126 citations · 375 across the 42 of their papers we have counts for
45 papers
Randomly initialized autoencoders: fixed points and edge-of-chaos
Leonid Berlyand, Roman Sarapin, Yitzchak Shmalo +2
In this paper we study autoencoders, a special class of deep neural nets (DNNs) whose performance can be characterized via their fixed points. This perspective naturally raises que…
How weak are weak factors? Uniform inference for signal strength in signal plus noise models
Anna Bykhovskaya, Vadim Gorin, Sasha Sodin
The paper analyzes four classical signal-plus-noise models: the factor model, spiked sample covariance matrices, the sum of a Wigner matrix and a low-rank perturbation, and canonic…
Irreducibility of the characteristic polynomials of random tridiagonal matrices
Lior Bary-Soroker, Daniele Garzoni, Sasha Sodin
Conditionally on the Riemann hypothesis for certain Dedekind zeta functions, we show that the characteristic polynomial of a class of random tridiagonal matrices of large dimension…
Sets of non-Lyapunov behaviour for scalar and matrix Schrödinger cocycles
Ilya Goldsheid, Sasha Sodin
We discuss the growth of the singular values of symplectic transfer matrices associated with ergodic discrete Schrödinger operators in one dimension, with scalar and matrix-valued…
Integrability of pushforward measures by analytic maps
Itay Glazer, Yotam I. Hendel, Sasha Sodin
Given a map between -analytic manifolds over a local field of characteristic , we introduce an invariant which quantifies the integrabil…
On the Hausdorff measure of sets of non-Lyapunov behaviour, and a Jarnik-type theorem for random Schroedinger operators
Sasha Sodin
We consider the growth of the norms of transfer matrices of ergodic discrete Schrödinger operators in one dimension. It is known that the set of energies at which the rate of expon…