相关论文: Complex-to-Real Sketches for Tensor Products with …

The Neural Tangent Kernel (NTK) characterizes the behavior of infinitely-wide neural networks trained under least squares loss by gradient descent. Recent works also report that NTK regression can outperform finitely-wide neural networks…

Modern data stream applications demand memory-efficient solutions for accurately tracking frequent items, such as heavy hitters and heavy changers, under strict resource constraints. Traditional sketches face inherent accuracy-memory…

The Grassmannian manifold G(k, n) serves as a fundamental tool in signal processing, computer vision, and machine learning, where problems often involve classifying, clustering, or comparing subspaces. In this work, we propose a…

This paper, broadly speaking, covers the use of randomness in two main areas: low-rank approximation and kernel methods. Low-rank approximation is very important in numerical linear algebra. Many applications depend on matrix decomposition…

This work deals with developing two fast randomized algorithms for computing the generalized tensor singular value decomposition (GTSVD) based on the tubal product (t-product). The random projection method is utilized to compute the…

In this paper, we study the problem of approximately computing the product of two real matrices. In particular, we analyze a dimensionality-reduction-based approximation algorithm due to Sarlos [1], introducing the notion of nuclear rank as…

In this note we illustrate how common matrix approximation methods, such as random projection and random sampling, yield projection-cost-preserving sketches, as introduced in [FSS13, CEM+15]. A projection-cost-preserving sketch is a matrix…

In order to compute fast approximations to the singular value decompositions (SVD) of very large matrices, randomized sketching algorithms have become a leading approach. However, a key practical difficulty of sketching an SVD is that the…

Accurate simulations of atomistic systems from first principles are limited by computational cost. In high-throughput settings, machine learning can reduce these costs significantly by accurately interpolating between reference…

A methodology for using random sketching in the context of model order reduction for high-dimensional parameter-dependent systems of equations was introduced in [Balabanov and Nouy 2019, Part I]. Following this framework, we here construct…

We introduce a novel bottom-up approach for the extraction of chart data. Our model utilizes images of charts as inputs and learns to detect keypoints (KP), which are used to reconstruct the components within the plot area. Our novelty lies…

Purpose: Parallel imaging and compressed sensing reconstructions of large MRI datasets often have a prohibitive computational cost that bottlenecks clinical deployment, especially for 3D non-Cartesian acquisitions. One common approach is to…

We develop a randomized extension of tensor Krylov subspace methods based on the Einstein product for solving large-scale multilinear systems arising in image and video restoration. The classical tensor global GMRES method relies on…

There is an increasing body of work exploring the integration of random projection into algorithms for numerical linear algebra. The primary motivation is to reduce the overall computational cost of processing large datasets. A suitably…

We present the first linear time complexity randomized algorithms for unbiased approximation of the celebrated family of general random walk kernels (RWKs) for sparse graphs. This includes both labelled and unlabelled instances. The…

We give a simple, low resource method to produce order embeddings from ontologies. Such embeddings map words to vectors so that order relations on the words, such as hypernymy/hyponymy, are represented in a direct way. Our method uses…

We present a tree-tensor-network-based method to study strongly correlated systems with nonlocal interactions in higher dimensions. Although the momentum-space and quantum-chemistry versions of the density matrix renormalization group…

In many real-world applications, data are represented by matrices or high-order tensors. Despite the promising performance, the existing two-dimensional discriminant analysis algorithms employ a single projection model to exploit the…

The CP tensor decomposition is a low-rank approximation of a tensor. We present a distributed-memory parallel algorithm and implementation of an alternating optimization method for computing a CP decomposition of dense tensor data that can…

An efficient technique based on low-rank separated approximations is proposed for computation of three-dimensional integrals arising in the energy deposition model that describes ion-atomic collisions. Direct tensor-product quadrature…