Related papers: Tensor renormalization group in bosonic field theo…

The Singular Value Decomposition (SVD) of matrices is a widely used tool in scientific computing. In many applications of machine learning, data analysis, signal and image processing, the large datasets are structured into tensors, for…

The renormalization of the topological term in the two-dimensional nonlinear O(3) model is studied by means of the Functional Renormalization Group. By considering the topological charge as a limit of a more general operator, it is shown…

We introduce a coarse-graining transformation for tensor networks that can be applied to study both the partition function of a classical statistical system and the Euclidean path integral of a quantum many-body system. The scheme is based…

Exact recovery of tensor decomposition (TD) methods is a desirable property in both unsupervised learning and scientific data analysis. The numerical defects of TD methods, however, limit their practical applications on real-world data. As…

We examine holographic renormalization by the singular value decomposition (SVD) of matrix data generated by the Monte Carlo snapshot of the 2D classical Ising model at criticality. To take the continuous limit of the SVD enables us to find…

In this paper we propose novel methods for completion (from limited samples) and de-noising of multilinear (tensor) data and as an application consider 3-D and 4- D (color) video data completion and de-noising. We exploit the recently…

For scalar QED on a three-dimensional toroidal lattice with a fine lattice spacing we consider the renormalization problem of choosing counter terms depending on the lattice spacing, so that the theory stays finite as the spacing goes to…

We propose a constructive algorithm that decomposes an arbitrary real tensor into a finite sum of orthonormal rank-1 outer products. The algorithm, named TTr1SVD, works by converting the tensor into a tensor-train rank-1 (TTr1) series via…

Tensor completion and robust principal component analysis have been widely used in machine learning while the key problem relies on the minimization of a tensor rank that is very challenging. A common way to tackle this difficulty is to…

Tensor network decomposition, originated from quantum physics to model entangled many-particle quantum systems, turns out to be a promising mathematical technique to efficiently represent and process big data in parsimonious manner. In this…

We show that integrable vertex and RSOS models with trigonometric Boltzmann weights and appropriate inhomogeneities provide a convenient lattice regularization for massive field theories and for the recently studied massless field theories…

In this paper, we study robust tensor completion by using transformed tensor singular value decomposition (SVD), which employs unitary transform matrices instead of discrete Fourier transform matrix that is used in the traditional tensor…

The higher order singular value decomposition (HOSVD) of tensors is a generalization of matrix SVD. The perturbation analysis of HOSVD under random noise is more delicate than its matrix counterpart. Recently, polynomial time algorithms…

We introduce an efficient algorithm for reducing bond dimensions in an arbitrary tensor network without changing its geometry. The method is based on a novel, quantitative understanding of local correlations in a network. Together with a…

In this paper, we present a natural implementation of singular value decomposition (SVD) and polar decomposition of an arbitrary multivector in nondegenerate real and complexified Clifford geometric algebras of arbitrary dimension and…

Under certain conditions, an element of a tensor product space can be identified with a compact operator and the singular value decomposition (SVD) applies to the latter. These conditions are not fulfilled in Sobolev spaces. In the previous…

In this paper, we perform a comprehensive study of the renormalization group (RG) method on thermal tensor networks (TTN). By Trotter-Suzuki decomposition, one obtains the 1+1D TTN representing the partition function of 1D quantum lattice…

The simplest possible noncommutative harmonic oscillator in two dimensions is used to quantize the free closed bosonic string in two flat dimensions. The partition function is not deformed by the introduction of noncommutativity, if we…

We use the level truncation scheme to obtain accurate descriptions of open bosonic string field configurations corresponding to large marginal deformations such as background Wilson lines. To do so, we solve for all fields as functions of…

We introduce a versatile and practical framework for applying matrix product state techniques to continuous quantum systems. We divide space into multiple segments and generate continuous basis functions for the many-body state in each…