This review covers recent results concerning the estimation of large covariance matrices
using tools from Random Matrix Theory (RMT). We introduce several RMT methods and …

Technological advances have dramatically expanded our ability to probe multi-neuronal
dynamics and connectivity in the brain. However, our ability to extract a simple conceptual …

We study the first gradient descent step on the first-layer parameters $\boldsymbol {W} $ in a
two-layer neural network: $ f (\boldsymbol {x})=\frac {1}{\sqrt {N}}\boldsymbol {a}^\top\sigma …

We perform an analysis of the average generalization dynamics of large neural networks
trained using gradient descent. We study the practically-relevant “high-dimensional” regime …

We propose a patch-based singular value shrinkage method for diffusion magnetic
resonance image estimation targeted at low signal to noise ratio and accelerated …

We consider recovery of low-rank matrices from noisy data by hard thresholding of singular
values, in which empirical singular values below a threshold λ are set to 0. We study the …

Understanding the impact of data structure on the computational tractability of learning is a
key challenge for the theory of neural networks. Many theoretical works do not explicitly …

Abstract We consider the Principal Component Analysis problem for large tensors of
arbitrary order k under a single-spike (or rank-one plus noise) model. On the one hand, we …

This paper investigates the theoretical foundations of the t-distributed stochastic neighbor
embedding (t-SNE) algorithm, a popular nonlinear dimension reduction and data …

In this work, we reveal a strong implicit bias of stochastic gradient descent (SGD) that drives
overly expressive networks to much simpler subnetworks, thereby dramatically reducing the …