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arXiv · 2104.05000

Saddlepoints in Unsupervised Least Squares

Samuel Gerber
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Abstract

This paper sheds light on the risk landscape of unsupervised least squares in the context of deep auto-encoding neural nets. We formally establish an equivalence between unsupervised least squares and principal manifolds. This link provides insight into the risk landscape of auto--encoding under the mean squared error, in particular all non-trivial critical points are saddlepoints. Finding saddlepoints is in itself difficult, overcomplete auto-encoding poses the additional challenge that the saddlepoints are degenerate. Within this context we discuss regularization of auto-encoders, in particular bottleneck, denoising and contraction auto-encoding and propose a new optimization strategy that can be framed as particular form of contractive regularization.

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Samuel Gerber. 2021-04-11. Saddlepoints in Unsupervised Least Squares. https://arxiv.org/abs/2104.05000

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