Application-tailored Linear Algebra Algorithms: A search-based Approach

TL;DR

This paper presents a knowledge-aware compiler that automatically generates optimized linear algebra algorithms by leveraging problem-specific information, leading to significant speedups in scientific computations.

Contribution

It introduces a novel search-based, knowledge-aware compiler for linear algebra that utilizes user-provided problem details to generate efficient algorithms.

Findings

Achieved 100-fold speedup in sensitivity analysis computations.

Attained 1000-fold speedup in genome study equations.

Demonstrated effectiveness of problem-specific knowledge in algorithm generation.

Abstract

In this paper, we tackle the problem of automatically generating algorithms for linear algebra operations by taking advantage of problem-specific knowledge. In most situations, users possess much more information about the problem at hand than what current libraries and computing environments accept; evidence shows that if properly exploited, such information leads to uncommon/unexpected speedups. We introduce a knowledge-aware linear algebra compiler that allows users to input matrix equations together with properties about the operands and the problem itself; for instance, they can specify that the equation is part of a sequence, and how successive instances are related to one another. The compiler exploits all this information to guide the generation of algorithms, to limit the size of the search space, and to avoid redundant computations. We applied the compiler to equations arising as part of sensitivity and genome studies; the algorithms produced exhibit, respectively, 100- and 1000-fold speedups.