Barren plateaus in quantum neural network training landscapes

JR McClean, S Boixo, VN Smelyanskiy… - Nature …, 2018 - nature.com
Many experimental proposals for noisy intermediate scale quantum devices involve training
a parameterized quantum circuit with a classical optimization loop. Such hybrid quantum …

Progress on the study of the Ginibre ensembles II: GinOE and GinSE

SS Byun, PJ Forrester - arXiv preprint arXiv:2301.05022, 2023 - arxiv.org
This is part II of a review relating to the three classes of random non-Hermitian Gaussian
matrices introduced by Ginibre in 1965. While part I restricted attention to the GinUE (Ginibre …

Precise characterization of the prior predictive distribution of deep ReLU networks

L Noci, G Bachmann, K Roth… - Advances in Neural …, 2021 - proceedings.neurips.cc
Recent works on Bayesian neural networks (BNNs) have highlighted the need to better
understand the implications of using Gaussian priors in combination with the compositional …

Statistical limits of dictionary learning: random matrix theory and the spectral replica method

J Barbier, N Macris - Physical Review E, 2022 - APS
We consider increasingly complex models of matrix denoising and dictionary learning in the
Bayes-optimal setting, in the challenging regime where the matrices to infer have a rank …

A GSVD-Based Precoding Scheme for MIMO-NOMA Relay Transmission

C Rao, Z Ding, K Cumanan… - IEEE Internet of Things …, 2023 - ieeexplore.ieee.org
Recently, the multiple-input–multiple-output (MIMO) nonorthogonal multiple-access (NOMA)
transmission, denoted as MIMO-NOMA, has been widely applied for Internet of Things (IoT) …

Bootstrapping cascaded random matrix models: Correlations in permutations of matrix products

N Byrnes, GRW Greaves, MR Foreman - Physical Review E, 2024 - APS
Random matrix theory is a useful tool in the study of the physics of multiple scattering
systems, often striking a balance between computation speed and physical rigour …

Replica method for eigenvalues of real Wishart product matrices

JA Zavatone-Veth, C Pehlevan - SciPost Physics Core, 2023 - scipost.org
We show how the replica method can be used to compute the asymptotic eigenvalue
spectrum of a real Wishart product matrix. For unstructured factors, this provides a compact …

Average whenever you meet: Opportunistic protocols for community detection

L Becchetti, A Clementi, P Manurangsi, E Natale… - arXiv preprint arXiv …, 2017 - arxiv.org
Consider the following asynchronous, opportunistic communication model over a graph $ G
$: in each round, one edge is activated uniformly and independently at random and (only) its …

Symmetries of the quaternionic Ginibre ensemble

G Dubach - Random Matrices: Theory and Applications, 2021 - World Scientific
We establish a few properties of eigenvalues and eigenvectors of the quaternionic Ginibre
ensemble (QGE), analogous to what is known in the complex Ginibre case (see [7, 11, 14]) …

Kac–Rice fixed point analysis for single-and multi-layered complex systems

JR Ipsen, PJ Forrester - Journal of Physics A: Mathematical and …, 2018 - iopscience.iop.org
We present a null model for single-and multi-layered complex systems constructed using
homogeneous and isotropic random Gaussian maps. By means of a Kac–Rice formalism …