Related papers: Engineering Boolean Matrix Multiplication for Mult…
Computing in-memory (CiM) has emerged as an attractive technique to mitigate the von-Neumann bottleneck. Current digital CiM approaches for in-memory operands are based on multi-wordline assertion for computing bit-wise Boolean functions…
The multiplication of a matrix by its transpose, $A^T A$, appears as an intermediate operation in the solution of a wide set of problems. In this paper, we propose a new cache-oblivious algorithm (ATA) for computing this product, based upon…
Computing the product of two sparse matrices (SpGEMM) is a fundamental operation in various combinatorial and graph algorithms as well as various bioinformatics and data analytics applications for computing inner-product similarities. For…
This paper proposes a frequent itemset mining algorithm based on the Boolean matrix method, aiming to solve the storage and computational bottlenecks of traditional frequent pattern mining algorithms in high-dimensional and large-scale…
In this paper, we present algorithms to solve matrix multiplication problems in the MPC model. In particular, we consider the problem under various processor/memory constraints in the MPC model and prove the following results. 1.…
We present algorithms for real and complex dot product and matrix multiplication in arbitrary-precision floating-point and ball arithmetic. A low-overhead dot product is implemented on the level of GMP limb arrays; it is about twice as fast…
Processing-in-memory (PIM) turns out to be a promising solution to breakthrough the memory wall and the power wall. While prior PIM designs yield successful implementation of bitwise Boolean logic operations locally in memory, it is…
It is well known that Strassen and Winograd algorithms can reduce the computational costs associated with dense matrix multiplication. We have already shown that they are also very effective for software-based multiple precision…
Offloading compute-intensive kernels to hardware accelerators relies on the large degree of parallelism offered by these platforms. However, the effective bandwidth of the memory interface often causes a bottleneck, hindering the…
We present an algorithm to reduce the computational effort for the multiplication of a given matrix with an unknown column vector. The algorithm decomposes the given matrix into a product of matrices whose entries are either zero or integer…
This work focuses on accelerating the multiplication of a dense random matrix with a (fixed) sparse matrix, which is frequently used in sketching algorithms. We develop a novel scheme that takes advantage of blocking and recomputation…
Recently, reinforcement algorithms discovered new algorithms that really jump-started a wave of excitements and a flourishing of publications. However, there is little on implementations, applications, and, especially, no absolute…
Neural-network (NN) inference is increasingly present on-board spacecraft to reduce downlink bandwidth and enable timely decision making. However, the power and reliability constraints of space missions limit the applicability of many…
Matrix multiplication is the bedrock in Deep Learning inference application. When it comes to hardware acceleration on edge computing devices, matrix multiplication often takes up a great majority of the time. To achieve better performance…
Hierarchical matrices provide a highly memory-efficient way of storing dense linear operators arising, for example, from boundary element methods, particularly when stored in the H^2 format. In such data-sparse representations, iterative…
Applications of Binary Neural Networks (BNNs) are promising for embedded systems with hard constraints on computing power. Contrary to conventional neural networks with the floating-point datatype, BNNs use binarized weights and activations…
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…
In this paper, we present fast algorithms for the product of two multivariate polynomials in sparse representation. The bit complexity of our algorithms are studied in detail for various types of coefficients, and we derive new complexity…
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…
Although reliable long precision floating-point arithmetic libraries such as QD and MPFR/GMP are necessary to solve ill-conditioned problems in numerical simulation, long precision BLAS-level computation such as matrix multiplication has…