ORCID: https://orcid.org/0000-0002-6310-075X; Rauhut, Holger
ORCID: https://orcid.org/0000-0003-4750-5092 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
[PDF, 2MB]

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 |
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Faculties: | Mathematics, Computer Science and Statistics > Mathematics > Chair of Mathematics of Information Processing |
Subjects: | 500 Science > 510 Mathematics |
URN: | urn:nbn:de:bvb:19-epub-127184-1 |
ISSN: | 2731-4235 |
Language: | English |
Item ID: | 127184 |
Date Deposited: | 30. Jun 2025 06:38 |
Last Modified: | 11. Jul 2025 19:09 |