Efficient operator scheduling is a fundamental challenge in software compilation and hardware synthesis. While recent differentiable approaches have sought to replace traditional ones like exact solvers or heuristics with gradient-based search, they typically rely on categorical distributions that fail to capture the ordinal nature of time and suffer from a parameter space that scales poorly. In this paper, we propose a novel differentiable framework, GauS, that models operator scheduling as a stochastic relaxation using Gaussian distributions, which fully utilize modern parallel computing devices like GPUs. By representing schedules as continuous Gaussian variables, we successfully capture the ordinal nature of time and reduce the optimization space by orders of magnitude. Our method is highly flexible to represent various objectives and constraints, which provides the first differentiable formulation for the complex pipelined scheduling problem. We evaluate our method on a range of benchmarks, demonstrating that Gaus achieves Pareto-optimal results.

翻译：高效算子调度是软件编译与硬件合成中的基础性挑战。尽管近期可微分方法试图通过梯度搜索替代精确求解器或启发式算法等传统方法，但这些方法通常依赖无法捕捉时间顺序属性的分类分布，且参数空间扩展性较差。本文提出一种新型可微分框架GauS，通过高斯分布将算子调度建模为随机松弛过程，充分利用现代并行计算设备（如GPU）。通过将调度方案表示为连续高斯变量，我们成功捕捉时间顺序属性，并将优化空间缩减多个数量级。该方法对各类目标与约束具有高度灵活性，首次为复杂流水线调度问题提供可微分形式化方案。我们在多个基准测试上验证了该方法，结果表明Gaus实现了帕累托最优结果。