Gradient Descent on Infinitely Wide Neural Networks: Global Convergence and Generalization
This work addresses the theoretical gap in optimization guarantees for neural networks, but it is incremental as it builds on existing literature for wide networks.
The paper tackles the challenge of obtaining convergence guarantees for non-convex optimization in neural networks by analyzing infinitely wide two-layer networks with homogeneous activations, showing that qualitative convergence guarantees can be derived.
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.