Publications de Alexis Marie Frederic Goujon

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

Michaël Unser, Stanislas Ducotterd, Alexis Marie Frederic Goujon

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

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

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

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, Joaquim Gonçalves Garcia Barreto Campos, Alexis Marie Frederic Goujon

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

Boosting Weakly Convex Ridge Regularizers with Spatial Adaptivity

Michaël Unser, Alexis Marie Frederic Goujon, Mehrsa Pourya, Sebastian Jonas Neumayer

2023

Learning Lipschitz-Controlled Activation Functions in Neural Networks for Plug-and-Play Image Reconstruction Methods

Michaël Unser, Dimitris Perdios, Sébastien Alexandre Emery, Pakshal Narendra Bohra, Alexis Marie Frederic Goujon

Ill-posed linear inverse problems are frequently encountered in image reconstruction tasks. Image reconstruction methods that combine the Plug-and-Play (PnP) priors framework with convolutional neural network (CNN) based denoisers have shown impressive per ...

2021

Shortest-support multi-spline bases for generalized sampling

Michaël Unser, Shayan Aziznejad, Alireza Naderi, Alexis Marie Frederic Goujon

Generalized sampling consists in the recovery of a function f, from the samples of the responses of a collection of linear shift-invariant systems to the input f . The reconstructed function is typically a member of a finitely generated integer-shift invar ...

2021

Emergent order in hydrodynamic spin lattices

Alexis Marie Frederic Goujon, John Bush

Macroscale analogues(1-3) of microscopic spin systems offer direct insights into fundamental physical principles, thereby advancing our understanding of synchronization phenomena(4) and informing the design of novel classes of chiral metamaterials(5-7). He ...

NATURE PORTFOLIO2021