Related papers: Tensor manipulation in GPL Maxima
Large language models (LLMs) have achieved remarkable success across various artificial intelligence tasks. However, their enormous sizes and computational demands pose significant challenges for the deployment on edge devices. To address…
We introduce DISTAL, a compiler for dense tensor algebra that targets modern distributed and heterogeneous systems. DISTAL lets users independently describe how tensors and computation map onto target machines through separate format and…
A new simulation package, GSEIM, for solving a set of ordinary differential equations is presented. The organisation of the program is illustrated with the help of a block diagram. Various features of GSEIM are discussed. Two ways of…
The efficacy of deep learning has resulted in its use in a growing number of applications. The Volta graphics processor unit (GPU) architecture from NVIDIA introduced a specialized functional unit, the "tensor core", that helps meet the…
Today, artificial neural networks are one of the major innovators pushing the progress of machine learning. This has particularly affected the development of neural network accelerating hardware. However, since most of these architectures…
Tensor processing units (TPUs) are one of the most well-known machine learning (ML) accelerators utilized at large scale in data centers as well as in tiny ML applications. TPUs offer several improvements and advantages over conventional ML…
Multilinear algebra kernel performance on modern massively-parallel systems is determined mainly by data movement. However, deriving data movement-optimal distributed schedules for programs with many high-dimensional inputs is a notoriously…
This paper is concerned with the computation of the principal components for a general tensor, known as the tensor principal component analysis (PCA) problem. We show that the general tensor PCA problem is reducible to its special case…
Neural networks have revolutionized many aspects of society but in the era of huge models with billions of parameters, optimizing and deploying them for commercial applications can require significant computational and financial resources.…
Large language models (LLMs) are both storage-intensive and computation-intensive, posing significant challenges when deployed on resource-constrained hardware. As linear layers in LLMs are mainly resource consuming parts, this paper…
Sampling equilibrium ensembles of dense polymer mixtures is a paradigmatically hard problem in computational physics, even in lattice-based models. Here, we develop a formalism based on interacting binary tensors that allows for tackling…
We describe a Common Lisp package suitable for the high-level design, specification, simulation, and instrumentation of real-time distributed algorithms and hardware on which to run them. We discuss various design decisions around the…
We consider the problem of tensor estimation from noisy observations with possibly missing entries. A nonparametric approach to tensor completion is developed based on a new model which we coin as sign representable tensors. The model…
We formulate a general framework for the study of operator systems arising from discrete groups. We study in detail the operator system of the free group on $n$ generators, as well as the operator systems of the free products of finitely…
Tensor network algorithms have been remarkably successful solving a variety of problems in quantum many-body physics. However, algorithms to optimize two-dimensional tensor networks known as PEPS lack many of the aspects that make the…
The current paper presents a new approach to multilinear dynamical systems analysis and control. The approach is based upon recent developments in tensor decompositions and a newly defined algebra of circulants. In particular, it is shown…
We describe and implement a symbolic algebra for scalar and vector-valued finite elements, enabling the computer generation of elements with tensor product structure on quadrilateral, hexahedral and triangular prismatic cells. The algebra…
Tensors are higher-order extensions of matrices. While matrix methods form the cornerstone of machine learning and data analysis, tensor methods have been gaining increasing traction. However, software support for tensor operations is not…
A tensor network is a diagram that specifies a way to "multiply" a collection of tensors together to produce another tensor (or matrix). Many existing algorithms for tensor problems (such as tensor decomposition and tensor PCA), although…
Bensolve is an open source implementation of Benson's algorithm and its dual variant. Both algorithms compute primal and dual solutions of vector linear programs (VLP), which include the subclass of multiple objective linear programs…