Using Rewrite Strategies for Efficient Functional Automatic Differentiation

TL;DR

This paper presents a novel approach to implementing efficient functional automatic differentiation using rewrite rules and strategy combinators, combining correctness with optimized performance in a functional array language.

Contribution

It introduces a method to optimize dual number-based AD in functional languages through rewrite strategies, enabling fine-grained control over optimization scheduling.

Findings

Preliminary micro-benchmark shows viability of the approach.

Demonstrates the potential for combining elegance and efficiency in functional AD.

Uses rewrite rules and strategies for optimization control.

Abstract

Automatic Differentiation (AD) has become a dominant technique in ML. AD frameworks have first been implemented for imperative languages using tapes. Meanwhile, functional implementations of AD have been developed, often based on dual numbers, which are close to the formal specification of differentiation and hence easier to prove correct. But these papers have focussed on correctness not efficiency. Recently, it was shown how an approach using dual numbers could be made efficient through the right optimizations. Optimizations are highly dependent on order, as one optimization can enable another. It can therefore be useful to have fine-grained control over the scheduling of optimizations. One method expresses compiler optimizations as rewrite rules, whose application can be combined and controlled using strategy languages. Previous work describes the use of term rewriting and strategies to generate high-performance code in a compiler for a functional language. In this work, we implement dual numbers AD in a functional array programming language using rewrite rules and strategy combinators for optimization. We aim to combine the elegance of differentiation using dual numbers with a succinct expression of the optimization schedule using a strategy language. We give preliminary evidence suggesting the viability of the approach on a micro-benchmark.