On the Safe Deployment of Matrix Multiplication in Massively Parallel Safety-Related Systems

Abstract

Deep learning technology has enabled the development of increasingly complex safety-related autonomous systems using high-performance computers, such as graphics processing units (GPUs), which provide the required high computing performance for the execution of parallel computing algorithms, such as matrix–matrix multiplications (a central computing element of deep learning software libraries). However, the safety certification of parallel computing software algorithms and GPU-based safety-related systems is a challenge to be addressed. For example, achieving the required fault-tolerance and diagnostic coverage for random hardware errors. This paper contributes with a safe matrix–matrix multiplication software implementation for GPUs with random hardware error-detection capabilities (permanent, transient) that can be used with different architectural patterns for fault-tolerance, and which serves as a foundation for the implementation of safe deep learning libraries for GPUs. The proposed contribution is complementary and can be combined with other techniques, such as algorithm-based fault tolerance. In particular, (i) we provide the high-performance matrix multiplication CUTLASS library with a catalog of diagnostic mechanisms to detect random hardware errors down to the arithmetic operation level; and (ii) we measure the performance impact incurred by the adoption of these mechanisms and their achievable diagnostic coverage with a set of representative matrix dimensions. To that end, we implement these algebraic operations, targeting CUDA cores with single instructions and multiple-thread math instructions in an NVIDIA Xavier NX GPU.