# Efficient Differentiable Programming in a Functional Array-Processing Language

arXiv: https://arxiv.org/abs/1806.02136 · HTML: https://mlsanity.com/paper/1806.02136/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 Jun 2018.

## Built on by (most cited first, 8 of 8)

- [Differentiable Agent-Based Simulation for Gradient-Guided Simulation-Based Optimization](https://mlsanity.com/paper/2103.12476/) (2021)
- [Functional Collection Programming with Semi-Ring Dictionaries](https://mlsanity.com/paper/2103.06376/) (2021)
- [Automatic Functional Differentiation in JAX](https://mlsanity.com/paper/2311.18727/) (2023)
- [Auto-Differentiation of Relational Computations for Very Large Scale Machine Learning](https://mlsanity.com/paper/2306.00088/) (2023)
- [Coarsening Optimization for Differentiable Programming](https://mlsanity.com/paper/2110.02307/) (2021)
- [Efficient and Sound Differentiable Programming in a Functional Array-Processing Language](https://mlsanity.com/paper/2212.10307/) (2022)
- [nablaSD: Differentiable Programming for Sparse Tensors](https://mlsanity.com/paper/2303.07030/) (2023)
- [LazyHMC: Hamiltonian Monte Carlo Simulation for Lazy, Infinite Dimensional Probabilistic Programs](https://mlsanity.com/paper/2608.08588/) (2026)

## Abstract (arXiv)

We present a system for the automatic differentiation of a higher-order functional array-processing language. The core functional language underlying this system simultaneously supports both source-to-source automatic differentiation and global optimizations such as loop transformations. Thanks to this feature, we demonstrate how for some real-world machine learning and computer vision benchmarks, the system outperforms the state-of-the-art automatic differentiation tools.