Publications by Alexis Marie Frederic Goujon

Controlled learning of pointwise nonlinearities in neural-network-like architectures

Michaël Unser, Alexis Marie Frederic Goujon, Stanislas Ducotterd

We present a general variational framework for the training of freeform nonlinearities in layered computational architectures subject to some slope constraints. The regularization that we add to the traditional training loss penalizes the second-order tota ...

2025

On the number of regions of piecewise linear neural networks

Michaël Unser, Alexis Marie Frederic Goujon

Many feedforward neural networks (NNs) generate continuous and piecewise-linear (CPWL) mappings. Specifically, they partition the input domain into regions on which the mapping is affine. The number of these so-called linear regions offers a natural metric ...

2024

Towards Trustworthy Deep Learning for Image Reconstruction

Alexis Marie Frederic Goujon

The remarkable ability of deep learning (DL) models to approximate high-dimensional functions from samples has sparked a revolution across numerous scientific and industrial domains that cannot be overemphasized. In sensitive applications, the good perform ...

EPFL2024

Improving Lipschitz-Constrained Neural Networks by Learning Activation Functions

Michaël Unser, Dimitris Perdios, Pakshal Narendra Bohra, Alexis Marie Frederic Goujon, Sebastian Jonas Neumayer, Stanislas Ducotterd

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 learning community. Unfortunately, it has been shown both theoretically and empi ...

2024

Learning Weakly Convex Regularizers for Convergent Image-Reconstruction Algorithms

Michaël Unser, Alexis Marie Frederic Goujon, Sebastian Jonas Neumayer

We propose to learn non-convex regularizers with a prescribed upper bound on their weak-convexity modulus. Such regularizers give rise to variational denoisers that minimize a convex energy. They rely on few parameters (less than 15,000) and offer a signal ...

2024

A Neural-Network-Based Convex Regularizer for Inverse Problems

Michaël Unser, Pakshal Narendra Bohra, Alexis Marie Frederic Goujon, Sebastian Jonas Neumayer, Stanislas Ducotterd

The emergence of deep-learning-based methods to solve image-reconstruction problems has enabled a significant increase in quality. Unfortunately, these new methods often lack reliability and explainability, and there is a growing interest to address these ...

2023

Delaunay-Triangulation-Based Learning With Hessian Total-Variation Regularization

Michaël Unser, Alexis Marie Frederic Goujon, Mehrsa Pourya

2023

Data for: "A Neural-Network-Based Convex Regularizer for Inverse Problems"

Michaël Unser, Pakshal Narendra Bohra, Alexis Marie Frederic Goujon, Sebastian Jonas Neumayer, Stanislas Ducotterd

Data for: "A Neural-Network-Based Convex Regularizer for Inverse Problems". The corresponding scripts can be accessed on GitHub (https://github.com/axgoujon/convex_ridge_regularizers). The data is organized as follows: - ct_data_sets.tar.gz: contains prepr ...

Zenodo2023

Approximation of Lipschitz Functions Using Deep Spline Neural Networks

Michaël Unser, Pakshal Narendra Bohra, Alexis Marie Frederic Goujon, Sebastian Jonas Neumayer

Although Lipschitz-constrained neural networks have many applications in machine learning, the design and training of expressive Lipschitz-constrained networks is very challenging. Since the popular rectified linear-unit networks have provable disadvantage ...

2023

Stable parameterization of continuous and piecewise-linear functions

Michaël Unser, Alexis Marie Frederic Goujon, Joaquim Gonçalves Garcia Barreto Campos

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 parametric representation, the mapping between the parameter and function s ...

2023