Variational Autoencoders Pursue PCA Directions (by Accident)
This provides theoretical insight into a key problem in representation learning for researchers, though it is incremental as it builds on existing VAE understanding.
The paper explains why Variational Autoencoders (VAEs) learn interpretable representations by showing that their diagonal encoder approximation and stochasticity enforce local orthogonality in the decoder, aligning with PCA embedding principles.
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.