The evolution of a deep neural network trained by the gradient descent in the
overparametrization regime can be described by its neural tangent kernel (NTK)\cite {jacot2018neural, …

We consider the statistics of the extreme eigenvalues of sparse random matrices, a class of
random matrices that includes the normalized adjacency matrices of the Erd{\H o}sR{\'e}nyi …

In this paper, we compare the solutions of the Dyson Brownian motion for general $$\beta $$
β and potential V and the associated McKean–Vlasov equation near the edge. Under …

Numerous deep learning algorithms have been inspired by and understood via the notion of
information bottleneck, where unnecessary information is (often implicitly) minimized while …

In this paper we show that a Brownian Gibbsian line ensemble whose top curve approximates
a parabola must be given by the parabolic Airy line ensemble. More specifically, we prove …

We study uniformly random lozenge tilings of general simply connected polygons. Under a
technical assumption that is presumably generic with respect to polygon shapes, we show …

Consider the normalized adjacency matrices of random d‐regular graphs on N vertices with
fixed degree d ⩾ 3 $d\geqslant 3$ . We prove that, with probability 1 − N − 1 + ε $1-N^{-1+\…

We consider the adjacency matrix of the ensemble of Erdős-Rényi random graphs which
consists of graphs on N vertices in which each edge occurs independently with probability p. …

In this paper, we study the edge behavior of Dyson Brownian motion with general β. Specifically,
we consider the scenario where the averaged initial density near the edge, on the scale …

This paper proves that robustness implies generalization via data-dependent generalization
bounds. As a result, robustness and generalization are shown to be connected closely in a …