相关论文: Tensor manipulation in GPL Maxima

In recent years, low-rank tensor completion (LRTC) has received considerable attention due to its applications in image/video inpainting, hyperspectral data recovery, etc. With different notions of tensor rank (e.g., CP, Tucker, tensor…

General Matrix Multiplication or GEMM kernels take centre place in high performance computing and machine learning. Recent NVIDIA GPUs include GEMM accelerators, such as NVIDIA's Tensor Cores. Their exploitation is hampered by the…

This work develops a numerical solver based on the combination of isogeometric analysis (IGA) and the tensor train (TT) decomposition for the approximation of partial differential equations (PDEs) on parameter-dependent geometries. First,…

Path-integral techniques are a powerful tool used in open quantum systems to provide an exact solution for the non-Markovian dynamics. However, the exponential scaling of the tensor size with quantum memory length of these techniques limits…

We propose a general algorithmic framework for constrained matrix and tensor factorization, which is widely used in signal processing and machine learning. The new framework is a hybrid between alternating optimization (AO) and the…

The complexity of matrix multiplication is measured in terms of $\omega$, the smallest real number such that two $n\times n$ matrices can be multiplied using $O(n^{\omega+\epsilon})$ field operations for all $\epsilon>0$; the best bound…

This paper presents a multilevel tensor compression algorithm called tensor butterfly algorithm for efficiently representing large-scale and high-dimensional oscillatory integral operators, including Green's functions for wave equations and…

Numerical methods for obtaining exact dynamics of non-Markovian open quantum systems are mostly limited to either small systems or to short-time evolution only. Here, we propose a new algorithm for computing process tensors--matrix product…

Going beyond stochastic gradient descent (SGD), what new phenomena emerge in wide neural networks trained by adaptive optimizers like Adam? Here we show: The same dichotomy between feature learning and kernel behaviors (as in SGD) holds for…

We describe a general-purpose computational toolkit for simulating open quantum systems, which provides numerically exact solutions for composites of zero-dimensional quantum systems that may be strongly coupled to multiple, quite general…

We present a method to compress the final linear layer of language models, reducing memory usage by up to 3.4x without significant performance loss. By grouping tokens based on Byte Pair Encoding (BPE) merges, we prevent materialization of…

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…

In the past two decades, some major efforts have been made to reduce exact (e.g. integer, rational, polynomial) linear algebra problems to matrix multiplication in order to provide algorithms with optimal asymptotic complexity. To provide…

Tensors are multiway arrays of data, and transverse operators are the operators that change the frame of reference. We develop the spectral theory of transverse tensor operators and apply it to problems closely related to classifying…

We consider the problem of jointly modeling and clustering populations of tensors by introducing a high-dimensional tensor mixture model with heterogeneous covariances. To effectively tackle the high dimensionality of tensor objects, we…

In this paper we introduce and study the Maximum-Average Subtensor ($p$-MAS) problem, in which one wants to find a subtensor of size $k$ of a given random tensor of size $N$, both of order $p$, with maximum sum of entries. We are motivated…

This paper presents the RBG-Maxwell framework, a relativistic collisional plasma simulator on GPUs. We provide detailed discussions on the fundamental equations, numerical algorithms, implementation specifics, and key testing outcomes. The…

Robust tensor CP decomposition involves decomposing a tensor into low rank and sparse components. We propose a novel non-convex iterative algorithm with guaranteed recovery. It alternates between low-rank CP decomposition through gradient…

While multilinear algebra appears natural for studying the multiway interactions modeled by hypergraphs, tensor methods for general hypergraphs have been stymied by theoretical and practical barriers. A recently proposed adjacency tensor is…

This work introduces SpinGlassPEPS$.$jl, a software package implemented in Julia, designed to find low-energy configurations of generalized Potts models, including Ising and QUBO problems, utilizing heuristic tensor network contraction…