68 citations · 133 across the 8 of their papers we have counts for
9 papers
Universality of high-dimensional scaling limits of stochastic gradient descent
Reza Gheissari, Aukosh Jagannath
We consider statistical tasks in high dimensions whose loss depends on the data only through its projection into a fixed-dimensional subspace spanned by the parameter vectors and c…
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)_…
Finding planted cliques using gradient descent
Reza Gheissari, Aukosh Jagannath, Yiming Xu
The planted clique problem is a paradigmatic model of statistical-to-computational gaps: the planted clique is information-theoretically detectable if its size but…
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…
Online stochastic gradient descent on non-convex losses from high-dimensional inference
Gerard Ben Arous, Reza Gheissari, Aukosh Jagannath
Stochastic gradient descent (SGD) is a popular algorithm for optimization problems arising in high-dimensional inference tasks. Here one produces an estimator of an unknown paramet…
Bounding flows for spherical spin glass dynamics
Gerard Ben Arous, Reza Gheissari, Aukosh Jagannath
We introduce a new approach to studying spherical spin glass dynamics based on differential inequalities for one-time observables. Using this approach, we obtain an approximate pha…
Algorithmic thresholds for tensor PCA
Gerard Ben Arous, Reza Gheissari, Aukosh Jagannath
We study the algorithmic thresholds for principal component analysis of Gaussian -tensors with a planted rank-one spike, via Langevin dynamics and gradient descent. In order to…
On the Spectral Gap of Spherical Spin Glass Dynamics
Reza Gheissari, Aukosh Jagannath
We consider the time to equilibrium for the Langevin dynamics of the spherical -spin glass model of system size . We show that the log-Sobolev constant and spectral gap are o…