Related papers: Compression of Far-Fields in the Fast Multipole Me…
Tensors of order three or higher have found applications in diverse fields, including image and signal processing, data mining, biomedical engineering and link analysis, to name a few. In many applications that involve for example time…
To improve the training efficiency of federated learning (FL), previous research has employed low-rank decomposition techniques to reduce communication overhead. In this paper, we seek to enhance the performance of these low-rank…
Compressed sensing extends from the recovery of sparse vectors from undersampled measurements via efficient algorithms to the recovery of matrices of low rank from incomplete information. Here we consider a further extension to the…
One of the most efficient ways to produce unconditional simulations is with the kernel convolution using fast Fourier transform (FFT) [1]. However, when data is located on a surface, this approach is not efficient because data needs to be…
In modern low-power embedded platforms, floating-point (FP) operations emerge as a major contributor to the energy consumption of compute-intensive applications with large dynamic range. Experimental evidence shows that 50% of the energy…
Tensors or multiarray data are generalizations of matrices. Tensor clustering has become a very important research topic due to the intrinsically rich structures in real-world multiarray datasets. Subspace clustering based on vectorizing…
In this article, we discuss the efficient implementation of powerful domain decomposition smoothers for multigrid methods for high order discontinuous Galerkin (DG) finite element methods. In particular, we study the inversion of matrices…
We introduce two nonlinear sufficient dimension reduction methods for regressions with tensor-valued predictors. Our goal is two-fold: the first is to preserve the tensor structure when performing dimension reduction, particularly the…
In this paper, we introduce a new tensor decomposition for third order tensors, which decomposes a third order tensor to three third order low rank tensors in a balanced way. We call such a decomposition the triple decomposition, and the…
Recent studies have demonstrated improved skill in numerical weather prediction via the use of spatially correlated observation error covariance information in data assimilation systems. In this case, the observation weighting matrices…
In this paper, we propose a dimension reduction method specifically designed for tensor-structured feature data in deep neural networks. The method is implemented as a hidden layer, called the TensorProjection layer, which transforms input…
Symmetric trace-free tensors are used in many areas of physics, including electromagnetism, relativistic celestial mechanics and geodesy, as well as in the study of gravitational radiation and gravitational lensing. Their use allows…
The structured sparsity can be leveraged in traditional far-field channels, greatly facilitating efficient sparse channel recovery by compressing the complexity of overheads to the level of the scatterer number. However, when experiencing a…
The validation, verification, and uncertainty quantification of computationally expensive theoretical models of quantum many-body systems require the construction of fast and accurate emulators. In this work, we develop emulators for…
This paper introduces matrix product state (MPS) decomposition as a new and systematic method to compress multidimensional data represented by higher-order tensors. It solves two major bottlenecks in tensor compression: computation and…
The emerging edge computing has promoted immense interests in compacting a neural network without sacrificing much accuracy. In this regard, low-rank tensor decomposition constitutes a powerful tool to compress convolutional neural networks…
Feature extraction for tensor data serves as an important step in many tasks such as anomaly detection, process monitoring, image classification, and quality control. Although many methods have been proposed for tensor feature extraction,…
The discretization of the double-layer potential integral equation for the interior Dirichlet Laplace problem in a domain with smooth boundary results in a linear system that has a bounded condition number. Thus, the number of iterations…
Large-scale neuroimaging studies have been collecting brain images of study individuals, which take the form of two-dimensional, three-dimensional, or higher dimensional arrays, also known as tensors. Addressing scientific questions arising…
Quantum simulation has shown great potential in many fields due to its powerful computational capabilities. However, the limited fidelity can lead to a severe limitation on the number of gate operations, which requires us to find optimized…