10 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…
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)_…
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…
Stochastic gradient descent in high dimensions for multi-spiked tensor PCA
Gérard Ben Arous, Cédric Gerbelot, Vanessa Piccolo
We study the high-dimensional dynamics of online stochastic gradient descent (SGD) for the multi-spiked tensor model. This multi-index model arises from the tensor principal compon…
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…
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…