Related papers: Invitation to Random Tensors
A method to generate new classes of random matrix ensembles is proposed. Random matrices from these ensembles are Lax matrices of classically integrable systems with a certain distribution of momenta and coordinates. The existence of an…
We propose a notation for tensors with named axes, which relieves the author, reader, and future implementers of machine learning models from the burden of keeping track of the order of axes and the purpose of each. The notation makes it…
Numerical applications and, more recently, machine learning applications rely on high-dimensional data that is typically organized into multi-dimensional tensors. Many existing frameworks, libraries, and domain-specific languages support…
The present lectures contain an introduction to possible new physics beyond the Standard Model. Having in mind first of all accelerator experiments of the nearest future we concentrate on supersymmetry, a new symmetry that relates bosons…
Higher-order tensors are becoming prevalent in many scientific areas such as computer vision, social network analysis, data mining and neuroscience. Traditional tensor decomposition approaches face three major challenges: model selecting,…
A fairly non-technical introduction to and survey of supersymmetry phenomenology with pedagogical emphasis, including exercises. Suitable for both theorists and experimentalists. The manuscript appeared as a Springer-Verlag monograph in…
Tensor ring (TR) decomposition is a simple but effective tensor network for analyzing and interpreting latent patterns of tensors. In this work, we propose a doubly randomized optimization framework for computing TR decomposition. It can be…
We introduce a novel class of sample-based explanations we term high-dimensional representers, that can be used to explain the predictions of a regularized high-dimensional model in terms of importance weights for each of the training…
We examine a class of embeddings based on structured random matrices with orthogonal rows which can be applied in many machine learning applications including dimensionality reduction and kernel approximation. For both the…
We prove two universality results for random tensors of arbitrary rank D. We first prove that a random tensor whose entries are N^D independent, identically distributed, complex random variables converges in distribution in the large N…
Many quantities we are interested in predicting are geometric tensors; we refer to this class of problems as geometric prediction. Attempts to perform geometric prediction in real-world scenarios have been limited to approximating them…
This is a survey of results on random group presentations, and on random subgroups of certain fixed groups. Being a survey, this paper does not contain new results, but it offers a synthetic view of a part of this very active field of…
It is described how one comes to the Wigner-Dyson random matrix theory (RMT) starting from a model of a disordered metal. The lectures start with a historical introduction where basic ideas of the RMT and theory of disordered metals are…
This is a tutorial on some basic non-asymptotic methods and concepts in random matrix theory. The reader will learn several tools for the analysis of the extreme singular values of random matrices with independent rows or columns. Many of…
This paper introduces a new object called the momentum tensor. Together with the velocity tensor it forms a basis for establishing the tensorial picture of classical and relativistic mechanics. Some properties of the momentum tensor are…
The present text is a collection of notes about differential geometry prepared to some extent as part of tutorials about topics and applications related to tensor calculus. They can be regarded as continuation to the previous notes on…
The present work provides an original framework for random matrix analysis based on revisiting the concentration of measure theory from a probabilistic point of view. By providing various notions of vector concentration ($q$-exponential,…
Random networks are increasingly used to analyse complex transportation networks, such as airline routes, roads and rail networks. So far, this research has been focused on describing the properties of the networks with the help of random…
We introduce a new, elementary method for studying random differences in arithmetic progressions and convergence phenomena along random sequences of integers. We apply our method to obtain significant improvements on previously known…
First we survey generating function methods for obtaining useful probability estimates about random matrices in the finite classical groups. Then we describe a probabilistic picture of conjugacy classes which is coherent and beautiful.…