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Publications associées (21)

From trees to barcodes and back again II: Combinatorial and probabilistic aspects of a topological inverse problem

Kathryn Hess Bellwald, Lida Kanari, Adélie Eliane Garin

In this paper we consider two aspects of the inverse problem of how to construct merge trees realizing a given barcode. Much of our investigation exploits a recently discovered connection between the symmetric group and barcodes in general position, based ...

2024

On the symmetries in the dynamics of wide two-layer neural networks

Lénaïc Chizat

We consider the idealized setting of gradient flow on the population risk for infinitely wide two-layer ReLU neural networks (without bias), and study the effect of symmetries on the learned parameters and predictors. We first describe a general class of s ...

AMER INST MATHEMATICAL SCIENCES-AIMS2023

A Theory of Finite-Width Neural Networks: Generalization, Scaling Laws, and the Loss Landscape

Berfin Simsek

Deep learning has achieved remarkable success in various challenging tasks such as generating images from natural language or engaging in lengthy conversations with humans.The success in practice stems from the ability to successfully train massive neural ...

EPFL2023

Dalton: Learned Partitioning for Distributed Data Streams

Anastasia Ailamaki, Eleni Zapridou, Ioannis Mytilinis

To sustain the input rate of high-throughput streams, modern stream processing systems rely on parallel execution. However, skewed data yield imbalanced load assignments and create stragglers that hinder scalability. Deciding on a static partitioning for a ...

2022

From Trees to Barcodes and Back Again:A Combinatorial, Probabilistic and Geometric Study of a Topological Inverse Problem

Adélie Eliane Garin

In this thesis, we investigate the inverse problem of trees and barcodes from a combinatorial, geometric, probabilistic and statistical point of view.Computing the persistent homology of a merge tree yields a barcode B. Reconstructing a tree from B involve ...

EPFL2022

Iron incorporation in synthetic precipitated calcium silicate hydrates

David Lyndon Emsley, Paul Bowen, Brennan James Walder, Jirawan Siramanont

Effect of Fe3+ on the precipitation of synthetic calcium silicate hydrates (C-S-H) under controlled conditions has been evaluated. Using extremely basic either initial calcium nitrate or sodium silicate solutions (pH > 11), incipient formation of ferrihydr ...

2021

The probability of intransitivity in dice and close elections

Jan Hazla

We study the phenomenon of intransitivity in models of dice and voting. First, we follow a recent thread of research for n-sided dice with pairwise ordering induced by the probability, relative to 1/2, that a throw from one die is higher than the other. We ...

2020

Subjective and physiological responses to façade and sunlight pattern geometry in virtual reality

Marilyne Andersen, Jan Wienold, Giorgia Chinazzo, Kynthia Chamilothori, João Pedro de Matos Rodrigues

This study investigates the joint impact of façade geometry and associated sunlight patterns on occupant subjective perception and physiological responses through a novel experimental method coupling physically-based simulations shown in virtual reality wi ...

2019

Particle number control for direct simulation Monte-Carlo methodology using kernel estimates

The efficiency of stochastic particle schemes for large scale simulations relies on the ability to preserve a uniform distribution of particles in the whole physical domain. While simple particle split and merge algorithms have been considered previously, ...

2019

Statistical Aspects of Wasserstein Distances

Victor Panaretos, Yoav Zemel

Wasserstein distances are metrics on probability distributions inspired by the problem of optimal mass transportation. Roughly speaking, they measure the minimal effort required to reconfigure the probability mass of one distribution in order to recover th ...

ANNUAL REVIEWS2019

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