Lipschitz-constrained neural networks have several advantages over unconstrained ones
and can be applied to a variety of problems, making them a topic of attention in the deep …

A ridge is a function that is characterized by a one-dimensional profile (activation) and a
multidimensional direction vector. Ridges appear in the theory of neural networks as …

The minimization of a data-fidelity term and an additive regularization functional gives rise to
a powerful framework for supervised learning. In this paper, we present a unifying …

We investigate the distributional extension of the-plane transform in and of related operators.
We parameterize the-plane domain as the Cartesian product of the Stiefel manifold of …

In supervised learning, the regularization path is sometimes used as a convenient
theoretical proxy for the optimization path of gradient descent initialized from zero. In this …

Identifying an appropriate function space for deep neural networks remains a key open
question. While shallow neural networks are naturally associated with Reproducing Kernel …

Deep neural networks are not well understood mathematically and their success in many
science and engineering applications is usually only backed by empirical evidence. In this …