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领域的基础性难题。尽管近期可微分方法试图用基于梯度的搜索替代传统精确求解器或启发式方法，但这些方法通常依赖于分类分布，未能捕捉时间的序数特性，且参数量随问题规模急剧增长。本文提出一种新颖的可微分框架GauS，该框架使用高斯分布对算子调度进行随机松弛建模，充分利用GPU等现代并行计算设备。通过将调度表示为连续高斯变量，我们成功捕捉了时间的序数特性，并将优化空间缩小数个数量级。本方法能灵活表征各类目标与约束，首次为复杂流水线调度问题提供了可微分建模方案。我们在多组基准测试中评估了该方法，实验表明GauS能够获得帕累托最优结果。