Concept

Hölder condition

Related publications (42)

Discretisation and continuity: The emergence of symbols in communication

Vocal signalling systems, as used by humans and various non-human animals, exhibit discrete and continuous properties that can naturally be used to express discrete and continuous information, such as distinct words to denote objects in the world and proso ...

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

MATHICSE Technical Report : Regularity and sparse approximation of the recursive first moment equations for the lognormal Darcy problem

Fabio Nobile, Francesca Bonizzoni

We study the Darcy boundary value problem with log-normal permeability field. We adopt a perturbation approach, expanding the solution in Taylor series around the nominal value of the coefficient, and approximating the expected value of the stochastic solu ...

MATHICSE2020

Regularity and sparse approximation of the recursive first moment equations for the lognormal Darcy problem

Fabio Nobile, Francesca Bonizzoni

We study the Darcy boundary value problem with lognormal permeability field. We adopt a perturbation approach, expanding the solution in Taylor series around the nominal value of the coefficient, and approximating the expected value of the stochastic solut ...

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

Least-Squares Padé approximation of parametric and stochastic Helmholtz maps

Fabio Nobile, Francesca Bonizzoni, Davide Pradovera

The present work deals with rational model order reduction methods based on the single-point Least-Square (LS) Padé approximation techniques introduced in Bonizzoni et al. (ESAIM Math. Model. Numer. Anal., 52(4), 1261–1284 2018, Math. Comput. 89, 1229–1257 ...

2020

On the density of the supremum of the solution to the linear stochastic heat equation

Robert Dalang, Fei Pu

We study the regularity of the probability density function of the supremum of the solution to the linear stochastic heat equation. Using a general criterion for the smoothness of densities for locally nondegenerate random variables, we establish the smoot ...

SPRINGER2020

Regularity results for rough solutions of the incompressible Euler equations via interpolation methods

Maria Colombo, Luigi Forcella, Luigi De Rosa

Given any solutionuof the Euler equations which is assumed to have some regularity in space-in terms of Besov norms, natural in this context-we show by interpolation methods that it enjoys a corresponding regularity in time and that the associated pressure ...

IOP2019

Decompositions Of Log-Correlated Fields With Applications

Janne Matias Junnila

In this article, we establish novel decompositions of Gaussian fields taking values in suitable spaces of generalized functions, and then use these decompositions to prove results about Gaussian multiplicative chaos. We prove two decomposition theorems. Th ...

2019

An accelerated communication-efficient primal-dual optimization framework for structured machine learning

Martin Jaggi, Chenxin Ma

Distributed optimization algorithms are essential for training machine learning models on very large-scale datasets. However, they often suffer from communication bottlenecks. Confronting this issue, a communication-efficient primal-dual coordinate ascent ...

2019

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