# Even Heads Fix Odd Errors: Mechanistic Discovery and Surgical Repair in Transformer Attention

arXiv: https://arxiv.org/abs/2508.19414 · HTML: https://mlsanity.com/paper/2508.19414/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 17 references that are in the map.
- First posted on arXiv 26 Aug 2025.

## Builds on (most cited first, 12 of 12)

- [Llama 2: Open Foundation and Fine-Tuned Chat Models](https://mlsanity.com/paper/2307.09288/) (2023)
- [Locating and Editing Factual Associations in GPT](https://mlsanity.com/paper/2202.05262/) (2022)
- [Pythia: A Suite for Analyzing Large Language Models Across Training and Scaling](https://mlsanity.com/paper/2304.01373/) (2023)
- [Sparse Autoencoders Find Highly Interpretable Features in Language Models](https://mlsanity.com/paper/2309.08600/) (2023)
- [Interpretability in the Wild: a Circuit for Indirect Object Identification in GPT-2 small](https://mlsanity.com/paper/2211.00593/) (2022)
- [Steering Language Models With Activation Engineering](https://mlsanity.com/paper/2308.10248/) (2023)
- [Towards Automated Circuit Discovery for Mechanistic Interpretability](https://mlsanity.com/paper/2304.14997/) (2023)
- [GSM-Symbolic: Understanding the Limitations of Mathematical Reasoning in Large Language Models](https://mlsanity.com/paper/2410.05229/) (2024)
- [Llama Scope: Extracting Millions of Features from Llama-3.1-8B with Sparse Autoencoders](https://mlsanity.com/paper/2410.20526/) (2024)
- [A Survey on Sparse Autoencoders: Interpreting the Internal Mechanisms of Large Language Models](https://mlsanity.com/paper/2503.05613/) (2025)
- [Language Models Encode Numbers Using Digit Representations in Base 10](https://mlsanity.com/paper/2410.11781/) (2024)
- [Large Language Models and Mathematical Reasoning Failures](https://mlsanity.com/paper/2502.11574/) (2025)

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

- [Surgical Repair of Insecure Code Generation in LLMs](https://mlsanity.com/paper/2604.16697/) (2026)

## Abstract (arXiv)

We present a mechanistic case study of a format-dependent reasoning failure in Llama-3.1-8B-Instruct, where the model incorrectly judges "9.11" as larger than "9.8" in chat or Q&A formats, but answers correctly in simple format. Through systematic intervention, we discover transformers implement even/odd attention head specialization: even indexed heads handle numerical comparison, while odd heads serve incompatible functions. The bug requires exactly 8 even heads at Layer 10 for perfect repair. Any combination of 8+ even heads succeeds, while 7 or fewer completely fails, revealing sharp computational thresholds with perfect redundancy among the 16 even heads. SAE analysis reveals the mechanism: format representations separate (10% feature overlap at Layer 7), then re-entangle with different weightings (80% feature overlap at Layer 10), with specific features showing 1.5x amplification in failing formats. We achieve perfect repair using only 25% of attention heads and identify a 60% pattern replacement threshold, demonstrating that apparent full-module requirements hide sophisticated substructure with implications for interpretability and efficiency. All of our code is available at https://github.com/gussand/surgeon.