EvoCG: Self-Evolving Precision Control for Faster Conjugate Gradient

Abstract

Modern GPUs offer far higher throughput in low precision than in FP64, but exploiting this in conjugate gradient (CG) solvers is difficult because tolerance to reduced precision evolves with the Krylov state. We present EvoCG, a mixed-precision CG solver that treats tile-wise precision as an online control action rather than a fixed setting: a reinforcement-learning policy in the iteration loop selects per-tile precision from the evolving solver state, made profitable by co-design with a Tile-CSC unified mixed-precision SpMV kernel and a low-overhead in-loop runtime. Across 47 SPD matrices from eight scientific domains, EvoCG is the fastest solver overall, with geometric-mean speedups of 2.52x, 3.06x, 2.48x, 1.93x, and 6.99x over cuSPARSE, PETSc, Ginkgo, Mille-FP64, and Mille-Mixed. On the same substrate, it improves time-to-solution over EvoCG-FP64 by 1.28x at only 11.4% more iterations and 1.09% overhead, with FP64-recomputed final true-residual norms nearly identical to those of FP64, and extends to Jacobi-preconditioned CG without retraining, yielding a further 1.15x geometric-mean speedup over EvoCG-FP64.