4 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…
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 expo…