# Implicit Rank Minimization in Gradient Descent

## October 14, 2020

I came across this paper “Implicit Rank-Minimizing Autoencoder” [1] by FAIR which was shared by Yann LeCun on his facebook timeline. In this paper, the authors show that inserting a few linear layers between the encoder and the decoder decreases the dimensionality of the latent space. The authors build on the results of [2] which showed how overparameterization of linear neural networks results in implicit regularization of the rank when trained via gradient descent(GD).
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