Related papers: STARK: Structured Dictionary Learning Through Rank…

The low-complexity assumption in linear systems can often be expressed as rank deficiency in data matrices with generalized Hankel structure. This makes it possible to denoise the data by estimating the underlying structured low-rank…

Tensor data with rich structural information becomes increasingly important in process modeling, monitoring, and diagnosis. Here structural information is referred to structural properties such as sparsity, smoothness, low-rank, and…

Semantic parsing is the problem of deriving machine interpretable meaning representations from natural language utterances. Neural models with encoder-decoder architectures have recently achieved substantial improvements over traditional…

Tensor decomposition methods have proven effective in various applications, including compression and acceleration of neural networks. At the same time, the problem of determining optimal decomposition ranks, which present the crucial…

In this paper, we aim at the problem of tensor data completion. Tensor-train decomposition is adopted because of its powerful representation ability and linear scalability to tensor order. We propose an algorithm named Sparse Tensor-train…

We discuss how recently discovered techniques and tools from compressed sensing can be used in tensor decompositions, with a view towards modeling signals from multiple arrays of multiple sensors. We show that with appropriate bounds on a…

What learning algorithms can be run directly on compressively-sensed data? In this work, we consider the question of accurately and efficiently computing low-rank matrix or tensor factorizations given data compressed via random projections.…

Scientific problems require resolving multi-scale phenomena across different resolutions and learning solution operators in infinite-dimensional function spaces. Neural operators provide a powerful framework for this, using…

A tensor network is a diagram that specifies a way to "multiply" a collection of tensors together to produce another tensor (or matrix). Many existing algorithms for tensor problems (such as tensor decomposition and tensor PCA), although…

Tucker decomposition has been widely used in a variety of applications to obtain latent factors of tensor data. In these applications, a common need is to compute Tucker decomposition for a given time range. Furthermore, real-world tensor…

There has been growing interest in extending traditional vector-based machine learning techniques to their tensor forms. An example is the support tensor machine (STM) that utilizes a rank-one tensor to capture the data structure, thereby…

Higher-order tensors are well-suited for representing multi-dimensional data, such as images and videos, which typically characterize low-rank structures. Low-rank tensor decomposition has become essential in machine learning and computer…

In this paper, we present an overview of constrained PARAFAC models where the constraints model linear dependencies among columns of the factor matrices of the tensor decomposition, or alternatively, the pattern of interactions between…

Recent advances in IoT and biometric sensing technologies have led to the generation of massive and high-dimensional tensor data, yet achieving accurate and efficient low-rank approximation remains a major challenge. Most existing tensor…

Solving arithmetic word problems is a cornerstone task in assessing language understanding and reasoning capabilities in NLP systems. Recent works use automatic extraction and ranking of candidate solution equations providing the answer to…

Data tensors of orders 2 and greater are now routinely being generated. These data collections are increasingly huge and growing. Many scientific and medical data tensors are tensor fields (e.g., images, videos, geographic data) in which…

A rank-adaptive integrator for the approximate solution of high-order tensor differential equations by tree tensor networks is proposed and analyzed. In a recursion from the leaves to the root, the integrator updates bases and then evolves…

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 paper studies tensor-based Robust Principal Component Analysis (RPCA) using atomic-norm regularization. Given the superposition of a sparse and a low-rank tensor, we present conditions under which it is possible to exactly recover the…

This work aims to help resolve the two main stumbling blocks in the application of Deep Neural Networks (DNNs), that is, the exceedingly large number of trainable parameters and their physical interpretability. This is achieved through a…