We develop a variational framework to understand the properties of the functions learned by
neural networks fit to data. We propose and study a family of continuous-domain linear …

Studying the function spaces defined by neural networks helps to understand the
corresponding learning models and their inductive bias. While in some limits neural …

We study the problem of one-dimensional regression of data points with total-variation (TV)
regularization (in the sense of measures) on the second derivative, which is known to …

The formulation of inverse problems in the continuum eliminates discretization errors and
allows for the exact incorporation of priors. In this paper, we formulate a continuous-domain …

In this paper, we characterize the extremal points of the unit ball of the Benamou–Brenier
energy and of a coercive generalization of it, both subjected to the homogeneous continuity …

We introduce a general framework for the reconstruction of periodic multivariate functions
from finitely many and possibly noisy linear measurements. The reconstruction task is …

Beside the minimizationof the prediction error, two of the most desirable properties of a
regression scheme are stability and interpretability. Driven by these principles, we propose …

We study the problem of interpolating one-dimensional data with total variation
regularization on the second derivative, which is known to promote piecewise-linear …

We present a novel framework for the reconstruction of 1D composite signals assumed to be
a mixture of two additive components, one sparse and the other smooth, given a finite …

Non-convex methods for linear inverse problems with low-dimensional models have
emerged as an alternative to convex techniques. We propose a theoretical framework where …