# A Differential-form Pullback Programming Language for Higher-order Reverse-mode Automatic Differentiation

arXiv: https://arxiv.org/abs/2002.08241 · HTML: https://mlsanity.com/paper/2002.08241/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Feb 2020.

## Built on by (most cited first, 1 of 1)

- [Efficient and Sound Differentiable Programming in a Functional Array-Processing Language](https://mlsanity.com/paper/2212.10307/) (2022)

## Abstract (arXiv)

Building on the observation that reverse-mode automatic differentiation (AD) -- a generalisation of backpropagation -- can naturally be expressed as pullbacks of differential 1-forms, we design a simple higher-order programming language with a first-class differential operator, and present a reduction strategy which exactly simulates reverse-mode AD. We justify our reduction strategy by interpreting our language in any differential λ-category that satisfies the Hahn-Banach Separation Theorem, and show that the reduction strategy precisely captures reverse-mode AD in a truly higher-order setting.