Tristan Milne

TL;DR: The loss surface of a feed-forward neural network with ReLU non-linearities, regularized with weight decay, is studied to prove that local minima of the regularized loss function in this set are isolated, and that every differentiable critical point inThis set is a local minimum.

TL;DR: In this article, the Dirichlet to Neumann operator for the Riemannian wave equation on a compact manifold was studied and the authors proved that the DirICHlet to NN operator can be reconstructed from a compact RiemANNian manifold where sources and observations are on disjoint sets, provided a spectral condition on the Laplace-Beltrami operator is satisfied.

TL;DR: This article showed that the loss surface of a feed-forward neural network with ReLU nonlinearities, regularized with weight decay, is piecewise strongly convex on an important open set which contains, under some conditions, all of its global minimizers.

TL;DR: In this article, it was shown that the gradient of Wasserstein GANs with Gradient Penalty (WGAN-GP) can compute the minimum of a different optimal transport problem, the so-called congested transport.