# Emergence of Minimal Circuits for Indirect Object Identification in Attention-Only Transformers

arXiv: https://arxiv.org/abs/2510.25013 · HTML: https://mlsanity.com/paper/2510.25013/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Circuits and mechanistic analysis, one of 13 directions in Mechanistic interpretability.
- Builds on 15 of its 30 references that are in the map.
- First posted on arXiv 28 Oct 2025.

## Placed in

- Mechanistic interpretability / [Circuits and mechanistic analysis](https://mlsanity.com/mechinterp/circuits-and-mechanistic-analysis/)

## Builds on (most cited first, 15 of 15)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [LLaMA: Open and Efficient Foundation Language Models](https://mlsanity.com/paper/2302.13971/) (2023)
- [Transformer Feed-Forward Layers Are Key-Value Memories](https://mlsanity.com/paper/2012.14913/) (2020)
- [Interpretability in the Wild: a Circuit for Indirect Object Identification in GPT-2 small](https://mlsanity.com/paper/2211.00593/) (2022)
- [Progress measures for grokking via mechanistic interpretability](https://mlsanity.com/paper/2301.05217/) (2023)
- [Towards Automated Circuit Discovery for Mechanistic Interpretability](https://mlsanity.com/paper/2304.14997/) (2023)
- [Mechanistic Interpretability for AI Safety -- A Review](https://mlsanity.com/paper/2404.14082/) (2024)
- [Super-Convergence: Very Fast Training of Neural Networks Using Large Learning Rates](https://mlsanity.com/paper/1708.07120/) (2017)
- [A Toy Model of Universality: Reverse Engineering How Networks Learn Group Operations](https://mlsanity.com/paper/2302.03025/) (2023)
- [A Mechanistic Analysis of a Transformer Trained on a Symbolic Multi-Step Reasoning Task](https://mlsanity.com/paper/2402.11917/) (2024)
- [Towards Empirical Interpretation of Internal Circuits and Properties in Grokked Transformers on Modular Polynomials](https://mlsanity.com/paper/2402.16726/) (2024)

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

- [Mechanistic Interpretability for Neural Networks: Circuits, Sparse Features and Symbolic Reasoning](https://mlsanity.com/paper/2607.07316/) (2026)

## Abstract (arXiv)

Mechanistic interpretability aims to reverse-engineer large language models (LLMs) into human-understandable computational circuits. However, the complexity of pretrained models often obscures the minimal mechanisms required for specific reasoning tasks. In this work, we train small, attention-only transformers from scratch on a symbolic version of the Indirect Object Identification (IOI) task, a benchmark for studying coreference-like reasoning in transformers. Surprisingly, a single-layer model with only two attention heads achieves perfect IOI accuracy, despite lacking MLPs and normalization layers. Through residual stream decomposition, spectral analysis, and embedding interventions, we find that the two heads specialize into additive and contrastive subcircuits that jointly implement IOI resolution. Furthermore, we show that a two-layer, one-head model composes information from the previous layer primarily through query-key interactions. These results demonstrate that task-specific training induces highly interpretable, minimal circuits, offering a controlled testbed for probing the computational foundations of transformer reasoning.