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In recent years, the fervent demand for computational power across various domains has prompted hardware manufacturers to introduce specialized computing hardware aimed at enhancing computational capabilities. Particularly, the utilization…
Matrix multiplication optimization remains a fundamental challenge in computational mathematics. This work introduces a novel approach that discovers matrix multiplication schemes whose coefficients are restricted to the set $\{-1, 0, 1\}$…
AI models are increasing in size and recent advancement in the community has shown that unlike HPC applications where double precision datatype are required, lower-precision datatypes such as fp8 or int4 are sufficient to bring the same…
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…
Among generalized additive models, additive Mat\'ern Gaussian Processes (GPs) are one of the most popular for scalable high-dimensional problems. Thanks to their additive structure and stochastic differential equation representation,…
Sparse matrix multiplication is an important kernel for large-scale graph processing and other data-intensive applications. In this paper, we implement various asynchronous, RDMA-based sparse times dense (SpMM) and sparse times sparse…
As the demand for AI computation rapidly increases, more hardware is being developed to efficiently perform the low-precision matrix multiplications required by such workloads. However, these operations are generally not directly applicable…
Field Programmable Gate Arrays generate algorithmic specific architectures that improve the code's FLOP per watt ratio. Such devices are re-gaining interest due to the rise of new tools that facilitate their programming, such as OmpSs. The…
Matrix-matrix multiplication is a key computational kernel for numerous applications in science and engineering, with ample parallelism and data locality that lends itself well to high-performance implementations. Many matrix…
General matrix multiplication (GEMM) on spatial accelerators is highly sensitive to mapping choices in both execution efficiency and energy consumption. However, the mapping space exhibits combinatorial explosion, which makes it extremely…
Electronic devices primarily aim to offer low power consumption, high speed, and a compact area. The performance of very large-scale integration (VLSI) devices is influenced by arithmetic operations, where multiplication is a crucial…
Deep Neural Networks (DNNs) predominantly rely on General Matrix Multiply (GEMM) kernels, which are often accelerated using specialized hardware architectures. Recently, analog photonic GEMM accelerators have emerged as a promising…
We revisit the fundamental Boolean Matrix Multiplication (BMM) problem. With the invention of algebraic fast matrix multiplication over 50 years ago, it also became known that BMM can be solved in truly subcubic $O(n^\omega)$ time, where…
Scaling up the sparse matrix-vector multiplication kernel on modern Graphics Processing Units (GPU) has been at the heart of numerous studies in both academia and industry. In this article we present a novel non-parametric, self-tunable,…
Matrix multiplication consumes a large fraction of the time taken in many machine-learning algorithms. Thus, accelerator chips that perform matrix multiplication faster than conventional processors or even GPU's are of increasing interest.…
A parallel algorithm has perfect strong scaling if its running time on P processors is linear in 1/P, including all communication costs. Distributed-memory parallel algorithms for matrix multiplication with perfect strong scaling have only…
This paper proposes new factorizations for computing the Neumann series. The factorizations are based on fast algorithms for small prime sizes series and the splitting of large sizes into several smaller ones. We propose a different basis…
Symmetric Nonnegative Matrix Factorization (SNMF) models arise naturally as simple reformulations of many standard clustering algorithms including the popular spectral clustering method. Recent work has demonstrated that an elementary…
Matrix factorization (MF) discovers latent features from observations, which has shown great promises in the fields of collaborative filtering, data compression, feature extraction, word embedding, etc. While many problem-specific…
Computation of the large sparse matrix exponential has been an important topic in many fields, such as network and finite-element analysis. The existing scaling and squaring algorithm (SSA) is not suitable for the computation of the large…