# AbstractDifferentiation.jl: Backend-Agnostic Differentiable Programming in Julia

arXiv: https://arxiv.org/abs/2109.12449 · HTML: https://mlsanity.com/paper/2109.12449/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 39 references that are in the map.
- First posted on arXiv 25 Sep 2021.

## Builds on (most cited first, 11 of 11)

- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Universal Differential Equations for Scientific Machine Learning](https://mlsanity.com/paper/2001.04385/) (2020)
- [A Differentiable Programming System to Bridge Machine Learning and Scientific Computing](https://mlsanity.com/paper/1907.07587/) (2019)
- [SPNets: Differentiable Fluid Dynamics for Deep Neural Networks](https://mlsanity.com/paper/1806.06094/) (2018)
- [JuMP: A Modeling Language for Mathematical Optimization](https://mlsanity.com/paper/1508.01982/) (2015)
- [Instead of Rewriting Foreign Code for Machine Learning, Automatically Synthesize Fast Gradients](https://mlsanity.com/paper/2010.01709/) (2020)
- [Effective Extensible Programming: Unleashing Julia on GPUs](https://mlsanity.com/paper/1712.03112/) (2017)
- [Convex Optimization in Julia](https://mlsanity.com/paper/1410.4821/) (2014)
- [MathOptInterface: a data structure for mathematical optimization problems](https://mlsanity.com/paper/2002.03447/) (2020)
- [A Benchmark of Selected Algorithmic Differentiation Tools on Some Problems in Computer Vision and Machine Learning](https://mlsanity.com/paper/1807.10129/) (2018)
- [Control of Stochastic Quantum Dynamics by Differentiable Programming](https://mlsanity.com/paper/2101.01190/) (2021)

## Built on by (most cited first, 2 of 2)

- [Flexible Differentiable Optimization via Model Transformations](https://mlsanity.com/paper/2206.06135/) (2022)
- [Chemellia: An Ecosystem for Atomistic Scientific Machine Learning](https://mlsanity.com/paper/2305.12010/) (2023)

## Abstract (arXiv)

No single Automatic Differentiation (AD) system is the optimal choice for all problems. This means informed selection of an AD system and combinations can be a problem-specific variable that can greatly impact performance. In the Julia programming language, the major AD systems target the same input and thus in theory can compose. Hitherto, switching between AD packages in the Julia Language required end-users to familiarize themselves with the user-facing API of the respective packages. Furthermore, implementing a new, usable AD package required AD package developers to write boilerplate code to define convenience API functions for end-users. As a response to these issues, we present AbstractDifferentiation.jl for the automatized generation of an extensive, unified, user-facing API for any AD package. By splitting the complexity between AD users and AD developers, AD package developers only need to implement one or two primitive definitions to support various utilities for AD users like Jacobians, Hessians and lazy product operators from native primitives such as pullbacks or pushforwards, thus removing tedious -- but so far inevitable -- boilerplate code, and enabling the easy switching and composing between AD implementations for end-users.