  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.
