Related papers: Symbolical Index Reduction and Completion Rules fo…

Symbolic regression is a powerful system identification technique in industrial scenarios where no prior knowledge on model structure is available. Such scenarios often require specific model properties such as interpretability, robustness,…

In this work, we develop an optimization framework for problems whose solutions are well-approximated by Hierarchical Tucker (HT) tensors, an efficient structured tensor format based on recursive subspace factorizations. By exploiting the…

The structure tensor method is often used for 2D and 3D analysis of imaged structures, but its results are in many cases very dependent on the user's choice of method parameters. We simplify this parameter choice in first order structure…

This article discusses an efficient implementation of tensors of arbitrary rank by using some of the idioms introduced by the recently published C++ ISO Standard (C++11). With the aims at providing a basic building block for…

In the literature, tensors have been effectively used for capturing the context information in language models. However, the existing methods usually adopt relatively-low order tensors, which have limited expressive power in modeling…

This paper introduces an objective metric for evaluating a parsing scheme. It is based on Shannon's original work with letter sequences, which can be extended to part-of-speech tag sequences. It is shown that this regular language is an…

In low-rank tensor completion tasks, due to the underlying multiple large-scale singular value decomposition (SVD) operations and rank selection problem of the traditional methods, they suffer from high computational cost and high…

This chapter studies the problem of decomposing a tensor into a sum of constituent rank one tensors. While tensor decompositions are very useful in designing learning algorithms and data analysis, they are NP-hard in the worst-case. We will…

A numerical approach to compute tensor integrals in one-loop calculations is presented. The algorithm is based on a recursion relation which allows to express high rank tensor integrals as a function of lower rank ones. At each level of…

There is a significant expansion in both volume and range of applications along with the concomitant increase in the variety of data sources. These ever-expanding trends have highlighted the necessity for more versatile analysis tools that…

We describe a new, convenient, recursive tensor integral reduction scheme for one-loop $n$-point Feynman integrals. The reduction is based on the algebraic Davydychev-Tarasov formalism where the tensors are represented by scalars with…

Function approximation from input and output data is one of the most investigated problems in signal processing. This problem has been tackled with various signal processing and machine learning methods. Although tensors have a rich history…

Finding a denotational semantics for higher order quantum computation is a long-standing problem in the semantics of quantum programming languages. Most past approaches to this problem fell short in one way or another, either limiting the…

Modelling compositionality has been a longstanding area of research in the field of vector space semantics. The categorical approach to compositionality maps grammar onto vector spaces in a principled way, but comes under fire for requiring…

Tensor methods have emerged as a powerful paradigm for consistent learning of many latent variable models such as topic models, independent component analysis and dictionary learning. Model parameters are estimated via CP decomposition of…

Multidimensional arrays (NDArrays) are a central abstraction in modern scientific computing environments. Unfortunately, they can make reasoning about programs harder as the number of different array shapes used in an execution of a program…

This research introduces an improved framework for constructing matrix product operators (MPOs) and tree tensor network operators (TTNOs), crucial tools in quantum simulations. A given (Hamiltonian) operator typically has a known symbolic…

This study aims to solve the over-reliance on the rank estimation strategy in the standard tensor factorization-based tensor recovery and the problem of a large computational cost in the standard t-SVD-based tensor recovery. To this end, we…

In this paper, we present an approach to integer factorization using distributed representations formed with Vector Symbolic Architectures. The approach formulates integer factorization in a manner such that it can be solved using neural…

We address prediction problems on tabular categorical data, where each instance is defined by multiple categorical attributes, each taking values from a finite set. These attributes are often referred to as fields, and their categorical…