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 …

Since the work of Robert May in 1972, the local asymptotic stability of large ecological
systems has been a focus of theoretical ecology. Here we review May's work in the light of …

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 …

Deep learning methods operate in regimes that defy the traditional statistical mindset.
Neural network architectures often contain more parameters than training samples, and are …

Interpolators—estimators that achieve zero training error—have attracted growing attention
in machine learning, mainly because state-of-the art neural networks appear to be models of …

This survey describes probabilistic algorithms for linear algebraic computations, such as
factorizing matrices and solving linear systems. It focuses on techniques that have a proven …

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 …

This book is an invitation to the world of free probability theory. Free probability is a quite
young mathematical theory with many avatars. It owes its existence to the visions of one …

Random matrices now play a role in many areas of theoretical, applied, and computational
mathematics. Therefore, it is desirable to have tools for studying random matrices that are …

A theoretical understanding of generalization remains an open problem for many machine
learning models, including deep networks where overparameterization leads to better …