2 layer neural networks as Wasserstein gradient flows

[1] Artificial neural networks (ANNs) consist of layers of artificial "neurons" which take in information from the previous layer and output information to the next layer. Gradient descent is a common method for updating the weights of each neuron based on training data. While in practice every layer of a neural network has only finitely many neurons, it is beneficial to consider a neural network layer with infinitely many neurons, for the sake of developing a theory that explains how ANNs work. In particular, from this viewpoint the process of updating the neuron weights for a shallow neural network can be described by a Wasserstein gradient flow.