Concept
Operator norm
Related publications (43)
Non-normal forms
Yves-Marie François Ducimetière
In this thesis, we propose to formally derive amplitude equations governing the weakly nonlinear evolution of non-normal dynamical systems, when they respond to harmonic or stochastic forcing, or to an initial condition. This approach reconciles the non-mo ...
EPFL2024Near-Minimax Optimal Estimation With Shallow ReLU Neural Networks
We study the problem of estimating an unknown function from noisy data using shallow ReLU neural networks. The estimators we study minimize the sum of squared data-fitting errors plus a regularization term proportional to the squared Euclidean norm of the ...
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC2023Fairness and Explainability in Clustering Problems
In this thesis we present and analyze approximation algorithms for three different clustering problems. The formulations of these problems are motivated by fairness and explainability considerations, two issues that have recently received attention in the ...
EPFL2023Geometric Considerations in Lattice Programming
We provide faster algorithms and fine-grained reductions for lattice problems in general norms. ...
EPFL2023Penalising the biases in norm regularisation enforces sparsity
Nicolas Henri Bernard Flammarion, Etienne Patrice Boursier
Controlling the parameters' norm often yields good generalisation when training neural networks. Beyond simple intuitions, the relation between parameters' norm and obtained estimators theoretically remains misunderstood. For one hidden ReLU layer networks ...
2023Convergence of adaptive algorithms for constrained weakly convex optimization
Volkan Cevher, Ahmet Alacaoglu, Yurii Malitskyi
We analyze the adaptive first order algorithm AMSGrad, for solving a constrained stochastic optimization problem with a weakly convex objective. We prove the rate of convergence for the squared norm of the gradient of Moreau envelope, ...
2021Fredholm transformation on Laplacian and rapid stabilization for the heat equations
We revisit the rapid stabilization of the heat equation on the 1-dimensional torus using the backstepping method with a Fredholm transformation. We prove that, under some assumption on the control operator, two scalar controls are necessary and sufficient ...
2021Proximity Results and Faster Algorithms for Integer Programming Using the Steinitz Lemma
We consider integer programming problems in standard form max{c(T)x : Ax = b, x >= 0, x is an element of Z(n)} where A is an element of Z(mxn), b is an element of Z(m), and c is an element of Z(n). We show that such an integer program can be solved in time ...
ASSOC COMPUTING MACHINERY2020A Unifying Representer Theorem for Inverse Problems and Machine Learning
Regularization addresses the ill-posedness of the training problem in machine learning or the reconstruction of a signal from a limited number of measurements. The method is applicable whenever the problem is formulated as an optimization task. The standar ...
2020New dense superball packings in three dimensions
We construct a new family of lattice packings for superballs in three dimensions (unit balls for the l(3)(p) norm) with p epsilon (1, 1.58]. We conjecture that the family also exists for p epsilon (1.58, log(2) 3 = 1.5849625 ...]. Like in the densest latti ...
WALTER DE GRUYTER GMBH2020