Galley: Modern Query Optimization for Sparse Tensor Programs

Abstract: The tensor programming abstraction has become a foundational paradigm for modern computing. This framework allows users to write high performance programs for bulk computation via a high-level imperative interface. Recent work has extended this paradigm to sparse tensors (i.e. tensors where most entries are not explicitly represented) with the use of sparse tensor compilers. These systems excel at producing efficient code for computation over sparse tensors, which may be stored in a wide variety of formats. However, they require the user to manually choose the order of operations and the data formats at every step. Unfortunately, these decisions are both highly impactful and complicated, requiring significant effort to manually optimize. In this work, we present Galley, a system for declarative sparse tensor programming. Galley performs cost-based optimization to lower these programs to a logical plan then to a physical plan. It then leverages sparse tensor compilers to execute the physical plan efficiently. We show that Galley achieves high performance on a wide variety of problems including machine learning algorithms, subgraph counting, and iterative graph algorithms.