Related papers: Tuning Technique for Multiple Precision Dense Matr…

In this paper, we propose a mixed-precision convolution unit architecture which supports different integer and floating point (FP) precisions. The proposed architecture is based on low-bit inner product units and realizes higher precision…

Consecutive matrix multiplications are commonly used in graph neural networks and sparse linear solvers. These operations frequently access the same matrices for both reading and writing. While reusing these matrices improves data locality,…

Accurate prediction of training time in distributed deep learning is crucial for resource allocation, cost estimation, and job scheduling. We observe that the floating-point precision setting is a key determinant of training time, leading…

We present an optimized single-precision implementation of the Sparse Approximate Matrix Multiply (\SpAMM{}) [M. Challacombe and N. Bock, arXiv {\bf 1011.3534} (2010)], a fast algorithm for matrix-matrix multiplication for matrices with…

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…

Solving partial differential equations (PDEs) by numerical methods meet computational cost challenge for getting the accurate solution since fine grids and small time steps are required. Machine learning can accelerate this process, but…

A multiply-accumulate (MAC) operation is the main computation unit for DSP applications. DSP blocks are one of the efficient solutions to implement MACs in FPGA's. However, since the DSP blocks have wide multiplier and adder blocks, MAC…

The training process of neural networks is known to be time-consuming, and having a deep architecture only aggravates the issue. This process consists mostly of matrix operations, among which matrix multiplication is the bottleneck. Several…

In this paper, we propose a scalable approximate multiplier design, scaleTRIM, that approximates the multiplication operation using fitted linear functions, also referred to as linearization. We show that multiplication operations can be…

Distributed-memory matrix multiplication (MM) is a key element of algorithms in many domains (machine learning, quantum physics). Conventional algorithms for dense MM rely on regular/uniform data decomposition to ensure load balance. These…

We present new algorithms to detect and correct errors in the lower-upper factorization of a matrix, or the triangular linear system solution, over an arbitrary field. Our main algorithms do not require any additional information or…

Accurate structural relaxation is critical for advanced materials design. Traditional approaches built on physics-derived first-principles calculations are computationally expensive, motivating the creation of machine-learning interatomic…

Sparse matrices are an integral part of scientific simulations. As hardware evolves new sparse matrix storage formats are proposed aiming to exploit optimizations specific to the new hardware. In the era of heterogeneous computing, users…

We consider a discrete optimization formulation for learning sparse classifiers, where the outcome depends upon a linear combination of a small subset of features. Recent work has shown that mixed integer programming (MIP) can be used to…

We consider optimization problems involving the multiplication of variable matrices to be selected from a given family, which might be a discrete set, a continuous set or a combination of both. Such nonlinear, and possibly discrete,…

Binary quadratic programming problems have attracted much attention in the last few decades due to their potential applications. This type of problems are NP-hard in general, and still considered a challenge in the design of efficient…

Ootomo, Ozaki, and Yokota [Int. J. High Perform. Comput. Appl., 38 (2024), p. 297-313] have proposed a strategy to recast a floating-point matrix multiplication in terms of integer matrix products. The factors A and B are split into integer…

Mixed-precision algorithms have been proposed as a way for scientific computing to benefit from some of the gains seen for artificial intelligence (AI) on recent high performance computing (HPC) platforms. A few applications dominated by…

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 study coded distributed matrix multiplication from an approximate recovery viewpoint. We consider a system of $P$ computation nodes where each node stores $1/m$ of each multiplicand via linear encoding. Our main result shows that the…