V-ABFT: Variance-Based Adaptive Threshold for Fault-Tolerant Matrix Multiplication in Mixed-Precision Deep Learning

Abstract

Algorithm-Based Fault Tolerance (ABFT) is widely adopted to detect silent data corruptions (SDCs) in matrix multiplication, a cornerstone operation in deep learning systems. However, existing threshold determination methods face critical challenges: analytical bounds are overly conservative, while probabilistic approaches like A-ABFT yield thresholds $160$--$4200\times$ larger than actual rounding errors. We present V-ABFT, a variance-based adaptive threshold algorithm that achieves tighter error bounds by directly modeling the verification difference. By leveraging statistical variance estimation, V-ABFT reduces the threshold-to-actual-error ratio to approximately $7$--$20\times$ for FP32/FP64 and $48$--$158\times$ for BF16, representing a \textbf{6--48$\times$ improvement} over A-ABFT while maintaining zero false positive rate across BF16, FP16, FP32, and FP64 precisions. Furthermore, we demonstrate that for fused-kernel ABFT implementations that verify before output quantization, low-precision GEMM can use FP32-level thresholds ($e_{\max} \approx 10^{-6}$), enabling \textbf{$\sim$1000$\times$ finer detection granularity} compared to offline verification with low-precision output ($e_{\max} \approx 10^{-3}$). We reproduce A-ABFT's experimental setup and validate our implementation against the original paper's results. Our method requires only $O(n)$ complexity using max/min/mean statistics, compared to A-ABFT's $O(pn)$ for finding $p$ largest values. Extensive experiments on synthetic data and real model weights (LLaMA-7B, GPT-2, ViT) demonstrate V-ABFT's effectiveness across diverse distributions. V-ABFT is platform-agnostic and has been integrated into fault-tolerant GEMM implementations on both NPUs and GPUs.