Related papers: A Linear-complexity Tensor Butterfly Algorithm for…
This paper considers clustered multi-task compressive sensing, a hierarchical model that solves multiple compressive sensing tasks by finding clusters of tasks that leverage shared information to mutually improve signal reconstruction. The…
We propose an efficient tensor-train-based algorithm for simulating open quantum systems with the inchworm method, where the reduced dynamics of the open quantum system is expressed as a perturbative series of high-dimensional integrals.…
Tensor decomposition is a mathematically supported technique for data compression. It consists of applying some kind of a Low Rank Decomposition technique on the tensors or matrices in order to reduce the redundancy of the data. However, it…
Most currently used tensor regression models for high-dimensional data are based on Tucker decomposition, which has good properties but loses its efficiency in compressing tensors very quickly as the order of tensors increases, say greater…
We propose a new method for the efficient approximation of a class of highly oscillatory weighted integrals where the oscillatory function depends on the frequency parameter $\omega \geq 0$, typically varying in a large interval. Our…
Most deep neural networks (DNNs) consist fundamentally of convolutional and/or fully connected layers, wherein the linear transform can be cast as the product between a filter matrix and a data matrix obtained by arranging feature tensors…
Tensor train (TT) format is a common approach for computationally efficient work with multidimensional arrays, vectors, matrices, and discretized functions in a wide range of applications, including computational mathematics and machine…
In the current work, a number of algorithms are developed and compared for the numerical solution of periodic (quasi-static) linear elastic mechanical boundary-value problems (BVPs) based on two different discretizations of Fourier series.…
Binary Neural Networks (BNNs) enable efficient deep learning by saving on storage and computational costs. However, as the size of neural networks continues to grow, meeting computational requirements remains a challenge. In this work, we…
We derive a method to efficiently compute the Green function of on arbitrary Hamiltonians defined on semi-infinite and periodic quasi-one-dimensional lattices. Computing the Green function is the backbone of quantum transport, electronic…
Convolution with Green's function of a differential operator appears in a lot of applications e.g. Lippmann-Schwinger integral equation. Algorithms for computing such are usually non-trivial and require non-uniform mesh. However, recently…
In this paper, we aim at the completion problem of high order tensor data with missing entries. The existing tensor factorization and completion methods suffer from the curse of dimensionality when the order of tensor N>>3. To overcome this…
Currently, existing tensor recovery methods fail to recognize the impact of tensor scale variations on their structural characteristics. Furthermore, existing studies face prohibitive computational costs when dealing with large-scale…
Spectral clustering and co-clustering are well-known techniques in data analysis, and recent work has extended spectral clustering to square, symmetric tensors and hypermatrices derived from a network. We develop a new tensor spectral…
Large CNNs have delivered impressive performance in various computer vision applications. But the storage and computation requirements make it problematic for deploying these models on mobile devices. Recently, tensor decompositions have…
This paper presents a novel {\em Interpolated Factored Green Function} method (IFGF) for the accelerated evaluation of the integral operators in scattering theory and other areas. Like existing acceleration methods in these fields, the IFGF…
A method based on separated integration to estimate anharmonic corrections to energy and vibration of molecules in a second-order diagrammatic vibrational many-body Green's function formalism has already been presented. A severe bottleneck…
Recent AI applications such as Collaborative Intelligence with neural networks involve transferring deep feature tensors between various computing devices. This necessitates tensor compression in order to optimize the usage of…
This paper is concerned with the approximation of tensors using tree-based tensor formats, which are tensor networks whose graphs are dimension partition trees. We consider Hilbert tensor spaces of multivariate functions defined on a…
An algorithm for a family of self-starting high-order implicit time integration schemes with controllable numerical dissipation is proposed for both linear and nonlinear transient problems. This work builds on the previous works of the…