Modern computationally-intensive applications often operate under time constraints, necessitating acceleration methods and distribution of computational workloads across multiple entities. However, the outcome is either achieved within the desired timeline or not, and in the latter case, valuable resources are wasted. In this paper, we introduce solutions for layered-resolution computation. These solutions allow lower-resolution results to be obtained at an earlier stage than the final result. This innovation notably enhances the deadline-based systems, as if a computational job is terminated due to time constraints, an approximate version of the final result can still be generated. Moreover, in certain operational regimes, a high-resolution result might be unnecessary, because the low-resolution result may already deviate significantly from the decision threshold, for example in AI-based decision-making systems. Therefore, operators can decide whether higher resolution is needed or not based on intermediate results, enabling computations with adaptive resolution. We present our framework for two critical and computationally demanding jobs: distributed matrix multiplication (linear) and model inference in machine learning (nonlinear). Our theoretical and empirical results demonstrate that the execution delay for the first resolution is significantly shorter than that for the final resolution, while maintaining overall complexity comparable to the conventional one-shot approach. Our experiments further illustrate how the layering feature increases the likelihood of meeting deadlines and enables adaptability and transparency in massive, large-scale computations.

翻译：现代计算密集型应用通常受时间约束，亟需加速方法并将计算负载分布到多个实体上。然而，结果要么在预期时间内完成，要么无法完成——后者会浪费宝贵的计算资源。本文提出分层分辨率计算方案，允许在最终结果生成前提前获得低分辨率结果。该创新显著提升了基于截止期限的系统性能：若计算任务因时间约束而终止，仍能生成最终结果的近似版本。此外，在某些运行场景中（例如基于AI的决策系统），若低分辨率结果已显著偏离决策阈值，高分辨率结果可能不再必要。因此，操作者可根据中间结果判断是否需要更高分辨率，实现自适应分辨率计算。我们针对两类关键计算密集型任务提出框架：分布式矩阵乘法（线性任务）与机器学习模型推理（非线性任务）。理论与实验结果表明，首个分辨率版本的执行延迟显著短于最终版本，同时整体复杂度与传统一次性方法相当。实验进一步揭示了分层特性如何提升截止期限满足概率，并增强大规模计算的适应性与透明度。