Improved Convergence Guarantees for Shallow Neural Networks
This addresses a foundational theoretical problem in machine learning for researchers, but it is incremental as it builds on existing work with specific model assumptions.
The paper tackles the problem of proving convergence of shallow neural networks trained via gradient descent to a global minimum, improving on prior state-of-the-art results by allowing both layers to be trained simultaneously at different rates.
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] (training the first layer only) and [Nguyen 21, Section 3.2] (training both layers with Le Cun's initialization). 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''.