Optimal Neural Network Approximation of Wasserstein Gradient Direction via Convex Optimization. (arXiv:2205.13098v1 [cs.LG])

The computation of Wasserstein gradient direction is essential for posterior
sampling problems and scientific computing. The approximation of the
Wasserstein gradient with finite samples requires solving a variational
problem. We study the variational problem in the family of two-layer networks
with squared-ReLU activations, towards which we derive a semi-definite
programming (SDP) relaxation. This SDP can be viewed as an approximation of the
Wasserstein gradient in a broader function family including two-layer networks.
By solving the convex SDP, we obtain the …

approximation arxiv gradient network neural network optimization