GauS: Differentiable Scheduling Optimization via Gaussian Reparameterization

TL;DR

GauS introduces a Gaussian-based differentiable framework for operator scheduling, effectively capturing temporal order and reducing optimization complexity, leading to Pareto-optimal solutions in hardware and software synthesis tasks.

Contribution

The paper presents the first differentiable scheduling method using Gaussian relaxation, improving over categorical approaches by better modeling time and scaling efficiently.

Findings

Achieves Pareto-optimal scheduling results on benchmarks.

Effectively models temporal order with Gaussian variables.

Reduces optimization space significantly.

Abstract

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.