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There have been many recent advances in representation learning; however,unsupervised representation learning can still struggle with modelidentification issues related to rotations of the latent space. VariationalAuto-Encoders (VAEs) and their extensions such as $\beta$-VAEs have been shownto improve local alignment of latent variables with PCA directions, which canhelp to improve model disentanglement under some conditions. Borrowinginspiration from Independent Component Analysis (ICA) and sparse coding, wepropose applying an $L_1$ loss to the VAE's generative Jacobian during trainingto encourage local latent variable alignment with independent factors ofvariation in images of multiple objects or images with multiple parts. Wedemonstrate our results on a variety of datasets, giving qualitative andquantitative results using information theoretic and modularity measures thatshow our added $L_1$ cost encourages local axis alignment of the latentrepresentation with individual factors of variation.

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