Stochastic Rounding 2.0, with a View towards Complexity Analysis

Abstract: Stochastic Rounding is a probabilistic rounding mode that is surprisingly effective in large-scale computations and low-precision arithmetic. Its random nature promotes error cancellation rather than error accumulation, resulting in slower growth of roundoff errors as the problem size increases, especially when compared to traditional deterministic rounding methods, such as rounding-to-nearest. We advocate for SR as a foundational tool in the complexity analysis of algorithms, and suggest several research directions.