Publications related to Intrinsic metric

On 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 ...

2024

Spatiotemporal energy-density distribution of time-reversed electromagnetic fields

Marcos Rubinstein, Farhad Rachidi-Haeri, Hamidreza Karami, Elias Per Joachim Le Boudec, Nicolas Mora Parra

Time reversal exploits the invariance of electromagnetic wave propagation in reciprocal and lossless media to localise radiating sources. Time-reversed measurements are back-propagated in a simulated domain and converge to the unknown source location. The ...

2023

Linear Lipschitz and C-1 extension operators through random projection

Federico Stra

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 SCIENCE2021

Fair colorful k-center clustering

Ola Nils Anders Svensson, Xinrui Jia

An instance of colorful k-center consists of points in a metric space that are colored red or blue, along with an integer k and a coverage requirement for each color. The goal is to find the smallest radius rho such that there exist balls of radius rho aro ...

SPRINGER HEIDELBERG2021

Data-Driven Convergence Prediction of Astrobots Swarms

Denis Gillet, Jean-Paul Richard Kneib, Matin Macktoobian, Francesco Basciani

Astrobots are robotic artifacts whose swarms are used in astrophysical studies to generate the map of the observable universe. These swarms have to be coordinated with respect to various desired observations. Such coordination\footnote{\z{A coordination sa ...

2021

On the effectiveness of adversarial training against common corruptions

Nicolas Henri Bernard Flammarion, Maksym Andriushchenko, Klim Kireev

The literature on robustness towards common corruptions shows no consensus on whether adversarial training can improve the performance in this setting. First, we show that, when used with an appropriately selected perturbation radius, ℓp adversarial traini ...

2021

Regression Networks for Meta-Learning Few-Shot Classification

Matthias Grossglauser, Arnout Jan J Devos

We propose regression networks for the problem of few-shot classification, where a classifier must generalize to new classes not seen in the training set, given only a small number of examples of each class. In high dimensional embedding spaces the directi ...

2020

Fair Colorful k-Center Clustering

Ola Nils Anders Svensson, Xinrui Jia

An instance of colorful k-center consists of points in a metric space that are colored red or blue, along with an integer k and a coverage requirement for each color. The goal is to find the smallest radius ρ such that there exist balls of radius ρ around ...

Springer2020

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Intrinsic metric

On the number of regions of piecewise linear neural networks

Fairness and Explainability in Clustering Problems

Spatiotemporal energy-density distribution of time-reversed electromagnetic fields

Well-posedness Issues For the Half-Wave Maps Equation With Hyperbolic And Spherical Targets

Linear Lipschitz and C-1 extension operators through random projection

Fair colorful k-center clustering

Data-Driven Convergence Prediction of Astrobots Swarms

On the effectiveness of adversarial training against common corruptions

Regression Networks for Meta-Learning Few-Shot Classification

Fair Colorful k-Center Clustering

Graph Chatbot

Chat with Graph Search

Fairness and Explainability in Clustering Problems

Data-Driven Convergence Prediction of Astrobots Swarms

On the number of regions of piecewise linear neural networks

Linear Lipschitz and C-1 extension operators through random projection

Well-posedness Issues For the Half-Wave Maps Equation With Hyperbolic And Spherical Targets

On the effectiveness of adversarial training against common corruptions

Spatiotemporal energy-density distribution of time-reversed electromagnetic fields

Fair colorful k-center clustering

Regression Networks for Meta-Learning Few-Shot Classification

Fair Colorful k-Center Clustering