Google Research

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

  • Adam Paszke
  • Alexey Radul
  • Daniel Johnson
  • David Duvenaud
  • Dimitrios Vytiniotis
  • Dougal Maclaurin
  • Jonathan Ragan-Kelley
  • Matthew Johnson
Proceedings of the ACM on Programming Languages (PACMPL), vol. 5 (2021), 88:1-88:29


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.

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