Related papers: Block Tensor Unfoldings
Block encoding lies at the core of many existing quantum algorithms. Meanwhile, efficient and explicit block encodings of dense operators are commonly acknowledged as a challenging problem. This paper presents a comprehensive study of the…
Clustering and closure coefficients are among the most widely applied indicators in the description of the topological structure of a network. Many distinct definitions have been proposed over time, particularly in the case of weighted…
We give here an efficient method to reconstruct the block interleaver and recover the convolutional code when several noisy interleaved codewords are given. We reconstruct the block interleaver without assumption on its structure. By…
We consider a class of block operator matrices arising in the study of scattering passive systems, especially in the context of boundary control problems. We prove that these block operator matrices are indeed a subclass of block operator…
Finding the rank of a tensor is a problem that has many applications. Unfortunately it is often very difficult to determine the rank of a given tensor. Inspired by the heuristics of convex relaxation, we consider the nuclear norm instead of…
Higher order tensor inversion is possible for even order. We have shown that a tensor group endowed with the Einstein (contracted) product is isomorphic to the general linear group of degree $n$. With the isomorphic group structures, we…
The analysis and visualization of tensor fields is a very challenging task. Besides the cases of zeroth- and first-order tensors, most techniques focus on symmetric second-order tensors. Only a few works concern totally symmetric tensors of…
This paper establishes a rigorous connection between circuit representations and tensor factorizations, two seemingly distinct yet fundamentally related areas. By connecting these fields, we highlight a series of opportunities that can…
We analyze the problem of high-order polynomial approximation from a many-body physics perspective, and demonstrate the descriptive power of entanglement entropy in capturing model capacity and task complexity. Instantiated with a…
Modular tensor categories are generalizations of the representation categories of quantum groups at roots of unity axiomatizing the properties necessary to produce 3-dimensional TQFTs. Although other constructions have since been found,…
In this paper, we provide a system theoretic treatment of a new class of multilinear time-invariant (MLTI) systems in which the states, inputs and outputs are tensors, and the system evolution is governed by multilinear operators. The MLTI…
We discuss what has been achieved in the past twenty years on the construction and study of a braided finite tensor category structure on a suitable module category for a suitable vertex operator algebra. We identify the main difficult…
Matrix and tensor operations form the basis of a wide range of fields and applications, and in many cases constitute a substantial part of the overall computational complexity. The ability of general-purpose GPUs to speed up many of these…
The decoupling of multivariate functions is a powerful modeling paradigm for learning multivariate input-output relations from data. For the single-layer case, established CPD-based methods are available, but the multi-layer case remained…
Deconvolving ("unfolding'') detector distortions is a critical step in the comparison of cross section measurements with theoretical predictions in particle and nuclear physics. However, most existing approaches require histogram binning…
During the last years, low-rank tensor approximation has been established as a new tool in scientific computing to address large-scale linear and multilinear algebra problems, which would be intractable by classical techniques. This survey…
We describe a framework for reformulating and solving optimization problems that generalizes the well-known framework originally introduced by Benders. We discuss details of the application of the procedures to several classes of…
Higher-order data with high dimensionality arise in a diverse set of application areas such as computer vision, video analytics and medical imaging. Tensors provide a natural tool for representing these types of data. Although there has…
Machine learning (ML) models are widely used in many important domains. For efficiently processing these computational- and memory-intensive applications, tensors of these over-parameterized models are compressed by leveraging sparsity,…
It is shown how one can apply the classification of the holonomy algebras of Lorentzian manifolds to solve some problems. In particular, a new proof to the classification of Lorentzian manifolds with recurrent curvature tensor is given; the…