Stochastic Rounding 2.0, with a View towards Complexity Analysis

TL;DR

Stochastic Rounding 2.0 explores the benefits of probabilistic rounding in large-scale, low-precision computations, emphasizing its error-canceling properties and potential for complexity analysis.

Contribution

Introduces an advanced view of stochastic rounding as a fundamental tool for analyzing algorithm complexity and suggests new research directions.

Findings

Stochastic Rounding reduces error growth compared to deterministic methods.

Error cancellation in stochastic rounding leads to more stable computations.

Proposes stochastic rounding as a basis for 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.