相关论文: Tensor manipulation in GPL Maxima

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…

Larger deep learning models usually lead to higher model quality with an ever-increasing GPU memory footprint. Although tensor checkpointing techniques have been proposed to enable training under a restricted GPU memory budget, the input…

Tensor analysis has been a widely studied in physics applications including circuit theory and electric machines. This paper reviews some of the main features of this type of representation for unbalanced power distribution systems and…

Deploying proprietary Deep Neural Networks (DNNs) on commodity edge devices demands hardware-backed Digital Rights Management (DRM) capable of withstanding both software-level and physical adversaries. In Unified Memory Architecture (UMA)…

Neural network (NN) accelerators have been integrated into a wide-spectrum of computer systems to accommodate the rapidly growing demands for artificial intelligence (AI) and machine learning (ML) applications. NN accelerators share the…

Tensor accelerators now represent a growing share of compute resources in modern CPUs and GPUs. However, they are hard to program, leading developers to use vendor-provided kernel libraries that support tensor accelerators. As a result, the…

Mnesors are defined as elements of a semimodule over the min-plus integers. This two-sorted structure is able to merge graduation properties of vectors and idempotent properties of boolean numbers, which makes it appropriate for hybrid…

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…

We introduce a method for transforming low-order tensors into higher-order tensors and apply it to tensors defined by graphs and hypergraphs. The transformation proceeds according to a surgery-like procedure that splits vertices, creates…

Transformer-based neural networks have achieved state-of-the-art task performance in a number of machine learning domains including natural language processing and computer vision. To further improve their accuracy, recent work has explored…

Incorporation of machine learning (ML) techniques into atomic-scale modeling has proven to be an extremely effective strategy to improve the accuracy and reduce the computational cost of simulations. It also entails conceptual and practical…

We present an algorithm for the derivation of Dyson-Schwinger equations of general theories that is suitable for an implementation within a symbolic programming language. Moreover, we introduce the Mathematica package DoDSE which provides…

The uninterpretability of DNNs has led to the adoption of abstract interpretation-based certification as a practical means to establish trust in real-world systems that rely on DNNs. However, the current landscape supports only a limited…

The Density Matrix Renormalization Group (DMRG) algorithm is a powerful tool for solving eigenvalue problems to model quantum systems. DMRG relies on tensor contractions and dense linear algebra to compute properties of condensed matter…

Tensor programs often need to process large tensors (vectors, matrices, or higher order tensors) that require a specialized storage format for their memory layout. Several such layouts have been proposed in the literature, such as the…

To synthesize Maxwell optics systems, the mathematical apparatus of tensor and vector analysis is generally employed. This mathematical apparatus implies executing a great number of simple stereotyped operations, which are adequately…

We describe TensoriaCalc, a tensor calculus package written to be smoothly consistent with the Wolfram Language, so as to ensure ease of usage. It allows multiple metrics to be defined in a given session; and, once a metric is computed,…

Tensor Networks are graph representations of summation expressions in which vertices represent tensors and edges represent tensor indices or vector spaces. In this work, we present EinExprs.jl, a Julia package for contraction path…

This work evaluates the potential of large language models (LLMs) to power digital assistants capable of complex action execution. These assistants rely on pre-trained programming knowledge to execute multi-step goals by composing objects…

Matrix-multiply-accumulate (MMA) units, or tensor cores, are now widespread across modern computing architectures. Yet, their use for particle-grid operators remains limited. In implicit particle methods, mass-matrix assembly is a…