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 …

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 …

We investigate the training dynamics of two-layer neural networks when learning multi-index
target functions. We focus on multi-pass gradient descent (GD) that reuses the batches …

We study the training dynamics of a shallow neural network with quadratic activation
functions and quadratic cost in a teacher-student setup. In line with previous works on the …

We develop an approach for studying the local convexity of a certain class of random
objectives around the iterates of an AMP algorithm. Our approach involves applying the …

We consider increasingly complex models of matrix denoising and dictionary learning in the
Bayes-optimal setting, in the challenging regime where the matrices to infer have a rank …

The spherical p-spin model is a fundamental model in statistical mechanics of a disordered
system with a random first-order transition. The dynamics of this model is interesting both for …

In this paper, we investigate the limiting behavior of a continuous-time counterpart of the
Stochastic Gradient Descent (SGD) algorithm applied to two-layer overparameterized neural …

We present a method to obtain the average and the typical value of the number of critical
points of the empirical risk landscape for generalized linear estimation problems and …

We propose a new framework for tensor decomposition based on trace invariants, which are
particular cases of tensor networks. In general, tensor networks are diagrams/graphs that …