17 citations · 44 across the 10 of their papers we have counts for
6 papers · 1 filter
Dual bounds for the positive definite functions approach to mutually unbiased bases
Afonso S. Bandeira, Nikolaus Doppelbauer, Dmitriy Kunisky
A long-standing open problem asks if there can exist 7 mutually unbiased bases (MUBs) in , or, more generally, MUBs in for any that is not…
Experimental performance of graph neural networks on random instances of max-cut
Weichi Yao, Afonso S. Bandeira, Soledad Villar
This note explores the applicability of unsupervised machine learning techniques towards hard optimization problems on random inputs. In particular we consider Graph Neural Network…
A Gramian Description of the Degree 4 Generalized Elliptope
Afonso S. Bandeira, Dmitriy Kunisky
One of the most widely studied convex relaxations in combinatorial optimization is the relaxation of the cut polytope to the elliptope , which correspo…
On the Landscape of Synchronization Networks: A Perspective from Nonconvex Optimization
Shuyang Ling, Ruitu Xu, Afonso S. Bandeira
Studying the landscape of nonconvex cost function is key towards a better understanding of optimization algorithms widely used in signal processing, statistics, and machine learnin…
Spurious Valleys in Two-layer Neural Network Optimization Landscapes
Luca Venturi, Afonso S. Bandeira, Joan Bruna
Neural networks provide a rich class of high-dimensional, non-convex optimization problems. Despite their non-convexity, gradient-descent methods often successfully optimize these…
Convergence of trust-region methods based on probabilistic models
Afonso S. Bandeira, Katya Scheinberg, Luis Nunes Vicente
In this paper we consider the use of probabilistic or random models within a classical trust-region framework for optimization of deterministic smooth general nonlinear functions.…