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K-means is a popular clustering algorithm with significant applications in numerous scientific and engineering areas. One drawback of K-means is its inability to identify non-linearly separable clusters, which may lead to inaccurate…

Tensor processing units (TPUs) are one of the most well-known machine learning (ML) accelerators utilized at large scale in data centers as well as in tiny ML applications. TPUs offer several improvements and advantages over conventional ML…

A fast non-convex low-rank matrix decomposition method for potential field data separation is proposed. The singular value decomposition of the large size trajectory matrix, which is also a block Hankel matrix, is obtained using a fast…

We discuss a generalization of the Cohn-Umans method, a potent technique developed for studying the bilinear complexity of matrix multiplication by embedding matrices into an appropriate group algebra. We investigate how the Cohn-Umans…

Dense Matrix Multiplication (MatMul) is arguably one of the most ubiquitous compute-intensive kernels, spanning linear algebra, DSP, graphics, and machine learning applications. Thus, MatMul optimization is crucial not only in…

We propose a strategy for the generation of fast and accurate versions of non-commutative recursive matrix multiplication algorithms. To generate these algorithms, we consider matrix and tensor norm bounds governing the stability and…

Kernel methods provide an elegant and principled approach to nonparametric learning, but so far could hardly be used in large scale problems, since na\"ive implementations scale poorly with data size. Recent advances have shown the benefits…

We present a GPU-accelerated cosmological simulation code, PhotoNs-GPU, based on algorithm of Particle Mesh Fast Multipole Method (PM-FMM), and focus on the GPU utilization and optimization. A proper interpolated method for truncated…

Slow working nodes, known as stragglers, can greatly reduce the speed of distributed computation. Coded matrix multiplication is a recently introduced technique that enables straggler-resistant distributed multiplication of large matrices.…

Matrix decompositions are ubiquitous in machine learning, including applications in dimensionality reduction, data compression and deep learning algorithms. Typical solutions for matrix decompositions have polynomial complexity which…

We develop and implement in this paper a fast sparse assembly algorithm, the fundamental operation which creates a compressed matrix from raw index data. Since it is often a quite demanding and sometimes critical operation, it is of…

Sparse Matrix-Matrix Multiplication (SpMM) is a fundamental computation in graph analytics, scientific simulation, and sparse deep learning workloads. However, the extreme irregularity of real-world sparse matrices prevents existing…

Hierarchical matrix approximations have gained significant traction in the machine learning and scientific community as they exploit available low-rank structures in kernel methods to compress the kernel matrix. The resulting compressed…

Transpose convolution has shown prominence in many deep learning applications. However, transpose convolution layers are computationally intensive due to the increased feature map size due to adding zeros after each element in each row and…

We propose and analyze a compact and non-volatile nanomagnetic (all-spin) non-binary matrix multiplier performing the multiply-and-accumulate (MAC) operation using two magnetic tunnel junctions - one activated by strain to act as the…

Sparse matricized tensor times Khatri-Rao product (MTTKRP) is one of the most computationally expensive kernels in sparse tensor computations. This work focuses on optimizing the MTTKRP operation on GPUs, addressing both performance and…

Efficiently processing basic linear algebra subroutines is of great importance for a wide range of computational problems. In this paper, we consider techniques to implement matrix functions on a quantum computer, which are composed of…

Matrix multiplication (MatMul) is the computational backbone of modern machine learning, yet its classical complexity remains a bottleneck for large-scale data processing. We propose a hybrid quantum-classical algorithm for matrix…

Fast algorithms for matrix multiplication, namely those that perform asymptotically fewer scalar operations than the classical algorithm, have been considered primarily of theoretical interest. Apart from Strassen's original algorithm, few…

Graph Convolutional Networks (GCNs) are recently getting much attention in bioinformatics and chemoinformatics as a state-of-the-art machine learning approach with high accuracy. GCNs process convolutional operations along with graph…