Kernel scheduling is the problem of finding the most efficient implementation for a computational kernel. Identifying this implementation involves experimenting with the parameters of compiler optimizations, such as the size of tiling windows and unrolling factors. This paper shows that it is possible to organize these parameters as points in a coordinate space. The function that maps these points to the running time of kernels, in general, will not determine a convex surface. However, this paper provides empirical evidence that the origin of this surface—an unoptimized kernel—and its global optimum—the fastest kernel—reside on a convex region. We call this hypothesis the “droplet expectation”. Consequently, a search method based on the coordinate descent algorithm tends to find the optimal kernel configuration quickly if the hypothesis holds. This approach—called Droplet Search—has been available in Apache TVM since April of 2023. Experimental results with six large deep learning models on various computing devices (ARM, Intel, AMD, and NVIDIA) indicate that Droplet Search is not only as effective as other AutoTVM search techniques but also two to ten times faster. Moreover, models generated by Droplet Search are competitive with those produced by TVM’s AutoScheduler (Ansor), despite the latter using four to five times more code transformations than AutoTVM.

内核调度是为计算内核找到最有效的实现的问题。识别此实现涉及尝试编译器优化的参数，例如平铺窗口的大小和展开因子。本文表明可以将这些参数组织为坐标空间中的点。通常，将这些点映射到内核运行时间的函数不会确定凸面。然而，本文提供的经验证据表明，该表面的起源（未优化的内核）及其全局最优值（最快的内核）位于凸区域。我们将这种假设称为“水滴期望”。因此，如果假设成立，基于坐标下降算法的搜索方法往往会快速找到最佳核配置。这种称为 Droplet Search 的方法自 2023 年 4 月起已在 Apache TVM 中使用。在各种计算设备（ARM、Intel、AMD 和 NVIDIA）上对六种大型深度学习模型进行的实验结果表明，Droplet Search 不仅与其他 AutoTVM 搜索技术的速度也快两到十倍。此外，Droplet Search 生成的模型与 TVM 的 AutoScheduler (Ansor) 生成的模型具有竞争力，尽管后者使用的代码转换数量是 AutoTVM 的四到五倍。