Gradient Descent on Infinitely Wide Neural Networks: Global Convergence and Generalization

• URL: http://arxiv.org/abs/2110.08084v1
• Date: Fri, 15 Oct 2021 13:25:32 GMT
• Title: Gradient Descent on Infinitely Wide Neural Networks: Global Convergence and Generalization
• Authors: Francis Bach (SIERRA), Lena\"ic Chizat (EPFL)
• Abstract summary: Many supervised machine learning methods are cast as optimization problems. For prediction models which are linear in their parameters, this often leads to problems for prediction guarantees. In this paper, we consider two-layer neural networks with homogeneous activation functions.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Many supervised machine learning methods are naturally cast as optimization problems. For prediction models which are linear in their parameters, this often leads to convex problems for which many mathematical guarantees exist. Models which are non-linear in their parameters such as neural networks lead to non-convex optimization problems for which guarantees are harder to obtain. In this review paper, we consider two-layer neural networks with homogeneous activation functions where the number of hidden neurons tends to infinity, and show how qualitative convergence guarantees may be derived.

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