Gradient flow dynamics of shallow ReLU networks for square loss and orthogonal inputs
This provides theoretical insights into training dynamics for neural networks, but it is incremental as it focuses on a specific, simplified setting.
The authors tackled the problem of understanding gradient flow dynamics for shallow ReLU networks with orthogonal inputs and square loss, showing that gradient flow converges to zero loss and exhibits an implicit bias towards minimum variation norm, with specific dynamics like initial alignment and saddle-to-saddle behavior.
The training of neural networks by gradient descent methods is a cornerstone of the deep learning revolution. Yet, despite some recent progress, a complete theory explaining its success is still missing. This article presents, for orthogonal input vectors, a precise description of the gradient flow dynamics of training one-hidden layer ReLU neural networks for the mean squared error at small initialisation. In this setting, despite non-convexity, we show that the gradient flow converges to zero loss and characterise its implicit bias towards minimum variation norm. Furthermore, some interesting phenomena are highlighted: a quantitative description of the initial alignment phenomenon and a proof that the process follows a specific saddle to saddle dynamics.