Related papers: Representation of tensor functions using lower-ord…
Tensor ring (TR) decomposition is a powerful tool for exploiting the low-rank nature of multiway data and has demonstrated great potential in a variety of important applications. In this paper, nonnegative tensor ring (NTR) decomposition…
Tensor models play an increasingly prominent role in many fields, notably in machine learning. In several applications, such as community detection, topic modeling and Gaussian mixture learning, one must estimate a low-rank signal from a…
Fourth-rank tensors of complete Voigt's symmetry, that embody the elastic properties of crystalline anisotropic substances, were constructed for all 2D crystal systems. Using them we obtained explicit expressions for inverse of Young's…
Tensor product function (TPF) approximations have been widely adopted in solving high-dimensional problems, such as partial differential equations and eigenvalue problems, achieving desirable accuracy with computational overhead that scales…
Despite tremendous progress over the past decade, deep learning methods generally fall short of human-level systematic generalization. It has been argued that explicitly capturing the underlying structure of data should allow connectionist…
Tensor networks offer a variational formalism to efficiently represent wave-functions of extended quantum many-body systems on a lattice. In a tensor network N, the dimension \chi of the bond indices that connect its tensors controls the…
We introduce T-Basis, a novel concept for a compact representation of a set of tensors, each of an arbitrary shape, which is often seen in Neural Networks. Each of the tensors in the set is modeled using Tensor Rings, though the concept…
The validity of two approximative linear tensor models to be used for grating based X-ray or neutron dark-field tensor tomography is investigated in a simulation study. While the dark-field contrast originating from anisotropic microscopic…
The goals of this work are two-fold: firstly, to propose a new theoretical framework for representing random fields on a large class of multidimensional geometrical domain in the tensor train format; secondly, to develop a new algorithm…
Tomographic imaging is useful for revealing the internal structure of a 3D sample. Classical reconstruction methods treat the object of interest as a vector to estimate its value. Such an approach, however, can be inefficient in analyzing…
Predictive state representation~(PSR) uses a vector of action-observation sequence to represent the system dynamics and subsequently predicts the probability of future events. It is a concise knowledge representation that is well studied in…
Recently, there has been an increasing interest in employing rotational motion measurements for seismic source inversion, structural imaging and ambient noise analysis. We derive reciprocity and representation theorems for rotational…
There are several different notions of "low rank" for tensors, associated to different formats. Among them, the Tensor Train (TT) format is particularly well suited for tensors of high order, as it circumvents the curse of dimensionality:…
Accurate simulations of atomistic systems from first principles are limited by computational cost. In high-throughput settings, machine learning can reduce these costs significantly by accurately interpolating between reference…
Real or complex tensor model observables, the backbone of the tensor theory space, are classical (unitary, orthogonal, symplectic) Lie group invariants. These observables represent as colored graphs, and that representation gives an handle…
Based on the tensor tree network with the Born machine framework, we propose a general method for constructing a generative model by expressing the target distribution function as the amplitude of the quantum wave function represented by a…
We develop quaternionic analysis using as a guiding principle representation theory of various real forms of the conformal group. We first review the Cauchy-Fueter and Poisson formulas and explain their representation theoretic meaning. The…
We present a brief survey on the modern tensor numerical methods for multidimensional stationary and time-dependent partial differential equations (PDEs). The guiding principle of the tensor approach is the rank-structured separable…
This paper is concerned with the approximation of tensors using tree-based tensor formats, which are tensor networks whose graphs are dimension partition trees. We consider Hilbert tensor spaces of multivariate functions defined on a…
Representations of multivariate functions with low-dimensional functions that depend on subsets of original coordinates (corresponding of different orders of coupling) are useful in quantum dynamics and other applications, especially where…