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We describe a necessary and sufficient condition for the convergence tominimum Bayes risk when training two-layer ReLU-networks by gradient descent inthe mean field regime with omni-directional initial parameter distribution.This article extends recent results of Chizat and Bach to ReLU-activatednetworks and to the situation in which there are no parameters which exactlyachieve MBR. The condition does not depend on the initalization of parametersand concerns only the weak convergence of the realization of the neuralnetwork, not its parameter distribution.

On the Convergence of Gradient Descent Training for Two-layer ReLU-networks in the Mean Field Regime