# Looplets: A Language For Structured Coiteration

arXiv: https://arxiv.org/abs/2209.05250 · HTML: https://mlsanity.com/paper/2209.05250/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Sep 2022.

## Built on by (most cited first, 4 of 4)

- [Compressing Structured Tensor Algebra](https://mlsanity.com/paper/2407.13726/) (2024)
- [Ember: A Compiler for Efficient Embedding Operations on Decoupled Access-Execute Architectures](https://mlsanity.com/paper/2504.09870/) (2025)
- [FuseFlow: A Fusion-Centric Compilation Framework for Sparse Deep Learning on Streaming Dataflow](https://mlsanity.com/paper/2511.04768/) (2025)
- [JLIR: A Julia-Native MLIR-Inspired Intermediate Representation with Automatic JACC Kernel Extraction](https://mlsanity.com/paper/2609.04585/) (2026)

## Abstract (arXiv)

Real world arrays often contain underlying structure, such as sparsity, runs of repeated values, or symmetry. Specializing for structure yields significant speedups. But automatically generating efficient code for structured data is challenging, especially when arrays with different structure interact. We show how to abstract over array structures so that the compiler can generate code to coiterate over any combination of them. Our technique enables new array formats (such as 1DVBL for irregular clustered sparsity), new iteration strategies (such as galloping intersections), and new operations over structured data (such as concatenation or convolution).