Boursier, EtiennePillaud-Vivien, LoucasFlammarion, Nicolas2022-06-082022-06-082022-06-082022https://infoscience.epfl.ch/handle/20.500.14299/188422The 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.implicit biastwo-layer neural networksgradient flowgradient descentglobal convergenceReLU networksvariation normnon-convex optimisationtext::working paper