Publications related to Metric map

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

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

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

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

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

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

Lipschitz constant estimation for Neural Networks via sparse polynomial optimization

Volkan Cevher, Paul Thierry Yves Rolland, Fabian Ricardo Latorre Gomez

We introduce LiPopt, a polynomial optimization framework for computing increasingly tighter upper bounds on the Lipschitz constant of neural networks. The underlying optimization problems boil down to either linear (LP) or semidefinite (SDP) programming. W ...

2020

Geometric landscapes for material discovery within energy–structure–function maps

Berend Smit, Seyedmohamad Moosavi, Henglu Xu

Porous molecular crystals are an emerging class of porous materials formed by crystallisation of molecules with weak intermolecular interactions, which distinguishes them from extended nanoporous materials like metal–organic frameworks (MOFs). To aid disco ...

2020

Efficient Proximal Mapping of the 1-path-norm of Shallow Networks

Volkan Cevher, Paul Thierry Yves Rolland, Fabian Ricardo Latorre Gomez, Shaul Nadav Hallak

We demonstrate two new important properties of the 1-path-norm of shallow neural networks. First, despite its non-smoothness and non-convexity it allows a closed form proximal operator which can be efficiently computed, allowing the use of stochastic proxi ...

2020

Deep Neural Networks With Trainable Activations and Controlled Lipschitz Constant

Michaël Unser, Shayan Aziznejad, Harshit Gupta, Joaquim Gonçalves Garcia Barreto Campos

We introduce a variational framework to learn the activation functions of deep neural networks. Our aim is to increase the capacity of the network while controlling an upper-bound of the actual Lipschitz constant of the input-output relation. To that end, ...

IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC2020

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Metric map

Stable parameterization of continuous and piecewise-linear functions

Benign Overfitting in Deep Neural Networks under Lazy Training

Controlling the Complexity and Lipschitz Constant improves Polynomial Nets

Predicting in Uncertain Environments: Methods for Robust Machine Learning

An Efficient Sampling Algorithm for Non-smooth Composite Potentials

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

Lipschitz constant estimation for Neural Networks via sparse polynomial optimization

Geometric landscapes for material discovery within energy–structure–function maps

Efficient Proximal Mapping of the 1-path-norm of Shallow Networks

Deep Neural Networks With Trainable Activations and Controlled Lipschitz Constant

Graph Chatbot

Chat with Graph Search

Stable parameterization of continuous and piecewise-linear functions

Controlling the Complexity and Lipschitz Constant improves Polynomial Nets

Lipschitz constant estimation for Neural Networks via sparse polynomial optimization

An Efficient Sampling Algorithm for Non-smooth Composite Potentials

Benign Overfitting in Deep Neural Networks under Lazy Training

Predicting in Uncertain Environments: Methods for Robust Machine Learning

Deep Neural Networks With Trainable Activations and Controlled Lipschitz Constant

Efficient Proximal Mapping of the 1-path-norm of Shallow Networks

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

Geometric landscapes for material discovery within energy–structure–function maps