  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''.
