
note = {cite arxiv:1812.06775},
timestamp = {2019-03-06T13:41:06.000+0100},
title = {Variational Autoencoders Pursue PCA Directions (by Accident)},
url = {http://arxiv.org/abs/1812.06775},
year = 2018
}