# Explaining Attention with Program Synthesis

arXiv: https://arxiv.org/abs/2606.19317 · HTML: https://mlsanity.com/paper/2606.19317/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 33 of its 42 references that are in the map.
- First posted on arXiv 17 Jun 2026.

## Builds on (most cited first, 30 of 33)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [Think you have Solved Question Answering? Try ARC, the AI2 Reasoning Challenge](https://mlsanity.com/paper/1803.05457/) (2018)
- [HellaSwag: Can a Machine Really Finish Your Sentence?](https://mlsanity.com/paper/1905.07830/) (2019)
- [Program Synthesis with Large Language Models](https://mlsanity.com/paper/2108.07732/) (2021)
- [PIQA: Reasoning about Physical Commonsense in Natural Language](https://mlsanity.com/paper/1911.11641/) (2019)
- [Visualizing and Understanding Convolutional Networks](https://mlsanity.com/paper/1311.2901/) (2013)
- [Sparse Autoencoders Find Highly Interpretable Features in Language Models](https://mlsanity.com/paper/2309.08600/) (2023)
- [BERT Rediscovers the Classical NLP Pipeline](https://mlsanity.com/paper/1905.05950/) (2019)
- [What Does BERT Look At? An Analysis of BERT's Attention](https://mlsanity.com/paper/1906.04341/) (2019)
- [Attention is not Explanation](https://mlsanity.com/paper/1902.10186/) (2019)
- [Analyzing Multi-Head Self-Attention: Specialized Heads Do the Heavy Lifting, the Rest Can Be Pruned](https://mlsanity.com/paper/1905.09418/) (2019)
- [Progress measures for grokking via mechanistic interpretability](https://mlsanity.com/paper/2301.05217/) (2023)
- [Are Sixteen Heads Really Better than One?](https://mlsanity.com/paper/1905.10650/) (2019)
- [Crowdsourcing Multiple Choice Science Questions](https://mlsanity.com/paper/1707.06209/) (2017)
- [Network Dissection: Quantifying Interpretability of Deep Visual Representations](https://mlsanity.com/paper/1704.05796/) (2017)
- [Attention is not not Explanation](https://mlsanity.com/paper/1908.04626/) (2019)
- [TinyLlama: An Open-Source Small Language Model](https://mlsanity.com/paper/2401.02385/) (2024)
- [TinyStories: How Small Can Language Models Be and Still Speak Coherent English?](https://mlsanity.com/paper/2305.07759/) (2023)
- [Illuminating search spaces by mapping elites](https://mlsanity.com/paper/1504.04909/) (2015)
- [A Multiscale Visualization of Attention in the Transformer Model](https://mlsanity.com/paper/1906.05714/) (2019)
- [Is Self-Repair a Silver Bullet for Code Generation?](https://mlsanity.com/paper/2306.09896/) (2023)
- [Thinking Like Transformers](https://mlsanity.com/paper/2106.06981/) (2021)
- [Compositional Explanations of Neurons](https://mlsanity.com/paper/2006.14032/) (2020)
- [The Bottom-up Evolution of Representations in the Transformer: A Study with Machine Translation and Language Modeling Objectives](https://mlsanity.com/paper/1909.01380/) (2019)
- [Natural Language Descriptions of Deep Visual Features](https://mlsanity.com/paper/2201.11114/) (2022)
- [What Is One Grain of Sand in the Desert? Analyzing Individual Neurons in Deep NLP Models](https://mlsanity.com/paper/1812.09355/) (2018)
- [Which Attention Heads Matter for In-Context Learning?](https://mlsanity.com/paper/2502.14010/) (2025)

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

- [When Models Don't Manipulate Manifolds: The Geometry of a Comparison Task](https://mlsanity.com/paper/2609.37680/) (2026)

## Abstract (arXiv)

A longstanding goal of research on interpretable deep learning is to replace opaque neural computations with human-meaningful symbolic descriptions. In this paper, we propose an approach for approximating the behavior of components of deep networks with executable programs. We focus on attention heads in transformer language models. For a given head, we first compute its associated attention matrices on a collection of randomly selected training examples. Next, we prompt a pre-trained language model with a summary of these matrices, and instruct it to generate a set of Python programs that can reproduce the associated attention patterns given only text from the input sentence. Finally, we re-rank programs according to how well our final set of programs predict behavior on held-out inputs. We demonstrate that a set of fewer than 1,000 such generated programs can reproduce the attention patterns of heads in GPT-2, TinyLlama-1.1B, and Llama-3B, achieving an average Intersection-over-Union similarity above 75% on TinyStories. Moreover, the best-fit programs can replace neural attention heads without substantially affecting model behavior: replacing 25% of attention heads with programmatic surrogates across the three models incurs only a 16% average perplexity increase, while maintaining performance on a variety of downstream question answering benchmarks. This work contributes a scalable pipeline for reverse-engineering attention heads in transformer models using human-readable, executable code, advancing a path toward symbolic transparency in neural models.