3 papers
cs.LG2022
Approximation of Lipschitz Functions using Deep Spline Neural Networks
Sebastian Neumayer, Alexis Goujon, Pakshal Bohra +1
Lipschitz-constrained neural networks have many applications in machine learning. Since designing and training expressive Lipschitz-constrained networks is very challenging, there…
math.NA2022
Stable Parametrization of Continuous and Piecewise-Linear Functions
Alexis Goujon, Joaquim Campos, Michael Unser
Rectified-linear-unit (ReLU) neural networks, which play a prominent role in deep learning, generate continuous and piecewise-linear (CPWL) functions. While they provide a powerful…
math.NA2020
Shortest-support Multi-Spline Bases for Generalized Sampling
Alexis Goujon, Shayan Aziznejad, Alireza Naderi +1
Generalized sampling consists in the recovery of a function , from the samples of the responses of a collection of linear shift-invariant systems to the input . The reconstru…