Polyhedral Specification and Code Generation of Sparse Tensor Contraction with Co-Iteration

TL;DR

This paper introduces a polyhedral framework for generating efficient sparse tensor contraction code, enabling flexible layouts and achieving significant performance improvements over existing methods.

Contribution

It extends the polyhedral model to support sparse tensor computations, including layout specification and co-iteration, with a novel SMT-based code synthesis approach.

Findings

Achieves 1.63× faster parallel performance than TACO on average.

Supports flexible layout and computation combinations.

Potential to improve speedup to 2.72× with optimized algorithms.

Abstract

This paper presents a code generator for sparse tensor contraction computations. It leverages a mathematical representation of loop nest computations in the sparse polyhedral framework (SPF), which extends the polyhedral model to support non-affine computations, such as arise in sparse tensors. SPF is extended to perform layout specification, optimization, and code generation of sparse tensor code: 1) we develop a polyhedral layout specification that decouples iteration spaces for layout and computation; and, 2) we develop efficient co-iteration of sparse tensors by combining polyhedra scanning over the layout of one sparse tensor with the synthesis of code to find corresponding elements in other tensors through an SMT solver. We compare the generated code with that produced by a state-of-the-art tensor compiler, TACO. We achieve on average 1.63$\times$ faster parallel performance than TACO on sparse-sparse co-iteration and describe how to improve that to 2.72$\times$ average speedup by switching the find algorithms. We also demonstrate that decoupling iteration spaces of layout and computation enables additional layout and computation combinations to be supported.