Related papers: Beyond Random Matrix Theory for Deep Networks
We investigate random density matrices obtained by partial tracing larger random pure states. We show that there is a strong connection between these random density matrices and the Wishart ensemble of random matrix theory. We provide…
We consider discrete orthogonal polynomial ensembles which are discrete analogues of the orthogonal polynomial ensembles in random matrix theory. These ensembles occur in certain problems in combinatorial probability and can be thought of…
We investigate to what extent the microscopic Wigner-Gaudin-Mehta-Dyson (WGMD) (or sine kernel) statistics of random matrix theory remain valid on mesoscopic scales. To that end, we compute the connected two-point spectral correlation…
The quasiprobability distribution of the discrete Wigner function provides a complete description of a quantum state and is, therefore, a useful alternative to the usual density matrix description. Moreover, the experimental quantum state…
While mixture density networks (MDNs) have been extensively used for regression tasks, they have not been used much for classification tasks. One reason for this is that the usability of MDNs for classification is not clear and…
In this paper, we study an application of deep learning to the advanced LIGO and advanced Virgo coincident detection of gravitational waves (GWs) from compact binary star mergers. This deep learning method is an extension of the Deep…
We propose to impose symmetry in neural network parameters to improve parameter usage and make use of dedicated convolution and matrix multiplication routines. Due to significant reduction in the number of parameters as a result of the…
We study the averaging-based distributed optimization solvers over random networks. We show a general result on the convergence of such schemes using weight-matrices that are row-stochastic almost surely and column-stochastic in expectation…
In this paper, we consider the empirical spectral distribution of the sample correlation matrix and investigate its asymptotic behavior under mild assumptions on the data's distribution, when dimension and sample size increase at the same…
Schierenberg et al. [Phys. Rev. E 85, 061130 (2012)] recently applied the Wigner surmise, i.e., substitution of \infty \times \infty matrices by their 2 \times 2 counterparts for the computation of level spacing distributions, to random…
We prove the convergence of the empirical spectral measure of Wishart matrices with size-dependent entries and characterize the limiting law by its moments. We apply our result to the cases where the entries are Bernoulli variables with…
Recently we considered a class of random matrices obtained by choosing distinct codewords at random from linear codes over finite fields and proved that under some natural algebraic conditions their empirical spectral distribution converges…
We present DeepTract, a deep-learning framework for estimating white matter fibers orientation and streamline tractography. We adopt a data-driven approach for fiber reconstruction from diffusion weighted images (DWI), which does not assume…
Deep kernel processes are a recently introduced class of deep Bayesian models that have the flexibility of neural networks, but work entirely with Gram matrices. They operate by alternately sampling a Gram matrix from a distribution over…
We consider the problem of inference in discrete probabilistic models, that is, distributions over subsets of a finite ground set. These encompass a range of well-known models in machine learning, such as determinantal point processes and…
New experiments designed to discover a weakly interacting dark matter (DM) particle via spin dependent scattering can distinguish models of electroweak symmetry breaking. The plane of spin dependent versus spin independent DM scattering…
The complex Wishart ensemble is the statistical ensemble of $M \times N$ complex random matrices with $M \geq N$ such that the real and imaginary parts of each element are given by independent standard normal variables. The Marcenko--Pastur…
The paper studies the spectral properties of large Wigner, band and sample covariance random matrices with heavy tails of the marginal distributions of matrix entries.
A numerical approach is developed for detecting the equivalence of deep learning architectures. The method is based on generating Mixed Matrix Ensembles (MMEs) out of deep neural network weight matrices and {\it conjugate circular ensemble}…
We study the properties of the discrete Wigner distribution for two qubits introduced by Wotters. In particular, we analyze the entanglement properties within the Wigner distribution picture by considering the negativity of the Wigner…