Finch: Sparse and Structured Tensor Programming with Control Flow

TL;DR

Finch is a new programming language that enables flexible control flow and diverse structured tensor data types, leading to significant performance improvements in tensor computations involving sparsity, symmetry, and other structures.

Contribution

Finch introduces a unified programming model that combines control flow and structured data, allowing co-optimization and automatic specialization for diverse tensor structures.

Findings

Dramatic speedups in SpMV and SpGEMM operations

Effective handling of various tensor structures like sparsity and symmetry

Enhanced performance in image processing and graph analytics

Abstract

From FORTRAN to NumPy, tensors have revolutionized how we express computation. However, tensors in these, and almost all prominent systems, can only handle dense rectilinear integer grids. Real world tensors often contain underlying structure, such as sparsity, runs of repeated values, or symmetry. Support for structured data is fragmented and incomplete. Existing frameworks limit the tensor structures and program control flow they support to better simplify the problem. In this work, we propose a new programming language, Finch, which supports both flexible control flow and diverse data structures. Finch facilitates a programming model which resolves the challenges of computing over structured tensors by combining control flow and data structures into a common representation where they can be co-optimized. Finch automatically specializes control flow to data so that performance engineers can focus on experimenting with many algorithms. Finch supports a familiar programming language of loops, statements, ifs, breaks, etc., over a wide variety of tensor structures, such as sparsity, run-length-encoding, symmetry, triangles, padding, or blocks. Finch reliably utilizes the key properties of structure, such as structural zeros, repeated values, or clustered non-zeros. We show that this leads to dramatic speedups in operations such as SpMV and SpGEMM, image processing, and graph analytics.