Related papers: Accelerating Sparse Linear Solvers with an Optical…
Can linear systems be solved faster than matrix multiplication? While there has been remarkable progress for the special cases of graph structured linear systems, in the general setting, the bit complexity of solving an $n \times n$ linear…
In this paper, a fast algorithm for overcomplete sparse decomposition, called SL0, is proposed. The algorithm is essentially a method for obtaining sparse solutions of underdetermined systems of linear equations, and its applications…
Iterative solutions of sparse linear systems and sparse eigenvalue problems have a fundamental role in vital fields of scientific research and engineering. The crucial computing kernel for such iterative solutions is the multiplication of a…
Real-time remote sensing applications like search and rescue missions, military target detection, environmental monitoring, hazard prevention and other time-critical applications require onboard real time processing capabilities or…
Tomographic imaging has benefited from advances in X-ray sources, detectors and optics to enable novel observations in science, engineering and medicine. These advances have come with a dramatic increase of input data in the form of faster…
We propose a new algorithm to solve sparse linear systems of equations over the integers. This algorithm is based on a $p$-adic lifting technique combined with the use of block matrices with structured blocks. It achieves a sub-cubic…
Machine learning (ML) is successful in achieving human-level performance in various fields. However, it lacks the ability to explain an outcome due to its black-box nature. While existing explainable ML is promising, almost all of these…
Driven by deep learning, there has been a surge of specialized processors for matrix multiplication, referred to as TensorCore Units (TCUs). These TCUs are capable of performing matrix multiplications on small matrices (usually 4x4 or…
Efficiently solving large-scale sparse linear systems poses a significant challenge in computational science, especially in fields such as physics, engineering, machine learning, and finance. Traditional classical algorithms face…
We present a novel architecture for sparse pattern processing, using flash storage with embedded accelerators. Sparse pattern processing on large data sets is the essence of applications such as document search, natural language processing,…
The incoherent scatter radar (ISR) technique is a powerful remote sensing tool for ionosphere and thermosphere dynamics in the near-Earth space environment. Weak ISR scatter from naturally occurring Langmuir oscillations, or plasma lines,…
Many approaches to transform classification problems from non-linear to linear by feature transformation have been recently presented in the literature. These notably include sparse coding methods and deep neural networks. However, many of…
We present a sparse linear system solver that is based on a multifrontal variant of Gaussian elimination, and exploits low-rank approximation of the resulting dense frontal matrices. We use hierarchically semiseparable (HSS) matrices, which…
As an important application of spatial databases in pathology imaging analysis, cross-comparing the spatial boundaries of a huge amount of segmented micro-anatomic objects demands extremely data- and compute-intensive operations, requiring…
Optical computing systems provide an alternate hardware model which appears to be aligned with the demands of neural network workloads. However, the challenge of implementing energy efficient nonlinearities in optics -- a key requirement…
Novel materials and devices in photonics have the potential to revolutionize optical information processing, beyond conventional binary-logic approaches. Laser systems offer a rich repertoire of useful dynamical behaviors, including the…
Emerging AI applications such as ChatGPT, graph convolutional networks, and other deep neural networks require massive computational resources for training and inference. Contemporary computing platforms such as CPUs, GPUs, and TPUs are…
Packing and covering linear programs (PC-LPs) form an important class of linear programs (LPs) across computer science, operations research, and optimization. In 1993, Luby and Nisan constructed an iterative algorithm for approximately…
A fast algorithm for the approximation of a low rank LU decomposition is presented. In order to achieve a low complexity, the algorithm uses sparse random projections combined with FFT-based random projections. The asymptotic approximation…
Real-time trajectory optimization for nonlinear constrained autonomous systems is critical and typically performed by CPU-based sequential solvers. Specifically, reliance on global sparse linear algebra or the serial nature of dynamic…