Related papers: JULIA: Joint Multi-linear and Nonlinear Identifica…

We propose a set of convex low rank inducing norms for a coupled matrices and tensors (hereafter coupled tensors), which shares information between matrices and tensors through common modes. More specifically, we propose a mixture of the…

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…

Using the matrix product state (MPS) representation of tensor train decompositions, in this paper we propose a tensor completion algorithm which alternates over the matrices (tensors) in the MPS representation. This development is motivated…

This paper introduces a model for incomplete utterance restoration (IUR) called JET (\textbf{J}oint learning token \textbf{E}xtraction and \textbf{T}ext generation). Different from prior studies that only work on extraction or abstraction…

Efficient tensor computation is a cornerstone of modern deep learning (DL) workloads, yet existing approaches struggle to achieve flexible and performant design and implementation of tensor layouts -- mappings between logical tensors and…

We consider the problem of low-rank decomposition of incomplete multiway tensors. Since many real-world data lie on an intrinsically low dimensional subspace, tensor low-rank decomposition with missing entries has applications in many data…

Multilinear systems play an important role in scientific calculations of practical problems. In this paper, we consider a tensor splitting method with a relaxed Anderson acceleration for solving multilinear systems. The new method preserves…

Tabular data synthesis is crucial for addressing privacy and security concerns in industries reliant on tabular data. While recent advancements adopt large language models (LLMs) for realistic tabular data generation, their long training…

Machine learning and data mining algorithms are becoming increasingly important in analyzing large volume, multi-relational and multi--modal datasets, which are often conveniently represented as multiway arrays or tensors. It is therefore…

The development of compositional distributional models of semantics reconciling the empirical aspects of distributional semantics with the compositional aspects of formal semantics is a popular topic in the contemporary literature. This…

Previous computation models either have equivalent abilities in representing all computations but fail to provide primitive operators for programming complex algorithms or lack generalized expression ability to represent newly-added…

Tensor Networks are graph representations of summation expressions in which vertices represent tensors and edges represent tensor indices or vector spaces. In this work, we present EinExprs.jl, a Julia package for contraction path…

We introduce an algorithmic framework based on tensor networks for computing fluid flows around immersed objects in curvilinear coordinates. We show that the tensor network simulations can be carried out solely using highly compressed…

We consider the question: what is the abstraction that should be implemented by the computational engine of a machine learning system? Current machine learning systems typically push whole tensors through a series of compute kernels such as…

One of the main issues in computing a tensor decomposition is how to choose the number of rank-one components, since there is no finite algorithms for determining the rank of a tensor. A commonly used approach for this purpose is to find a…

We introduce a new theoretical framework for deriving lower bounds on data movement in bilinear algorithms. Bilinear algorithms are a general representation of fast algorithms for bilinear functions, which include computation of matrix…

Tensor networks provide a powerful framework for compressing multi-dimensional data. The optimal tensor network structure for a given data tensor depends on both data characteristics and specific optimality criteria, making tensor network…

Numerical integration is a classical problem emerging in many fields of science. Multivariate integration cannot be approached with classical methods due to the exponential growth of the number of quadrature nodes. We propose a method to…

We present a simple, general technique for reducing the sample complexity of matrix and tensor decomposition algorithms applied to distributions. We use the technique to give a polynomial-time algorithm for standard ICA with sample…

Tensor completion refers to the problem of recovering the missing, corrupted or unobserved entries in data represented by tensors. In this paper, we tackle the tensor completion problem in the scenario in which multiple tensor acquisitions…