相关论文: An Algorithm to Simplify Tensor Expressions

In many applications, such as classification of images or videos, it is of interest to develop a framework for tensor data instead of an ad-hoc way of transforming data to vectors due to the computational and under-sampling issues. In this…

We propose Riemannian preconditioned algorithms for the tensor completion problem via tensor ring decomposition. A new Riemannian metric is developed on the product space of the mode-2 unfolding matrices of the core tensors in tensor ring…

Decompositions of tensors into factor matrices, which interact through a core tensor, have found numerous applications in signal processing and machine learning. A more general tensor model which represents data as an ordered network of…

In this paper, the reduction of Feynman integrals in the parametric representation is considered. This method proves to be more efficient than the integration-by-part (IBP) method in the momentum space. Tensor integrals can directly be…

In this paper we present a Java implementation of the algorithm that computes Buchbereger's and reduced Groebner's basis step by step. The Java application enables graphical representation of the intersection of two surfaces in…

We consider the problem of solving mixed random linear equations with $k$ components. This is the noiseless setting of mixed linear regression. The goal is to estimate multiple linear models from mixed samples in the case where the labels…

We present an algorithm for normalizing \emph{Batched Einstein Summation} expressions by mapping mathematically equivalent formulations to a unique normal form. Batches of einsums with the same Einstein notation that exhibit substantial…

A Grobner basis-based algorithm for solving the Frobenius Instance Problem is presented, and this leads to an algorithm for solving the Frobenius Problem that can handle numbers with thousands of digits. Connections to irreducible…

Prime-based ordering which is proved to be admissible, is the encoding of indeterminates in power-products with prime numbers and ordering them by using the natural number order. Using Eiffel, four versions of Buchberger's improved…

With this paper we present an extension of our recent ISSAC paper about computations of Groebner(-Shirshov) bases over free associative algebras Z<X>. We present all the needed proofs in details, add a part on the direct treatment of the…

Producing large complex simulation datasets can often be a time and resource consuming task. Especially when these experiments are very expensive, it is becoming more reasonable to generate synthetic data for downstream tasks. Recently,…

In a previous paper a new approach has been introduced for computing, recursively and numerically, one-loop tensor integrals. Here we describe a few modifications of the original method that allow a more efficient numerical implementation…

Tensor decomposition serves as a powerful primitive in statistics and machine learning, and has numerous applications in problems such as learning latent variable models or mixture of Gaussians. In this paper, we focus on using power…

Finding the symmetric and orthogonal decomposition (SOD) of a tensor is a recurring problem in signal processing, machine learning and statistics. In this paper, we review, establish and compare the perturbation bounds for two natural types…

Prepositions are among the most frequent words in English and play complex roles in the syntax and semantics of sentences. Not surprisingly, they pose well-known difficulties in automatic processing of sentences (prepositional attachment…

This paper presents a novel approach to automatically solving arithmetic word problems. This is the first algorithmic approach that can handle arithmetic problems with multiple steps and operations, without depending on additional…

In this paper we consider finite-dimensional constrained Hamiltonian systems of polynomial type. In order to compute the complete set of constraints and separate them into the first and second classes we apply the modern algorithmic methods…

Iterative methods based on tensors have emerged as powerful tools for solving tensor equations, and have significantly advanced across multiple disciplines. In this study, we propose two-step tensor-based iterative methods to solve the…

This paper addresses the problem of finding the closest generalized essential matrix from a given $6\times 6$ matrix, with respect to the Frobenius norm. To the best of our knowledge, this nonlinear constrained optimization problem has not…

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…