Related papers: Spectral Methods from Tensor Networks
In tensor completion tasks, the traditional low-rank tensor decomposition models suffer from the laborious model selection problem due to their high model sensitivity. In particular, for tensor ring (TR) decomposition, the number of model…
Low-rank tensor recovery problems have been widely studied in many applications of signal processing and machine learning. Tucker decomposition is known as one of the most popular decompositions in the tensor framework. In recent years,…
Tensor networks are powerful factorization techniques which reduce resource requirements for numerically simulating principal quantum many-body systems and algorithms. The computational complexity of a tensor network simulation depends on…
In this paper, we present connections between three models used in different research fields: weighted finite automata~(WFA) from formal languages and linguistics, recurrent neural networks used in machine learning, and tensor networks…
Invariant theory is concerned with functions that do not change under the action of a given group. Here we communicate an approach based on tensor networks to represent polynomial local unitary invariants of quantum states. This graphical…
In this study, we introduce a novel family of tensor networks, termed constrained matrix product states (MPS), designed to incorporate exactly arbitrary discrete linear constraints, including inequalities, into sparse block structures.…
Modern sensing and metrology systems now stream terabytes of heterogeneous, high-dimensional (HD) data profiles, images, and dense point clouds, whose natural representation is multi-way tensors. Understanding such data requires regression…
The problem of partitioning a large and sparse tensor is considered, where the tensor consists of a sequence of adjacency matrices. Theory is developed that is a generalization of spectral graph partitioning. A best rank-$(2,2,\lambda)$…
High-dimensional data arise naturally in many areas of science and engineering, including machine learning, signal processing, computational physics, and statistics. Such data are often represented as tensors, multi-dimensional…
Accurately evaluating configurational integrals for dense solids remains a central and difficult challenge in the statistical mechanics of condensed systems. Here, we present a novel tensor network approach that reformulates the…
Tensor network contraction is central to problems ranging from many-body physics to computer science. We describe how to approximate tensor network contraction through bond compression on arbitrary graphs. In particular, we introduce a…
In many applications, it is needed to change the topology of a tensor network directly and without approximation. This work will introduce a general scheme that satisfies these needs. We will describe the procedure by two examples and show…
The groundbreaking performance of deep neural networks (NNs) promoted a surge of interest in providing a mathematical basis to deep learning theory. Low-rank tensor decompositions are specially befitting for this task due to their close…
This work presents a novel method for task optimization in industrial plants using quantum-inspired tensor network technology. This method obtains the best possible combination of tasks on a set of machines with directed constraints while…
Spectral algorithms are graph partitioning algorithms that partition a node set of a graph into groups by using a spectral embedding map. Clustering techniques based on the algorithms are referred to as spectral clustering and are widely…
This paper introduces several new algorithms for consensus over the special orthogonal group. By relying on a convex relaxation of the space of rotation matrices, consensus over rotation elements is reduced to solving a convex problem with…
A simple but efficient spectral approach for analyzing the community structure of complex networks is introduced. It works the same way for all types of networks, by spectrally splitting the adjacency matrix into a "unipartite" and a…
A network representation is useful for describing the structure of a large variety of complex systems. However, most real and engineered systems have multiple subsystems and layers of connectivity, and the data produced by such systems is…
We propose a universal approach to a range of enumeration problems in graphs. The key point is in contracting suitably chosen symmetric tensors placed at the vertices of a graph along the edges. In particular, this leads to an algorithm…
We introduce tensor numerical techniques for solving optimal control problems constrained by elliptic operators in $\mathbb{R}^d$, $d=2,3$, with variable coefficients, which can be represented in a low rank separable form. We construct a…