  While much effort has been devoted to deriving and analyzing effective convex
formulations of signal processing problems, the gradients of convex functions
also have critical applications ranging from gradient-based optimization to
optimal transport. Recent works have explored data-driven methods for learning
convex objective functions, but learning their monotone gradients is seldom
studied. In this work, we propose C-MGN and M-MGN, two monotone gradient neural
network architectures for directly learning the gradients of convex functions.
We show that, compared to state of the art methods, our networks are easier to
train, learn monotone gradient fields more accurately, and use significantly
fewer parameters. We further demonstrate their ability to learn optimal
transport mappings to augment driving image data.
