ALBERTI , Giovanni S

This paper addresses enforcing non-vanishing constraints for solutions to a 2nd-order elliptic partial differential equation by appropriate choices of boundary conditions. We show that, in dimension d >= 2, under suitable regularity assumptions, the family of 2d solutions such that their Jacobian has maximal rank in the domain is both open and...

Representing a manifold of very high-dimensional data with generative models has been shown to be computationally efficient in practice. However, this requires that the data manifold admits a global parameterization. In order to represent manifolds of arbitrary topology, we propose to learn a mixture model of variational autoencoders. Here,...