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Variational Autoencoders Recover PCA Directions (by Accident)

2019

Conference Paper

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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.

Author(s): Michal Rolinek and Dominik Zietlow and Georg Martius
Book Title: Proceedings IEEE Conf. on Computer Vision and Pattern Recognition (CVPR)
Year: 2019
Month: June

Department(s): Autonomous Learning
Research Project(s): Representation Learning
Bibtex Type: Conference Paper (inproceedings)

Event Name: IEEE International Conference on Computer Vision and Pattern Recognition (CVPR) 2019
Event Place: Long Beach, USA

Links: arXiv

BibTex

@inproceedings{RolinekZietlowMartius:VAERecPCA,
  title = {Variational Autoencoders Recover PCA Directions (by Accident)},
  author = {Rolinek, Michal and Zietlow, Dominik and Martius, Georg},
  booktitle = {Proceedings IEEE Conf. on Computer Vision and Pattern Recognition (CVPR)},
  month = jun,
  year = {2019},
  month_numeric = {6}
}