124 citations · 662 across the 33 of their papers we have counts for
36 papers
Wandering Exponents and the Free Energy of the High-Dimensional Elastic Polymer
Gerard Ben Arous, Pax Kivimae
We study the behavior of the elastic polymer, a model of a directed polymer in a continuous Gaussian random environment that is independent in time and correlated in space, as the…
Langevin dynamics for high-dimensional optimization: the case of multi-spiked tensor PCA
Gérard Ben Arous, Cédric Gerbelot, Vanessa Piccolo
We study nonconvex optimization in high dimensions through Langevin dynamics, focusing on the multi-spiked tensor PCA problem. In this tensor estimation model, the goal is to recov…
Spectral alignment of stochastic gradient descent for high-dimensional classification tasks
Gerard Ben Arous, Reza Gheissari, Jiaoyang Huang +1
We rigorously study the relation between the training dynamics via stochastic gradient descent (SGD) and the spectra of empirical Hessian and gradient matrices. We prove that in tw…
High-dimensional limit theorems for SGD: Effective dynamics and critical scaling
Gerard Ben Arous, Reza Gheissari, Aukosh Jagannath
We study the scaling limits of stochastic gradient descent (SGD) with constant step-size in the high-dimensional regime. We prove limit theorems for the trajectories of summary sta…
Sharp complexity asymptotics and topological trivialization for the (p, k) spiked tensor model
Antonio Auffinger, Gerard Ben Arous, Zhehua Li
We provide O(1) asymptotics for the average number of deep minima of the (p,k) spiked tensor model. We also derive an explicit formula for the limiting ground state energy on the N…
Exponential growth of random determinants beyond invariance
Gérard Ben Arous, Paul Bourgade, Benjamin McKenna
We give simple criteria to identify the exponential order of magnitude of the absolute value of the determinant for wide classes of random matrix models, not requiring the assumpti…