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The Variational Autoencoder (VAE) is a powerful architecture capable ofrepresentation learning and generative modeling. When it comes to learninginterpretable (disentangled) representations, VAE and its variants showunparalleled performance. However, the reasons for this are unclear, since avery particular alignment of the latent embedding is needed but the design ofthe VAE does not encourage it in any explicit way. We address this matter andoffer the following explanation: the diagonal approximation in the encodertogether with the inherent stochasticity force local orthogonality of thedecoder. The local behavior of promoting both reconstruction and orthogonalitymatches closely how the PCA embedding is chosen. Alongside providing anintuitive understanding, we justify the statement with full theoreticalanalysis as well as with experiments.

Variational Autoencoders Pursue PCA Directions (by Accident)