Publications related to Lipschitz continuity

Stability 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 ...

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

Benign 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 ...

2023

Gradient-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 ...

2022

Controlling 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 ...

2022

UNDERGRAD: A Universal Black-Box Optimization Method with Almost Dimension-Free Convergence Rate Guarantees

Volkan Cevher, Kimon Antonakopoulos

Universal methods for optimization are designed to achieve theoretically optimal convergence rates without any prior knowledge of the problem’s regularity parameters or the accurarcy of the gradient oracle employed by the optimizer. In this regard, existin ...

2022

An Efficient Sampling Algorithm for Non-smooth Composite Potentials

Nicolas Henri Bernard Flammarion

We consider the problem of sampling from a density of the form p(x) ? exp(-f (x) - g(x)), where f : Rd-+ R is a smooth function and g : R-d-+ R is a convex and Lipschitz function. We propose a new algorithm based on the Metropolis-Hastings framework. Under ...

MICROTOME PUBL2022

An Accelerated First-Order Method for Non-convex Optimization on Manifolds

Nicolas Boumal, Christopher Arnold Criscitiello

We describe the first gradient methods on Riemannian manifolds to achieve accelerated rates in the non-convex case. Under Lipschitz assumptions on the Riemannian gradient and Hessian of the cost function, these methods find approximate first-order critical ...

SPRINGER2022

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Lipschitz continuity

Stability of Image-Reconstruction Algorithms

Stable parameterization of continuous and piecewise-linear functions

Benign Overfitting in Deep Neural Networks under Lazy Training

Multi-Source Fusion for Voxel-Based 7-DoF Grasping Pose Estimation

Gradient-based optimisation of the conditional-value-at-risk using the multi-level Monte Carlo method

Controlling the Complexity and Lipschitz Constant improves Polynomial Nets

Predicting in Uncertain Environments: Methods for Robust Machine Learning

UNDERGRAD: A Universal Black-Box Optimization Method with Almost Dimension-Free Convergence Rate Guarantees

An Efficient Sampling Algorithm for Non-smooth Composite Potentials

An Accelerated First-Order Method for Non-convex Optimization on Manifolds

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Stability of Image-Reconstruction Algorithms

Multi-Source Fusion for Voxel-Based 7-DoF Grasping Pose Estimation

Benign Overfitting in Deep Neural Networks under Lazy Training

Predicting in Uncertain Environments: Methods for Robust Machine Learning

An Accelerated First-Order Method for Non-convex Optimization on Manifolds

Stable parameterization of continuous and piecewise-linear functions

Controlling the Complexity and Lipschitz Constant improves Polynomial Nets

UNDERGRAD: A Universal Black-Box Optimization Method with Almost Dimension-Free Convergence Rate Guarantees

An Efficient Sampling Algorithm for Non-smooth Composite Potentials

Gradient-based optimisation of the conditional-value-at-risk using the multi-level Monte Carlo method