Enhancing Variational Generation Through Self-Decomposition

In this article we introduce the notion of Split Variational Autoencoder (SVAE), whose output $\hat{x}$ is obtained as a weighted sum $\sigma \odot \hat{x_1} + (1-\sigma) \hat{x_2}$ two generated images $\hat{x_1},\hat{x_2}$, and $\sigma$ {\em learned} compositional map. The composing well $\sigma$-map are automatically synthesized by model. network trained usual with negative loglikelihood loss between training reconstructed images. No additional required for $\hat{x_1},\hat{x_2}$ or $\sigma$, neither any form human tuning. decomposition nondeterministic, but follows main schemes, that may roughly categorize either \say{syntactic} \say{semantic}. first case, map tends to exploit strong correlation adjacent pixels, splitting image in complementary high frequency sub-images. second typically focuses on contours objects, interesting variations its content, more marked distinctive features. according empirical observations, Fr\'echet Inception Distance (FID) $\hat{x_1}$ $\hat{x_2}$ usually lower (hence better) than $\hat{x}$, clearly suffers from being average former. sense, SVAE forces make choices, contrast intrinsic tendency average} alternatives aim minimize reconstruction towards specific sample. According FID metric, our technique, tested typical datasets such Mnist, Cifar10 CelebA, allows us outperform all previous purely variational architectures (not relying normalization flows).