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

There have been many recent advances in representation learning; however, unsupervised representation learning can still struggle with model identification issues. Variational Auto-Encoders (VAEs) and their extensions such as $\beta$-VAEs have been shown to locally align 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 the data. 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.