202 citations · 1.3k across the 61 of their papers we have counts for
77 papers
Mathematics of Data Science
Afonso S. Bandeira, Amit Singer, Thomas Strohmer
This book is about the mathematical foundations of data science. 1. Introduction 2. Curses, Blessings, and Surprises in High Dimensions 3. Singular Value Decomposition and Principa…
A lower bound for the Balan--Jiang matrix problem
Afonso S. Bandeira, Dustin G. Mixon, Stefan Steinerberger
We prove the existence of a positive semidefinite matrix such that any decomposition into rank-1 matrices has to have factors with a large …
Fitting an ellipsoid to a quadratic number of random points
Afonso S. Bandeira, Antoine Maillard, Shahar Mendelson +1
We consider the problem of fitting standard Gaussian random vectors in to the boundary of a centered ellipsoid, as . This problem…
Injectivity of ReLU networks: perspectives from statistical physics
Antoine Maillard, Afonso S. Bandeira, David Belius +2
When can the input of a ReLU neural network be inferred from its output? In other words, when is the network injective? We consider a single layer, , w…
On the concentration of Gaussian Cayley matrices
Afonso S. Bandeira, Dmitriy Kunisky, Dustin G. Mixon +1
Given a finite group, we study the Gaussian series of the matrices in the image of its left regular representation. We propose such random matrices as a benchmark for improvements…
Expander graphs are globally synchronizing
Pedro Abdalla, Afonso S. Bandeira, Martin Kassabov +3
The Kuramoto model is fundamental to the study of synchronization. It consists of a collection of oscillators with interactions given by a network, which we identify respectively w…