Concept
Generalized function
Publications associées (49)
Polynomial-time universality and limitations of deep learning
The goal of this paper is to characterize function distributions that general neural networks trained by descent algorithms (GD/SGD), can or cannot learn in polytime. The results are: (1) The paradigm of general neural networks trained by SGD is poly-time ...
WILEY2023THE WEYL LAW OF TRANSMISSION EIGENVALUES AND THE COMPLETENESS OF GENERALIZED TRANSMISSION EIGENFUNCTIONS WITHOUT COMPLEMENTING CONDITIONS
Hoài-Minh Nguyên, Jean Louis-Alexandre Fornerod
The transmission eigenvalue problem is a system of two second-order elliptic equations of two unknowns equipped with the Cauchy data on the boundary. In this work, we establish the Weyl law for the eigenvalues and the completeness of the generalized eigenf ...
Philadelphia2023Invariant integrals on topological groups
We generalize the fixed-point property for discrete groups acting on convex cones given by Monod in [23] to topological groups. At first, we focus on describing this fixed-point property from a functional point of view, and then we look at the class of gro ...
ACADEMIC PRESS INC ELSEVIER SCIENCE2022Leveraging topology, geometry, and symmetries for efficient Machine Learning
When learning from data, leveraging the symmetries of the domain the data lies on is a principled way to combat the curse of dimensionality: it constrains the set of functions to learn from. It is more data efficient than augmentation and gives a generaliz ...
EPFL2022A Shadow Perspective on Equivariant Hochschild Homologies
Kathryn Hess Bellwald, Inbar Klang
Shadows for bicategories, defined by Ponto, provide a useful framework that generalizes classical and topological Hochschild homology. In this paper, we define Hochschild-type invariants for monoids in a symmetric monoidal, simplicial model category V, as ...
OXFORD UNIV PRESS2022Linear Lipschitz and C-1 extension operators through random projection
We construct a regular random projection of a metric space onto a closed doubling subset and use it to linearly extend Lipschitz and C-1 functions. This way we prove more directly a result by Lee and Naor [5] and we generalize the C-l extension theorem by ...
ACADEMIC PRESS INC ELSEVIER SCIENCE2021The completeness of the generalized eigenfunctions and an upper bound for the counting function of the transmission eigenvalue problem for Maxwell equations
Hoài-Minh Nguyên, Jean Louis-Alexandre Fornerod
Cakoni and Nguyen recently proposed very general conditions on the coefficients of Maxwell equations for which they established the discreten ess of the set of eigenvalues of the transmission problem and studied their locations. In this paper, we establish ...
2021Mathematical Foundations of Robust and Distributionally Robust Optimization
Daniel Kuhn, Jianzhe Zhen, Wolfram Wiesemann
Robust and distributionally robust optimization are modeling paradigms for decision-making under uncertainty where the uncertain parameters are only known to reside in an uncertainty set or are governed by any probability distribution from within an ambigu ...
2021TV-based reconstruction of periodic functions
Julien René Pierre Fageot, Matthieu Martin Jean-André Simeoni
We introduce a general framework for the reconstruction of periodic multivariate functions from finitely many and possibly noisy linear measurements. The reconstruction task is formulated as a penalized convex optimization problem, taking the form of a sum ...
IOP PUBLISHING LTD2020A Structure Theorem for Level Sets of Multiplicative Functions and Applications
Given a level set E of an arbitrary multiplicative function f, we establish, by building on the fundamental work of Frantzikinakis and Host [14, 15], a structure theorem that gives a decomposition of into an almost periodic and a pseudo-random part ...
2020