Related papers: TensoriaCalc: A User-Friendly Tensor Calculus Pack…
Tensor calculation of suffix-contraction is carried out by a C-program. Tensors are represented graphically, and the algorithm makes use of the topology of graphs. Classical and quantum gravity, in the weak-field perturbative approach, is a…
In this work we use the tensorial language developed in [8] and [9] to differentiate functions of eigenvalues of symmetric matrices. We describe the formulae for the k-th derivative of such functions in two cases. The first case concerns…
Sparse tensors are prevalent in many data-intensive applications, yet existing differentiable programming frameworks are tailored towards dense tensors. This presents a significant challenge for efficiently computing gradients through…
The tensor notation used in several areas of mathematics is a useful one, but it is not widely available to the functional programming community. In a practical sense, the (embedded) domain-specific languages (DSLs) that are currently in…
Tensor operations play an essential role in various fields of science and engineering, including multiway data analysis. In this study, we establish a few basic properties of the range and null space of a tensor using block circulant…
Tensors are multidimensional arrays of numerical values and therefore generalize matrices to multiple dimensions. While tensors first emerged in the psychometrics community in the $20^{\text{th}}$ century, they have since then spread to…
A metric tensor for Riemann manifold Monte Carlo particularly suited for non-linear Bayesian hierarchical models is proposed. The metric tensor is built from symmetric positive semidefinite log-density gradient covariance (LGC) matrices,…
Recently, the tensor network states (TNS) methods have proven to be very powerful tools to investigate the strongly correlated many-particle physics in one and two dimensions. The implementation of TNS methods depends heavily on the…
We present the tensor computer algebra package xPert for fast construction and manipulation of the equations of metric perturbation theory, around arbitrary backgrounds. It is based on the combination of explicit combinatorial formulas for…
Tensor processing infrastructures such as deep learning frameworks and specialized hardware accelerators have revolutionized how computationally intensive code from domains such as deep learning and image processing is executed and…
The paper presents a REDUCE program for the simplification of tensor expressions that are considered as formal indexed objects. The proposed algorithm is based on the consideration of tensor expressions as vectors in some linear space. This…
Learning vector calculus techniques is one of the major missions to be accomplished by physics undergraduates. However, beginners report various difficulties dealing with the index notation due to its bulkiness. Meanwhile, there have been…
FORM, a symbolic manipulation system, has been widely used in a lot of calculations for High Energy Physics due to its high performance and fficient design. Mathematica, another computational software program, has also widely been used, but…
Quantum computers promise to efficiently solve important problems classical computers never will. However, in order to capitalize on these prospects, a fully automated quantum software stack needs to be developed. This involves a multitude…
We introduce an algorithm to decide isomorphism between tensors. The algorithm uses the Lie algebra of derivations of a tensor to compress the space in which the search takes place to a so-called densor space. To make the method practicable…
We are presenting an algorithm capable of simplifying tensor polynomials with indices when the building tensors have index symmetry properties. These properties include simple symmetry, cyclicity and those due to the presence of partial and…
We present the Mathematica package E6Tensors, a tool for explicit tensor calculations in E6 gauge theories. In addition to matrix expressions for the group generators of E6, it provides structure constants, various higher rank tensors and…
There is a need in general relativity for a consistent and useful mathematical theory defining the multiplication of tensor distributions in a geometric (diffeomorphism invariant) way. Significant progress has been made through the concept…
Multitask learning (MTL) can utilize the relatedness between multiple tasks for performance improvement. The advent of multimodal data allows tasks to be referenced by multiple indices. High-order tensors are capable of providing efficient…
We present the library Collier for the numerical evaluation of one-loop scalar and tensor integrals in perturbative relativistic quantum field theories. The code provides numerical results for arbitrary tensor and scalar integrals for…