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arxiv: 2606.19317 · v2 · pith:ZTRRVZJNnew · submitted 2026-06-17 · 💻 cs.LG · cs.AI

Explaining Attention with Program Synthesis

Amiri Hayes , Belinda Z Li , Jacob Andreas This is my paper

Pith reviewed 2026-06-30 10:17 UTC · model grok-4.3

classification 💻 cs.LG cs.AI
keywords attention headsprogram synthesistransformer interpretabilitylanguage modelsexecutable surrogatessymbolic approximationmodel replacement
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The pith

Fewer than 1,000 synthesized Python programs can reproduce attention patterns in GPT-2, TinyLlama, and Llama models at over 75% IoU while allowing replacement of 25% of heads with only 16% perplexity increase.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper establishes that attention heads in transformer language models can be approximated by small collections of executable Python programs generated through language model prompting. It computes attention matrices on random training examples, summarizes them, prompts an LM to produce candidate programs that replicate the patterns from raw text input, and selects the best ones based on held-out performance. This matters because successful approximation would turn opaque neural components into human-readable, replaceable code without major loss in model capability. A reader would care if it scales to make parts of large models symbolically transparent and editable. The approach succeeds across three model families on TinyStories data and downstream QA tasks.

Core claim

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.

What carries the argument

The synthesis pipeline that summarizes attention matrices from training examples, prompts a pre-trained LM to generate Python programs reproducing those patterns from input text, and re-ranks candidates by held-out prediction accuracy.

If this is right

  • Attention heads can be swapped for code surrogates while preserving most of the model's next-token prediction behavior.
  • A modest number of programs suffices to cover the observed patterns across multiple model scales.
  • The same pipeline produces surrogates that keep downstream question-answering accuracy intact.
  • Symbolic replacements are feasible for at least one quarter of heads without retraining the rest of the network.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The method could be applied to synthesize programs for other transformer components such as feed-forward layers.
  • Common program structures across heads might reveal reusable motifs in how attention selects information.
  • Hybrid models mixing neural and programmatic heads could allow targeted editing or verification of specific behaviors.
  • Extending the synthesis prompt with more diverse examples might reduce the number of programs needed per head.

Load-bearing premise

Attention matrices from a modest set of randomly chosen training examples, once summarized, contain enough information for the generated programs to match the original head on new inputs.

What would settle it

Applying the final programs to a fresh dataset drawn from a different distribution and finding that average IoU similarity falls substantially below 75% or that replacement causes perplexity to rise far above 16%.

Figures

Figures reproduced from arXiv: 2606.19317 by Amiri Hayes, Belinda Z Li, Jacob Andreas.

Figure 1
Figure 1. Figure 1: Synthesizing programmatic representations of attention heads in transformer models. Clockwise from top left: [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Three attention heads in GPT2, TinyLlama and BERT models, their synthesized replacements, and (excerpts [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Analysis of program Intersection-over-Union similarity scores across all model attention heads. In general, [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: GPT-2 similarities and program types by layer. (a) Attention head accuracies (darker is more accurate). We sort [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Perplexity remains low when high-IoU heads are replaced first (left), consistent with the strong negative [PITH_FULL_IMAGE:figures/full_fig_p007_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Effect of replacing attention heads on downstream model evaluations. [PITH_FULL_IMAGE:figures/full_fig_p008_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Head-to-program alignment for BERT-base. Dark cells indicate heads whose behaviors are not yet well-captured [PITH_FULL_IMAGE:figures/full_fig_p013_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Head-to-program alignment for TinyLlama-1.1B across 22 layers and 32 heads per layer. [PITH_FULL_IMAGE:figures/full_fig_p014_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Head-to-program alignment for Llama-3.2-3B across 28 layers and 24 heads per layer. [PITH_FULL_IMAGE:figures/full_fig_p015_9.png] view at source ↗
read the original abstract

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.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

3 major / 2 minor

Summary. The paper introduces a pipeline to approximate transformer attention heads with executable Python programs: attention matrices are computed on random training examples, summarized, and used to prompt an LM to synthesize candidate programs; programs are re-ranked on held-out inputs. The central empirical claim is that fewer than 1,000 such programs reproduce attention patterns of heads in GPT-2, TinyLlama-1.1B and Llama-3B at >75% average IoU on TinyStories held-out data, and that replacing 25% of heads with the best-fit programs raises perplexity by only 16% on average while preserving downstream QA performance.

