Improved Convergence Guarantees for Shallow Neural Networks

Abstract: We continue a long line of research aimed at proving convergence of depth 2 neural networks, trained via gradient descent, to a global minimum. Like in many previous works, our model has the following features: regression with quadratic loss function, fully connected feedforward architecture, RelU activations, Gaussian data instances and network initialization, adversarial labels. It is more general in the sense that we allow both layers to be trained simultaneously and at {\em different} rates. Our results improve on state-of-the-art Oymak Soltanolkotabi 20 and Nguyen 21, Section 3.2. We also report several simple experiments with synthetic data. They strongly suggest that, at least in our model, the convergence phenomenon extends well beyond the ``NTK regime''.