Related papers: Random Matrix Theory in Lattice Statistical Mechan…
A concept of randomness for infinite time register machines (ITRMs), resembling Martin-L\"of-randomness, is defined and studied. In particular, we show that for this notion of randomness, computability from mutually random reals implies…
Low-rank matrices play a fundamental role in modeling and computational methods for signal processing and machine learning. In many applications where low-rank matrices arise, these matrices cannot be fully sampled or directly observed, and…
Random Matrix Theory (RMT) is applied to analyze the weight matrices of Deep Neural Networks (DNNs), including both production quality, pre-trained models such as AlexNet and Inception, and smaller models trained from scratch, such as…
Many models for chaotic systems consist of joining two integrable systems with incompatible constants of motion. The quantum counterparts of such models have a propagator which factorizes into two integrable parts. Each part can be…
This paper focuses on analyzing and differentiating between lattice linear problems and algorithms. It introduces a new class of algorithms called \textit{(fully) lattice linear algorithms}. A property of these algorithms is that they…
Latent factor models are increasingly popular for modeling multi-relational knowledge graphs. By their vectorial nature, it is not only hard to interpret why this class of models works so well, but also to understand where they fail and how…
We employ Random Matrix Theory in order to investigate coherent perfect absorption (CPA) in lossy systems with complex internal dynamics. The loss strength $\gamma_{\rm CPA}$ and energy $E_{\rm CPA}$, for which a CPA occurs are expressed in…
Matrix approximation is a common tool in machine learning for building accurate prediction models for recommendation systems, text mining, and computer vision. A prevalent assumption in constructing matrix approximations is that the…
This paper aims at presenting a few models of quantum dynamics whose description involves the analysis of random unitary matrices for which dynamical localization has been proven to hold. Some models come from physical approximations…
This thesis deals with the geometric and integrable aspects associated with random matrix models. Its purpose is to provide various applications of random matrix theory, from algebraic geometry to partial differential equations of…
Random feature maps are ubiquitous in modern statistical machine learning, where they generalize random projections by means of powerful, yet often difficult to analyze nonlinear operators. In this paper, we leverage the "concentration"…
Power systems are developing very fast nowadays, both in size and in complexity; this situation is a challenge for Early Event Detection (EED). This paper proposes a data- driven unsupervised learning method to handle this challenge.…
This paper deals with model checking problems with respect to LTL properties under fairness assumptions. We first present an efficient algorithm to deal with a fragment of fairness assumptions and then extend the algorithm to handle…
We study the distribution of singular values of product of random matrices pertinent to the analysis of deep neural networks. The matrices resemble the product of the sample covariance matrices, however, an important difference is that the…
Random matrix theory (RMT) universality is the defining property of quantum mechanical chaotic systems, and can be probed by observables like the spectral form factor (SFF). In this paper, we describe systematic deviations from RMT…
In this paper, we propose a new modified likelihood ratio test (LRT) for simultaneously testing mean vectors and covariance matrices of two-sample populations in high-dimensional settings. By employing tools from Random Matrix Theory (RMT),…
Stochastic approximation algorithm is a useful technique which has been exploited successfully in probability theory and statistics for a long time. The step sizes used in stochastic approximation are generally taken to be deterministic and…
We propose an implementation of a two-dimensional $\mathbb{Z}_2$ lattice gauge theory model on a shallow quantum circuit, involving a number of single and two-qubits gates comparable to what can be achieved with present-day and near-future…
We investigate non-perturbative supersymmetry breaking in various models of quantum mechanics, including an interesting class of $PT$-invariant models, using lattice path integrals. These theories are discretized on a temporal Euclidean…
We introduce a theory of probability in $\lambda$-rings designed to efficiently describe random variables valued in multisets of complex numbers, varieties over a field, or other similar enriched settings. A key role is played by the…