715 citations · 1k across the 25 of their papers we have counts for
27 papers
Learning quadratic neural networks in high dimensions: SGD dynamics and scaling laws
Gérard Ben Arous, Murat A. Erdogdu, Nuri Mert Vural +1
We study the optimization and sample complexity of gradient-based training of a two-layer neural network with quadratic activation function in the high-dimensional regime, where th…
Scaling limit for the random walk on critical lattice trees
Gérard Ben Arous, Manuel Cabezas, Alexander Fribergh
We prove a scaling limit theorem for the simple random walk on critical lattice trees in , for . The scaling limit is the Brownian motion on the Integrated S…
Local geometry of high-dimensional mixture models: Effective spectral theory and dynamical transitions
Gerard Ben Arous, Reza Gheissari, Jiaoyang Huang +1
We study the local geometry of empirical risks in high dimensions via the spectral theory of their Hessian and information matrices. We focus on settings where the data, $(Y_\ell)_…
Permutation recovery of spikes in noisy high-dimensional tensor estimation
Gérard Ben Arous, Cédric Gerbelot, Vanessa Piccolo
We study the dynamics of gradient flow in high dimensions for the multi-spiked tensor problem, where the goal is to estimate unknown signal vectors (spikes) from noisy Gaussian…
The Larkin Mass and Replica Symmetry Breaking in the Elastic Manifold
Gerard Ben Arous, Pax Kivimae
This is the second of a series of three papers about the Elastic Manifold model. This classical model proposes a rich picture due to the competition between the inherent disorder a…
The Free Energy of the Elastic Manifold
Gerard Ben Arous, Pax Kivimae
This is the first of a series of three papers about the Elastic Manifold model. This classical model proposes a rich picture due to the competition between the inherent disorder an…