Related papers: Acceleration of multiple precision matrix multipli…
A switched-capacitor matrix multiplier is presented for approximate computing and machine learning applications. The multiply-and-accumulate operations perform discrete-time charge-domain signal processing using passive switches and 300 aF…
The machine learning explosion has created a prominent trend in modern computer hardware towards low precision floating-point operations. In response, there have been growing efforts to use low and mixed precision in general scientific…
We have developed a highly-tuned software library that accelerates the calculation of quadrupole terms in the Barnes-Hut tree code by use of a SIMD instruction set on the x86 architecture, Advanced Vector eXtensions 2 (AVX2). Our code is…
Dedicated hardware accelerators are suitable for parallel computational tasks. Moreover, they have the tendency to accept inexact results. These hardware accelerators are extensively used in image processing and computer vision…
We analyze a modified version of Nesterov accelerated gradient algorithm, which applies to affine fixed point problems with non self-adjoint matrices, such as the ones appearing in the theory of Markov decision processes with discounted or…
The alternating direction method of multipliers (ADMM) is a popular approach for solving optimization problems that are potentially non-smooth and with hard constraints. It has been applied to various computer graphics applications,…
Graph analytics techniques based on spectral methods process extremely large sparse matrices with millions or even billions of non-zero values. Behind these algorithms lies the Top-K sparse eigenproblem, the computation of the largest…
Discrete cosine transform (DCT) and other Fourier-related transforms have broad applications in scientific computing. However, off-the-shelf high-performance multi-dimensional DCT (MD DCT) libraries are not readily available in parallel…
Matrix multiplications between asymmetric bit-width operands, especially between 8- and 4-bit operands are likely to become a fundamental kernel of many important workloads including neural networks and machine learning. While existing SIMD…
This article is devoted to one particular case of using universal accelerated proximal envelopes to obtain computationally efficient accelerated versions of methods used to solve various optimization problem setups. We propose a proximally…
Fast approximations to matrix multiplication have the potential to dramatically reduce the cost of neural network inference. Recent work on approximate matrix multiplication proposed to replace costly multiplications with table-lookups by…
In recent years, with the rapid development of electro-optic modulators, optical computing has become a potential excellent candidate for various computing tasks. New structures and devices for optical computing are emerging one after…
The article presents a computationally effective algorithm for calculating the multiresolution discrete Fourier transform (MrDFT). The algorithm is based on the idea of reducing the computational complexity which was introduced by Wen and…
Multi-scalar multiplication (MSM) is crucial in cryptographic applications and computationally intensive in zero-knowledge proofs. MSM involves accumulating the products of scalars and points on an elliptic curve over a 377-bit modulus, and…
The advent of foundation models have revolutionized various fields, enabling unprecedented task accuracy and flexibility in computational linguistics, computer vision and other domains. Attention mechanism has become an essential component…
In this paper we develop the first fine-grained rounding error analysis of finite element (FE) cell kernels and assembly. The theory includes mixed-precision implementations and accounts for hardware-acceleration via matrix multiplication…
We present an implementation of Pagh's compressed matrix multiplication algorithm, a randomized algorithm that constructs sketches of matrices to compute an unbiased estimate of their product. By leveraging fast polynomial multiplication…
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…
Recent research has shown that large language models (LLMs) can utilize low-precision floating point (FP) quantization to deliver high efficiency while maintaining original model accuracy. In particular, recent works have shown the…
Efficient mixed-precision matrix multiply accumulate (MMA) operations are critical for accelerating deep learning workloads on GPGPUs. However, existing open-source dot product implementations for Tensor Cores rely on discrete arithmetic…