Local Disentanglement in Variational Auto-Encoders Using Jacobian $L_1$ Regularization

TL;DR

This paper introduces a novel $L_1$ Jacobian regularization technique for VAEs to enhance local disentanglement of latent variables, improving alignment with independent factors of variation in complex images.

Contribution

It proposes applying an $L_1$ loss to the Jacobian of the VAE's generative model, inspired by ICA and sparse coding, to improve local disentanglement.

Findings

Enhanced local axis alignment with factors of variation.

Quantitative improvements shown via information theoretic measures.

Qualitative results demonstrate better disentanglement.

Abstract

There have been many recent advances in representation learning; however, unsupervised representation learning can still struggle with model identification issues related to rotations of the latent space. Variational Auto-Encoders (VAEs) and their extensions such as $\beta$-VAEs have been shown to improve local alignment of latent variables with PCA directions, which can help to improve model disentanglement under some conditions. Borrowing inspiration from Independent Component Analysis (ICA) and sparse coding, we propose applying an $L_1$ loss to the VAE's generative Jacobian during training to encourage local latent variable alignment with independent factors of variation in images of multiple objects or images with multiple parts. We demonstrate our results on a variety of datasets, giving qualitative and quantitative results using information theoretic and modularity measures that show our added $L_1$ cost encourages local axis alignment of the latent representation with individual factors of variation.