A Novel Fault-Tolerant Architecture for Tiled Matrix Multiplication

Abstract

General matrix multiplication (GEMM) is common to many scientific and machine-learning applications. Convolution, the dominant computation in Convolutional Neural Networks (CNNs), can be formulated as a GEMM problem. Due to its widespread use, a new generation of processors features GEMM acceleration in hardware. Intel recently announced an Advanced Matrix Multiplication (AMX®) instruction set for GEMM, which is supported by 1kB AMX registers and a Tile Multiplication unit (TMUL) for multiplying tiles (sub-matrices) in hardware. Silent Data Corruption (SDC) is a well-known problem that occurs when hardware generates corrupt output. Google and Meta recently reported findings of SDC in GEMM in their data centers. Algorithm-Based Fault Tolerance (ABFT) is an efficient mechanism for detecting and correcting errors in GEMM, but classic ABFT solutions are not optimized for hardware acceleration. In this paper, we present a novel ABFT implementation directly on hardware. Though the exact implementation of Intel TMUL is not known, we propose two different TMUL architectures representing two design points in the area-power-performance spectrum and illustrate how ABFT can be directly incorporated into the TMUL hardware. This approach has two advantages: (i) an error can be concurrently detected at the tile level, which is an improvement over finding such errors only after performing the full matrix multiplication; and (ii) we further demonstrate that performing ABFT at the hardware level has no performance impact and only a small area, latency, and power overhead.