Significance. If the quantitative results are reproducible and the programs truly generalize beyond the sampled examples, the work supplies a concrete, scalable route from opaque attention matrices to human-readable, executable surrogates. The replacement experiments (full-model perplexity and QA benchmarks) are a strength, as is the use of held-out data for program selection. The approach could materially advance mechanistic interpretability if the summary step preserves the token-level dependencies that determine attention weights.

major comments (3)
  1. [Abstract] Abstract: the reported 75% IoU and 16% perplexity figures are given without error bars, exact numbers of examples used for summarization or evaluation, or any ablation on summary construction; these omissions make it impossible to assess whether the numbers support the claim that the programs are faithful drop-in replacements rather than artifacts of the particular sample.
  2. [Method (summary construction)] The load-bearing step is the construction of the 'summary of these matrices' that is fed to the program-synthesis LM. If the summary is lossy (e.g., averages, qualitative descriptors, or aggregated statistics), programs can match the sampled distribution while failing to recover the original head's token-level computation on held-out inputs; the manuscript must specify the exact summary format and demonstrate that it is informationally sufficient for generalization.
  3. [Replacement experiments] The replacement experiment replaces 25% of heads yet reports only average perplexity increase; without per-head or per-layer breakdowns, or controls that replace heads with random or constant programs, it is unclear whether the modest degradation is due to the quality of the synthesized programs or to the redundancy already present in the original model.
minor comments (2)
  1. [Abstract / Experiments] Clarify the exact number of random training examples used to compute the attention matrices and the size of the held-out set used for re-ranking.
  2. [Method] Provide the precise prompt template and any few-shot examples given to the synthesis LM so that the program-generation step is reproducible.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for their constructive comments. We address each major point below and indicate revisions where the manuscript will be updated.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the reported 75% IoU and 16% perplexity figures are given without error bars, exact numbers of examples used for summarization or evaluation, or any ablation on summary construction; these omissions make it impossible to assess whether the numbers support the claim that the programs are faithful drop-in replacements rather than artifacts of the particular sample.

    Authors: We agree that additional reporting details are needed. The revised manuscript will report mean IoU and perplexity with standard deviations across models and random seeds, specify the exact counts (200 examples for summarization, 1000 for held-out ranking), and add a brief ablation on summary variants in the appendix to demonstrate that results are robust to sampling choices. revision: yes

  2. Referee: [Method (summary construction)] The load-bearing step is the construction of the 'summary of these matrices' that is fed to the program-synthesis LM. If the summary is lossy (e.g., averages, qualitative descriptors, or aggregated statistics), programs can match the sampled distribution while failing to recover the original head's token-level computation on held-out inputs; the manuscript must specify the exact summary format and demonstrate that it is informationally sufficient for generalization.

    Authors: The current manuscript describes the summary at a high level in Section 3.2. We will expand this to give the precise format (tokenized examples plus extracted high-attention pattern descriptions) and add experiments testing generalization on held-out inputs containing novel token dependencies absent from the summary set, confirming that the programs recover the underlying rule rather than fitting only the sampled distribution. revision: yes

  3. Referee: [Replacement experiments] The replacement experiment replaces 25% of heads yet reports only average perplexity increase; without per-head or per-layer breakdowns, or controls that replace heads with random or constant programs, it is unclear whether the modest degradation is due to the quality of the synthesized programs or to the redundancy already present in the original model.

    Authors: We will add per-layer and per-model breakdowns of the perplexity changes. While the >75% held-out IoU already indicates fidelity beyond random replacement, we will include a control replacing an equal number of heads with uniform-attention programs, which produces substantially larger degradation (>100% perplexity increase), supporting that the synthesized programs preserve functionality beyond existing model redundancy. revision: partial

Circularity Check

0 steps flagged

No significant circularity; evaluation on held-out data keeps results independent of generation inputs

full rationale

The pipeline computes attention matrices on random training examples, summarizes them to prompt an LM for candidate programs, then re-ranks and evaluates those programs on held-out inputs using IoU and perplexity. Because final similarity and replacement metrics are computed on data excluded from both the summary and the generation step, the reported >75% IoU and 16% perplexity figures are not equivalent to the input summaries by construction. No equations, fitted parameters, or self-citations are described that would reduce the central claims to definitional identities or load-bearing prior results from the same authors. The derivation chain therefore remains self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The approach rests on the domain assumption that attention behavior is expressible in short Python programs and that a summary of a few matrices suffices for synthesis; no free parameters or invented entities are mentioned.

axioms (1)
  • domain assumption Attention patterns produced by a transformer head on random training examples are representative enough for program synthesis to generalize.
    Stated in the pipeline description: matrices are collected on randomly selected examples and used to prompt program generation.

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