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FPGAs are a promising platform for accelerating Deep Learning (DL) applications, due to their high performance, low power consumption, and reconfigurability. Recently, the leading FPGA vendors have enhanced their architectures to more…
Sparse generalized matrix-matrix multiplication (SpGEMM) is a fundamental operation for real-world network analysis. With the increasing size of real-world networks, the single-machine-based SpGEMM approach cannot perform SpGEMM on…
General Matrix Multiplication (GEMM) is a critical operation underpinning a wide range of applications in high-performance computing (HPC) and artificial intelligence (AI). The emergence of hardware optimized for low-precision arithmetic…
Matrix multiplication is a foundational operation in scientific computing and machine learning, yet its computational complexity makes it a significant bottleneck for large-scale applications. The shift to parallel architectures, primarily…
Large-scale floating-point matrix multiplication is a fundamental kernel in many scientific and engineering applications. Most existing work only focus on accelerating matrix multiplication on FPGA by adopting a linear systolic array. This…
Matrix multiplication computation acceleration has been a research hotspot across various domains. Due to the characteristics of some applications, approximate matrix multiplication can achieve significant performance improvements without…
The communication cost of algorithms (also known as I/O-complexity) is shown to be closely related to the expansion properties of the corresponding computation graphs. We demonstrate this on Strassen's and other fast matrix multiplication…
Fast algorithms for integer and polynomial multiplication play an important role in scientific computing as well as in other disciplines. In 1971, Sch{\"o}nhage and Strassen designed an algorithm that improved the multiplication time for…
The generic matrix multiply (GEMM) function is the core element of high-performance linear algebra libraries used in many computationally-demanding digital signal processing (DSP) systems. We propose an acceleration technique for GEMM based…
Determining the asymptotic algebraic complexity of matrix multiplication, succinctly represented by the matrix multiplication exponent $\omega$, is a central problem in algebraic complexity theory. The best upper bounds on $\omega$, leading…
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…
Sparse Matrix-Matrix multiplication is a key kernel that has applications in several domains such as scientific computing and graph analysis. Several algorithms have been studied in the past for this foundational kernel. In this paper, we…
Sparse General Matrix-Matrix Multiplication (SpGEMM) is a fundamental operation in numerous scientific computing and data analytics applications, often bottlenecked by irregular memory access patterns. This paper presents Hash based…
Numerical codes that require arbitrary precision floating point (APFP) numbers for their core computation are dominated by elementary arithmetic operations due to the super-linear complexity of multiplication in the number of mantissa bits.…
Min-plus product of two $n\times n$ matrices is a fundamental problem in algorithm research. It is known to be equivalent to APSP, and in general it has no truly subcubic algorithms. In this paper, we focus on the min-plus product on a…
We give an $O(N\cdot \log N\cdot 2^{O(\log^*N)})$ algorithm for multiplying two $N$-bit integers that improves the $O(N\cdot \log N\cdot \log\log N)$ algorithm by Sch\"{o}nhage-Strassen. Both these algorithms use modular arithmetic.…
Data movement is the dominating factor affecting performance and energy in modern computing systems. Consequently, many algorithms have been developed to minimize the number of I/O operations for common computing patterns. Matrix…
The main purpose of this paper is pedagogical. Despite its importance, all proofs of the correctness of Strassen's famous 1969 algorithm to multiply two 2x2 matrices with only seven multiplications involve some basis-dependent calculations…
Plaintext-ciphertext matrix multiplication (PC-MM) is an indispensable tool in privacy-preserving computations such as secure machine learning and encrypted signal processing. While there are many established algorithms for…
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…