Getting to the Point. Index Sets and Parallelism-Preserving Autodiff for Pointful Array Programming

TL;DR

This paper introduces a new array programming language that combines high-level clarity with low-level efficiency, supporting parallel automatic differentiation and explicit nested indexing.

Contribution

It proposes a novel language design that treats arrays as functions on index sets, with a typed effects system enabling parallel in-place updates and reverse-mode autodiff.

Findings

Benchmarking against Futhark shows competitive performance.

Explicit nested indexing improves expressiveness without performance loss.

Typed effects facilitate automatic parallelism in array updates.

Abstract

We present a novel programming language design that attempts to combine the clarity and safety of high-level functional languages with the efficiency and parallelism of low-level numerical languages. We treat arrays as eagerly-memoized functions on typed index sets, allowing abstract function manipulations, such as currying, to work on arrays. In contrast to composing primitive bulk-array operations, we argue for an explicit nested indexing style that mirrors application of functions to arguments. We also introduce a fine-grained typed effects system which affords concise and automatically-parallelized in-place updates. Specifically, an associative accumulation effect allows reverse-mode automatic differentiation of in-place updates in a way that preserves parallelism. Empirically, we benchmark against the Futhark array programming language, and demonstrate that aggressive inlining and type-driven compilation allows array programs to be written in an expressive, "pointful" style with little performance penalty.