Related papers: Quantifying the Effect of Matrix Structure on Mult…

Sparse matrices and linear algebra are at the heart of scientific simulations. Over the years, more than 70 sparse matrix storage formats have been developed, targeting a wide range of hardware architectures and matrix types, each of which…

Matrix extensions have emerged as an essential feature in modern CPUs to address the surging demands of AI workloads. However, existing designs often incur substantial hardware and software design overhead. Tight coupling with the CPU…

Various Neural Networks employ time-consuming matrix operations like matrix inversion. Many such matrix operations are faster to compute given the Singular Value Decomposition (SVD). Previous work allows using the SVD in Neural Networks…

Sparse matrix multiplication is an important component of linear algebra computations. Implementing sparse matrix multiplication on an associative processor (AP) enables high level of parallelism, where a row of one matrix is multiplied in…

Simplex-structured matrix factorization (SSMF) is a common task encountered in signal processing and machine learning. Minimum-volume constrained unmixing (MVCU) algorithms are among the most widely used methods to perform this task. While…

Current AI training infrastructure is dominated by single instruction multiple data (SIMD) and systolic array architectures, such as Graphics Processing Units (GPUs) and Tensor Processing Units (TPUs), that excel at accelerating parallel…

We consider a sparse matrix-matrix multiplication (SpGEMM) setting where one matrix is square and the other is tall and skinny. This special variant, called TS-SpGEMM, has important applications in multi-source breadth-first search,…

Exploiting sparsity enables hardware systems to run neural networks faster and more energy-efficiently. However, most prior sparsity-centric optimization techniques only accelerate the forward pass of neural networks and usually require an…

In the context of cryptanalysis, computing discrete logarithms in large cyclic groups using index-calculus-based methods, such as the number field sieve or the function field sieve, requires solving large sparse systems of linear equations…

Traditional solution approaches for problems in quantum mechanics scale as $\mathcal O(M^3)$, where $M$ is the number of electrons. Various methods have been proposed to address this issue and obtain linear scaling $\mathcal O(M)$. One…

The Kernel Polynomial Method (KPM) is a well-established scheme in quantum physics and quantum chemistry to determine the eigenvalue density and spectral properties of large sparse matrices. In this work we demonstrate the high optimization…

While Strassen's matrix multiplication algorithm reduces the complexity of naive matrix multiplication, general-purpose hardware is not suitable for achieving the algorithm's promised theoretical speedups. This leaves the question of if it…

We develop new theoretical results on matrix perturbation to shed light on the impact of architecture on the performance of a deep network. In particular, we explain analytically what deep learning practitioners have long observed…

This paper introduces sTiles, a GPU-accelerated framework for factorizing sparse structured symmetric matrices. By leveraging tile algorithms for fine-grained computations, sTiles uses a structure-aware task execution flow to handle…

The transfer-matrix technique is a convenient way for studying strip lattices in the Potts model since the compu- tational costs depend just on the periodic part of the lattice and not on the whole. However, even when the cost is reduced,…

Many effective solutions have been proposed to reduce the redundancy of models for inference acceleration. Nevertheless, common approaches mostly focus on eliminating less important filters or constructing efficient operations, while…

We propose a new sparse matrix format, PackSELL, designed to support diverse data representations and enable efficient sparse matrix-vector multiplication (SpMV) on GPUs. Building on sliced ELLPACK (SELL), PackSELL incorporates delta…

We propose a set of benchmarks that specifically targets a major cause of performance degradation in high performance computing platforms: irregular access patterns. These benchmarks are meant to be used to asses the performance of…

We propose a fine-grained hypergraph model for sparse matrix-matrix multiplication (SpGEMM), a key computational kernel in scientific computing and data analysis whose performance is often communication bound. This model correctly describes…

In this paper, the impacts of imperfect channel covariance matrix on the spectral efficiency (SE) of cell-free distributed massive multiple-input multiple-output (MIMO) systems are analyzed. We propose to estimate the channel covariance…