相关论文: Tensor manipulation in GPL Maxima

A fully tensorial theoretical framework for hypercomplex-valued neural networks is presented. The proposed approach enables neural network architectures to operate on data defined over arbitrary finite-dimensional algebras. The central…

We have developed a Mathematica package capable of performing gamma-matrix algebra in arbitrary (integer) dimensions. As an application we can compute Fierz transformations.

We introduce SignatureTensors.jl, a new package for computing signature tensors of paths in julia. We present its core functionality and demonstrate its use through illustrative examples. The package is compatible with the computer algebra…

The problem of simplifying tensor expressions is addressed in two parts. The first part presents an algorithm designed to put tensor expressions into a canonical form, taking into account the symmetries with respect to index permutations…

This paper discusses the algorithms and implementations of three Mathematica packages for the study of integrability and the computation of closed-form solutions of nonlinear polynomial PDEs. The first package, PainleveTest.m, symbolically…

In this letter, we propose a novel tensor-based modulation scheme for massive unsourced random access. The proposed modulation can be deemed as a summation of third-order tensors, of which the factors are representatives of subspaces. A…

Locally Purified Density Operators (LPDOs) are state-of-the-art tensor network ansatze candidates that efficiently represent mixed quantum states at scale. However, given their non-uniqueness, their representational complexity is generally…

This paper deals with the implementation of arbitrary precision calculations into the open-source discrete element framework YADE published under the GPL-2+ free software license. This new capability paves the way for the simulation…

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…

Modeling of multidimensional signal using tensor is more convincing than representing it as a collection of matrices. The tensor based approaches can explore the abundant spatial and temporal structures of the mutlidimensional signal. The…

Using the matrix product state (MPS) representation of tensor train decompositions, in this paper we propose a tensor completion algorithm which alternates over the matrices (tensors) in the MPS representation. This development is motivated…

The prevalent fully-connected tensor network (FCTN) has achieved excellent success to compress data. However, the FCTN decomposition suffers from slow computational speed when facing higher-order and large-scale data. Naturally, there…

Tensor Cores have been an important unit to accelerate Fused Matrix Multiplication Accumulation (MMA) in all NVIDIA GPUs since Volta Architecture. To program Tensor Cores, users have to use either legacy wmma APIs or current mma APIs.…

Training large AI models such as LLMs and DLRMs costs massive GPUs and computing time. The high training cost has become only affordable to big tech companies, meanwhile also causing increasing concerns about the environmental impact. This…

The mnesor theory is the adaptation of vectors to artificial intelligence. The scalar field is replaced by a lattice. Addition becomes idempotent and multiplication is interpreted as a selection operation. We also show that mnesors can be…

We describe how Computational Group Theory provides tools for manipulating tensors in explicit index notation. In special, we present an algorithm that puts tensors with free indices obeying permutation symmetries into the canonical form.…

Global discrete optimization is notoriously difficult due to the lack of gradient information and the curse of dimensionality, making exhaustive search infeasible. Tensor cross approximation is an efficient technique to approximate…

Since its introduction by Gauss, Matrix Algebra has facilitated understanding of scientific problems, hiding distracting details and finding more elegant and efficient ways of computational solving. Today's largest problems, which often…

Training large language models (LLMs) for different inference constraints is computationally expensive, limiting control over efficiency-accuracy trade-offs. Moreover, once trained, these models typically process tokens uniformly,…

Transformer-based models are becoming deeper and larger recently. For better scalability, an underlying training solution in industry is to split billions of parameters (tensors) into many tasks and then run them across homogeneous…