Guardband Optimization for the Preconditioned Conjugate Gradient Algorithm
Natalia Lylina, Stefan Holst, Hanieh Jafarzadeh, Alexandra Kourfali, Hans-Joachim Wunderlich · 2023
Many applications from Artificial Intelligence (AI) and Scientific Computing rely on efficient algorithms for solving large systems of linear equations. The Preconditioned Conjugate Gradient (PCG) algorithm is a promising option and it is a perfect candidate to be executed on specialized hardware accelerators widely used in AI. Hardware accelerators, like other modern devices, are prone to process variations. A conventional approach to handle the variability is to use pessimistic guardbands for all the devices within the population, which implies that the best and even the average accelerators are slowed down significantly. Since the PCG algorithm is inherently error resilient to some extent, it may also tolerate an error rate increase due to overclocking. On another side, increasing the frequency may increase the total execution time if more arithmetic operations are needed until the convergence. This paper presents a method to ensure efficient computing on each hardware accelerator instance running the PCG algorithm. A cross-layer approach identifies an optimized frequency that minimizes the total time to complete the PCG algorithm. Simple high-level checks ensure the quality of the solution. Experimental results validate the feasibility of the developed approach for large systems of linear equations.