Galley: Modern Query Optimization for Sparse Tensor Programs

TL;DR

Galley introduces a novel system for declarative sparse tensor programming that automates complex optimization decisions, resulting in significantly faster programs for machine learning and subgraph counting workloads.

Contribution

Galley is the first system to perform cost-based lowering of sparse tensor algebra and optimize arbitrary operators beyond sum and product.

Findings

Achieves 1-300x speedup over competing methods in machine learning tasks.

Attains 5-20x faster performance than a state-of-the-art relational database.

Reduces optimization overhead in sparse tensor program compilation.

Abstract

The tensor programming abstraction is a foundational paradigm which allows users to write high performance programs via a high-level imperative interface. Recent work on sparse tensor compilers has extended this paradigm to sparse tensors (i.e., tensors where most entries are not explicitly represented). With these systems, users define the semantics of the program and the algorithmic decisions in a concise language that can be compiled to efficient low-level code. However, these systems still require users to make complex decisions about program structure and memory layouts to write efficient programs. This work presents Galley, a system for declarative tensor programming that allows users to write efficient tensor programs without making complex algorithmic decisions. Galley is the first system to perform cost based lowering of sparse tensor algebra to the imperative language of sparse tensor compilers, and the first to optimize arbitrary operators beyond sum and product. First, it decomposes the input program into a sequence of aggregation steps through a novel extension of the FAQ framework. Second, Galley optimizes and converts each aggregation step to a concrete program, which is compiled and executed with a sparse tensor compiler. We show that Galley produces programs that are 1-300x faster than competing methods for machine learning over joins and 5-20x faster than a state-of-the-art relational database for subgraph counting workloads with a minimal optimization overhead.