Compiling Structured Tensor Algebra

TL;DR

This paper introduces StructTensor, a framework that symbolically computes tensor structures at compile time, enabling optimized dense and sparse tensor algebra computations with improved performance.

Contribution

It presents STUR, an intermediate language for capturing tensor computations and their structures, and demonstrates how symbolic structure computation enhances efficiency.

Findings

Outperforms state-of-the-art frameworks in tensor algebra tasks.

Effectively captures sparsity and redundancy for optimization.

Provides a sound mathematical basis for lossless tensor computation.

Abstract

Tensor algebra is essential for data-intensive workloads in various computational domains. Computational scientists face a trade-off between the specialization degree provided by dense tensor algebra and the algorithmic efficiency that leverages the structure provided by sparse tensors. This paper presents StructTensor, a framework that symbolically computes structure at compilation time. This is enabled by Structured Tensor Unified Representation (STUR), an intermediate language that can capture tensor computations as well as their sparsity and redundancy structures. Through a mathematical view of lossless tensor computations, we show that our symbolic structure computation and the related optimizations are sound. Finally, for different tensor computation workloads and structures, we experimentally show how capturing the symbolic structure can result in outperforming state-of-the-art frameworks for both dense and sparse tensor algebra.