Abstract for the talk on 17.03.2022 (17:00 h)Math Machine Learning seminar MPI MIS + UCLA
Gabin Maxime Nguegnang (RWTH Aachen University)
Convergence of gradient descent for learning deep linear neural networks
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We study the convergence properties of gradient descent for training deep linear neural networks, i.e., deep matrix factorizations, by extending a previous analysis for the related gradient flow. We show that under suitable conditions on the step sizes gradient descent converges to a critical point of the loss function, i.e., the square loss in this work. Furthermore, we demonstrate that for almost all initializations gradient descent converges to a global minimum in the case of two layers. In the case of three or more layers we show that gradient descent converges to a global minimum on the manifold matrices of some fixed rank, where the rank cannot be determined a priori.