Concept
Upper and lower bounds
Related publications (171)
Improving SAM Requires Rethinking its Optimization Formulation
Volkan Cevher, Kimon Antonakopoulos, Thomas Michaelsen Pethick, Wanyun Xie, Fabian Ricardo Latorre Gomez
This paper rethinks Sharpness-Aware Minimization (SAM), which is originally formulated as a zero-sum game where the weights of a network and a bounded perturbation try to minimize/maximize, respectively, the same differentiable loss. We argue that SAM shou ...
2024On the number of regions of piecewise linear neural networks
Michaël Unser, Alexis Marie Frederic Goujon
Many feedforward neural networks (NNs) generate continuous and piecewise-linear (CPWL) mappings. Specifically, they partition the input domain into regions on which the mapping is affine. The number of these so-called linear regions offers a natural metric ...
2024Peak Value-at-Risk Estimation for Stochastic Differential Equations using Occupation Measures
This paper proposes an algorithm to upper-bound maximal quantile statistics of a state function over the course of a Stochastic Differential Equation (SDE) system execution. This chance-peak problem is posed as a nonconvex program aiming to maximize the Va ...
New York2023Certification of Bottleneck Task Assignment With Shortest Path Criteria
Maryam Kamgarpour, Tony Alan Wood
Minimising the longest travel distance for a group of mobile robots with interchangeable goals requires knowledge of the shortest length paths between all robots and goal destinations. Determining the exact length of the shortest paths in an environment wi ...
2023The first Grushin eigenvalue on cartesian product domains
Joachim Stubbe, Luigi Provenzano, Paolo Luzzini
In this paper, we consider the first eigenvalue.1(O) of the Grushin operator.G :=.x1 + |x1|2s.x2 with Dirichlet boundary conditions on a bounded domain O of Rd = R d1+ d2. We prove that.1(O) admits a unique minimizer in the class of domains with prescribed ...
WALTER DE GRUYTER GMBH2023Chung-type law of the iterated logarithm and exact moduli of continuity for a class of anisotropic Gaussian random fields
We establish a Chung-type law of the iterated logarithm and the exact local and uniform moduli of continuity for a large class of anisotropic Gaussian random fields with a harmonizable-type integral representation and the property of strong local nondeterm ...
INT STATISTICAL INST2023Near-Optimal Communication Lower Bounds for Approximate Nash Equilibria
We prove an N2-o(1) lower bound on the randomized communication complexity of finding an epsilon-approximate Nash equilibrium (for constant epsilon > 0) in a two-player N x N game. ...
Philadelphia2023Upper bounds on technoemission rates from 60 years of "silence"
The lack of detection to date of electromagnetic technosignatures implies either that we have been unable to detect them due to incomplete sampling of the search space or that we cannot detect them because the Earth has been located during the entire histo ...
PERGAMON-ELSEVIER SCIENCE LTD2023Inferring the Rate of Technosignatures from 60 yr of Nondetection
For about the last 60 yr the search for extraterrestrial intelligence has been monitoring the sky for evidence of remotely detectable technological life beyond Earth, with no positive results to date. While the lack of detection can be attributed to the hi ...
IOP Publishing Ltd2023Intrinsic area near the origin for self-similar growth-fragmentations and related random surfaces
We study the behaviour of a natural measure defined on the leaves of the genealogical tree of some branching processes, namely self-similar growth-fragmentation processes. Each particle, or cell, is attributed a positive mass that evolves in continuous tim ...
2022