Convergence of gradient descent for learning linear neural networks

Nguegnang, Gabin Maxime ; Rauhut, Holger und Terstiege, Ulrich (18. July 2024): Convergence of gradient descent for learning linear neural networks. In: Advances in Continuous and Discrete Models, Vol. 2024, 23

Abstract

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 stepsizes gradient descent converges to a critical point of the loss function, i.e., the square loss in this article. 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.

• Item Type: Journal article
• Faculties: Mathematics, Computer Science and Statistics > Mathematics > Chair of Mathematics of Information Processing
• Subjects: 500 Science > 510 Mathematics
• ISSN: 2731-4235
• Language: English