Concept

Norm (mathematics)

Related publications (105)

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Transportation-based functional ANOVA and PCA for covariance operators

Victor Panaretos, Yoav Zemel, Valentina Masarotto

We consider the problem of comparing several samples of stochastic processes with respect to their second-order structure, and describing the main modes of variation in this second order structure, if present. These tasks can be seen as an Analysis of Vari ...

Inst Mathematical Statistics-Ims2024

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 ...

EPFL2024

WILD SOLUTIONS TO SCALAR EULER-LAGRANGE EQUATIONS

Carl Johan Peter Johansson

. We study very weak solutions to scalar Euler-Lagrange equations associated with quadratic convex functionals. We investigate whether W1,1 solutions are necessarily W 1,2 Nash and Schauder applicable. We answer this question positively for a suitable clas ...

Amer Mathematical Soc2024

Equity ownership and identification with the founding team

Eva Maria Weissenböck

Founders benefit from identifying with their founding teams because identification facilitates cooperation in the team, aligns founders' actions with the norms and interests of the team, and, ultimately, enhances team performance. High identification with ...

Hoboken2024

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 INC2023

Data-driven fixed-structure frequency-based H2 and H∞ controller design

Alireza Karimi, Vaibhav Gupta, Philippe Louis Schuchert

The frequency response data of a generalized system is used to design fixed-structure controllers for the H2 and H∞ synthesis problem. The minimization of the two and infinity norm of the transfer function between the exogenous inputs and performance outpu ...

2023

Penalising 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 ...

2023

Memoryless Worker-Task Assignment with Polylogarithmic Switching Cost

Adam Teodor Polak

We study the basic problem of assigning memoryless workers to tasks with dynamically changing demands. Given a set of w workers and a multiset T ⊆ [t] of |T| = w tasks, a memoryless worker-task assignment function is any function ϕ that assigns the workers ...

Schloss Dagstuhl -- Leibniz-Zentrum fur Informatik2022

Application of optimal spline subspaces for the removal of spurious outliers in isogeometric discretizations

Espen Sande

We show that isogeometric Galerkin discretizations of eigenvalue problems related to the Laplace operator subject to any standard type of homogeneous boundary conditions have no outliers in certain optimal spline subspaces. Roughly speaking, these optimal ...

ELSEVIER SCIENCE SA2022

Convergence 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

\tilde O(t^{-1/2})

rate of convergence for the squared norm of the gradient of Moreau envelope, ...

2021

Convergence 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

\tilde O(t^{-1/2})

rate of convergence for the squared norm of the gradient of Moreau envelope, ...

2021