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The training of neural networks by gradient descent methods is a cornerstoneof the deep learning revolution. Yet, despite some recent progress, a completetheory explaining its success is still missing. This article presents, fororthogonal input vectors, a precise description of the gradient flow dynamicsof training one-hidden layer ReLU neural networks for the mean squared error atsmall initialisation. In this setting, despite non-convexity, we show that thegradient flow converges to zero loss and characterise its implicit bias towardsminimum variation norm. Furthermore, some interesting phenomena arehighlighted: a quantitative description of the initial alignment phenomenon anda proof that the process follows a specific saddle to saddle dynamics.

Gradient flow dynamics of shallow ReLU networks for square loss and orthogonal inputs