相关论文: HPL-MxP Benchmark: Mixed-Precision Algorithms, Ite…

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…

Low precision arithmetic, in particular half precision floating point arithmetic, is now available in commercial hardware. Using lower precision can offer significant savings in computation and communication costs with proportional savings…

With the emergence of mixed precision capabilities in hardware, iterative refinement schemes for solving linear systems $Ax=b$ have recently been revisited and reanalyzed in the context of three or more precisions. These new analyses show…

This research investigates using a mixed-precision iterative refinement method using posit numbers instead of the standard IEEE floating-point format. The method is applied to solve a general linear system represented by the equation $Ax =…

In recent years, a new kind of accelerated hardware has gained popularity in the Artificial Intelligence (AI) and Machine Learning (ML) communities which enables extremely high-performance tensor contractions in reduced precision for deep…

The vision of super computer at every desk can be realized by powerful and highly parallel CPUs or GPUs or APUs. Graphics processors once specialized for the graphics applications only, are now used for the highly computational intensive…

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…

Renewed interest in mixed-precision algorithms has emerged due to growing data capacity and bandwidth concerns, as well as the advancement of GPUs, which enable significant speedup for low precision arithmetic. In light of this, we propose…

The plethora of complex artificial intelligence (AI) algorithms and available high performance computing (HPC) power stimulates the expeditious development of AI components with heterogeneous designs. Consequently, the need for cross-stack…

Hierarchical Matrix (H-matrix) is an approximation technique which splits a target dense matrix into multiple submatrices, and where a selected portion of submatrices are low-rank approximated. The technique substantially reduces both time…

Finely tuning MPI applications and understanding the influence of keyparameters (number of processes, granularity, collective operationalgorithms, virtual topology, and process placement) is critical toobtain good performance on…

This article studies a combination of the two state-of-the-art algorithms for the exact solution of linear programs (LPs) over the rational numbers, i.e., without any roundoff errors or numerical tolerances. By integrating the method of…

For critical applications that require a higher level of reliability, the Triple Modular Redundancy (TMR) scheme is usually employed to implement fault-tolerant arithmetic units. However, this method imposes a significant area and…

Mixed-integer linear programming (MILP) is widely employed for modeling combinatorial optimization problems. In practice, similar MILP instances with only coefficient variations are routinely solved, and machine learning (ML) algorithms are…

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…

We detail the performance optimizations made in rocHPL, AMD's open-source implementation of the High-Performance Linpack (HPL) benchmark targeting accelerated node architectures designed for exascale systems such as the Frontier…

We propose a simulation-based approach for performance modeling of parallel applications on high-performance computing platforms. Our approach enables full-system performance modeling: (1) the hardware platform is represented by an abstract…

As models become larger, ML accelerators are a scarce resource whose performance must be continually optimized to improve efficiency. Existing performance analysis tools are coarse grained, and fail to capture model performance at the…

In this article, we establish a class of new accelerated modulus-based iteration methods for solving the linear complementarity problem. When the system matrix is an $H_+$-matrix, we present appropriate criteria for the convergence…

This article presents the first mixed-integer linear programming (MILP)-based iterative algorithm to solve factorable mixed-integer nonlinear programs (MINLPs) with bounded, differentiable periodic functions to global optimality with an…