Related papers: Reducing Computational Complexity of Tensor Contra…

Tensors, which provide a powerful and flexible model for representing multi-attribute data and multi-way interactions, play an indispensable role in modern data science across various fields in science and engineering. A fundamental task is…

Tensor decomposition is an effective tool for learning multi-way structures and heterogeneous features from high-dimensional data, such as the multi-view images and multichannel electroencephalography (EEG) signals, are often represented by…

Deep convolutional neural networks (CNNs) with a large number of parameters require intensive computational resources, and thus are hard to be deployed in resource-constrained platforms. Decomposition-based methods, therefore, have been…

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…

Tensor classification has become increasingly crucial in statistics and machine learning, with applications spanning neuroimaging, computer vision, and recommendation systems. However, the high dimensionality of tensors presents significant…

Recurrent neural networks (RNNs) are powerful in the tasks oriented to sequential data, such as natural language processing and video recognition. However, since the modern RNNs, including long-short term memory (LSTM) and gated recurrent…

With the advances in data acquisition technology, tensor objects are collected in a variety of applications including multimedia, medical and hyperspectral imaging. As the dimensionality of tensor objects is usually very high,…

We present efficient and scalable parallel algorithms for performing mathematical operations for low-rank tensors represented in the tensor train (TT) format. We consider algorithms for addition, elementwise multiplication, computing norms…

Link prediction in dynamic networks remains a fundamental challenge in network science, requiring the inference of potential interactions and their evolving strengths through spatiotemporal pattern analysis. Traditional static network…

Neural networks are widely used for image-related tasks but typically demand considerable computing power. Once a network has been trained, however, its memory- and compute-footprint can be reduced by compression. In this work, we focus on…

Tensor product state (TPS) based methods are powerful tools to efficiently simulate quantum many-body systems in and out of equilibrium. In particular, the one-dimensional matrix-product (MPS) formalism is by now an established tool in…

Sparse tensor networks are commonly used to represent contractions over sparse tensors. Tensor contractions are higher-order analogs of matrix multiplication. Tensor networks arise commonly in many domains of scientific computing and data…

Hypergraphs and tensors extend classic graph and matrix theory to account for multiway relationships, which are ubiquitous in engineering, biological, and social systems. While the Kronecker product is a potent tool for analyzing the…

This paper introduces an extended tensor decomposition (XTD) method for model reduction. The proposed method is based on a sparse non-separated enrichment to the conventional tensor decomposition, which is expected to improve the…

Tensor decomposition has been widely used in machine learning and high-volume data analysis. However, large-scale tensor factorization often consumes huge memory and computing cost. Meanwhile, modernized computing hardware such as tensor…

Recently, introducing Tensor Decomposition (TD) techniques into unsupervised feature selection (UFS) has been an emerging research topic. A tensor structure is beneficial for mining the relations between different modes and helps relieve…

Tensor contractions are ubiquitous in computational chemistry and physics, where tensors generally represent states or operators and contractions express the algebra of these quantities. In this context, the states and operators often…

Low rank tensor decompositions are a powerful tool for learning generative models, and uniqueness results give them a significant advantage over matrix decomposition methods. However, tensors pose significant algorithmic challenges and…

Tensor networks have been successfully applied in simulation of quantum physical systems for decades. Recently, they have also been employed in classical simulation of quantum computing, in particular, random quantum circuits. This paper…

Convolutional neural networks typically consist of many convolutional layers followed by one or more fully connected layers. While convolutional layers map between high-order activation tensors, the fully connected layers operate on…