Related papers: EinDecomp: Decomposition of Declaratively-Specifie…
The main challenge with the tensor completion problem is a fundamental tension between computation power and the information-theoretic sample complexity rate. Past approaches either achieve the information-theoretic rate but lack practical…
The rapid development of parallel and distributed computing paradigms has brought about great revolution in computing. Thanks to the intrinsic parallelism of evolutionary computation (EC), it is natural to implement EC on parallel and…
Tensor decomposition plays a key role in identifying common features across a collection of matrices in many areas of science. A fundamental need in big data research is to process data tabulated as large-scale matrices using eigenvectors.…
We propose a new arc consistency enforcement paradigm that transforms arc consistency enforcement into recurrent tensor operations. In each iteration of the recurrence, all involved processes can be fully parallelized with tensor…
We present Rhino, a system for accelerating tensor programs with automatic parallelization on AI platform for real production environment. It transforms a tensor program written for a single device into an equivalent distributed program…
Tensor network decompositions offer an efficient description of certain many-body states of a lattice system and are the basis of a wealth of numerical simulation algorithms. In a recent paper [arXiv:0907.2994v1] we discussed how to…
Many real-world datasets are represented as tensors, i.e., multi-dimensional arrays of numerical values. Storing them without compression often requires substantial space, which grows exponentially with the order. While many tensor…
To ensure interpretability of extracted sources in tensor decomposition, we introduce in this paper a dictionary-based tensor canonical polyadic decomposition which enforces one factor to belong exactly to a known dictionary. A new…
Most machine learning models for structured data encode the structural knowledge of a node by leveraging simple aggregation functions (in neural models, typically a weighted sum) of the information in the node's neighbourhood. Nevertheless,…
We introduce a formal operational semantics that describes the fused execution of variable contraction problems, which compute indexed arithmetic over a semiring and generalize sparse and dense tensor algebra, relational algebra, and graph…
We study symmetric tensor decompositions, i.e., decompositions of the form $T = \sum_{i=1}^r u_i^{\otimes 3}$ where $T$ is a symmetric tensor of order 3 and $u_i \in \mathbb{C}^n$.In order to obtain efficient decomposition algorithms, it is…
The widespread use of multisensor technology and the emergence of big data sets have brought the necessity to develop more versatile tools to represent higher-order data with multiple aspects and high dimensionality. Data in the form of…
In this paper, we present ASPEN, an answer set programming (ASP) implementation of a recently proposed declarative framework for collective entity resolution (ER). While an ASP encoding had been previously suggested, several practical…
Graphical tensor notation is a simple way of denoting linear operations on tensors, originating from physics. Modern deep learning consists almost entirely of operations on or between tensors, so easily understanding tensor operations is…
We address the problem of optimizing mixed sparse and dense tensor algebra in a compiler. We show that standard loop transformations, such as strip-mining, tiling, collapsing, parallelization and vectorization, can be applied to irregular…
Answer Set Programming (ASP) is a purely declarative formalism developed in the field of logic programming and nonmonotonic reasoning: computational problems are encoded by logic programs whose answer sets, corresponding to solutions, are…
Tensor completion can estimate missing values of a high-order data from its partially observed entries. Recent works show that low rank tensor ring approximation is one of the most powerful tools to solve tensor completion problem. However,…
Tensor decomposition is a popular technique for tensor completion, However most of the existing methods are based on linear or shallow model, when the data tensor becomes large and the observation data is very small, it is prone to over…
In the machine learning fields, Recurrent Neural Network (RNN) has become a popular architecture for sequential data modeling. However, behind the impressive performance, RNNs require a large number of parameters for both training and…
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…