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Loss Landscapes of Regularized Linear Autoencoders
Daniel Kunin · Jonathan Bloom · Aleksandrina Goeva · Cotton Seed

Thu Jun 13 06:30 PM -- 09:00 PM (PDT) @ Pacific Ballroom #26
Autoencoders are a deep learning model for representation learning. When trained to minimize the distance between the data and its reconstruction, linear autoencoders (LAEs) learn the subspace spanned by the top principal directions but cannot learn the principal directions themselves. In this paper, we prove that $L_2$-regularized LAEs are symmetric at all critical points and learn the principal directions as the left singular vectors of the decoder. We smoothly parameterize the critical manifold and relate the minima to the MAP estimate of probabilistic PCA. We illustrate these results empirically and consider implications for PCA algorithms, computational neuroscience, and the algebraic topology of learning.

Author Information

Daniel Kunin (Stanford University)
Jonathan Bloom (Broad Institute)
Aleksandrina Goeva (Broad Institute of MIT and Harvard)
Cotton Seed (Broad Institute of MIT and Harvard)

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