Concept
Module de continuité
Publications associées (33)
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 ...
2023Stability of Image-Reconstruction Algorithms
Michaël Unser, Sebastian Jonas Neumayer, Pol del Aguila Pla
Robustness and stability of image-reconstruction algorithms have recently come under scrutiny. Their importance to medical imaging cannot be overstated. We review the known results for the topical variational regularization strategies ( ℓ2 and ℓ1 regulariz ...
2023Benign Overfitting in Deep Neural Networks under Lazy Training
Volkan Cevher, Grigorios Chrysos, Fanghui Liu, Zhenyu Zhu
This paper focuses on over-parameterized deep neural networks (DNNs) with ReLU activation functions and proves that when the data distribution is well-separated, DNNs can achieve Bayesoptimal test error for classification while obtaining (nearly) zero-trai ...
2023Gradient-based optimisation of the conditional-value-at-risk using the multi-level Monte Carlo method
Fabio Nobile, Sundar Subramaniam Ganesh
In this work, we tackle the problem of minimising the Conditional-Value-at-Risk (CVaR) of output quantities of complex differential models with random input data, using gradient-based approaches in combination with the Multi-Level Monte Carlo (MLMC) method ...
2022Controlling the Complexity and Lipschitz Constant improves Polynomial Nets
Volkan Cevher, Grigorios Chrysos, Fabian Ricardo Latorre Gomez
While the class of Polynomial Nets demonstrates comparable performance to neural networks (NN), it currently has neither theoretical generalization characterization nor robustness guarantees. To this end, we derive new complexity bounds for the set of Coup ...
2022Predicting in Uncertain Environments: Methods for Robust Machine Learning
One of the main goal of Artificial Intelligence is to develop models capable of providing valuable predictions in real-world environments. In particular, Machine Learning (ML) seeks to design such models by learning from examples coming from this same envi ...
EPFL2022