# Sparse Attention Decomposition Applied to Circuit Tracing

arXiv: https://arxiv.org/abs/2410.00340 · HTML: https://mlsanity.com/paper/2410.00340/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 29 references that are in the map.
- First posted on arXiv 1 Oct 2024.

## Builds on (most cited first, 20 of 20)

- [Interpretability in the Wild: a Circuit for Indirect Object Identification in GPT-2 small](https://mlsanity.com/paper/2211.00593/) (2022)
- [Toy Models of Superposition](https://mlsanity.com/paper/2209.10652/) (2022)
- [Towards Automated Circuit Discovery for Mechanistic Interpretability](https://mlsanity.com/paper/2304.14997/) (2023)
- [The Linear Representation Hypothesis and the Geometry of Large Language Models](https://mlsanity.com/paper/2311.03658/) (2023)
- [Sparse Feature Circuits: Discovering and Editing Interpretable Causal Graphs in Language Models](https://mlsanity.com/paper/2403.19647/) (2024)
- [Causal Abstractions of Neural Networks](https://mlsanity.com/paper/2106.02997/) (2021)
- [Finding Neurons in a Haystack: Case Studies with Sparse Probing](https://mlsanity.com/paper/2305.01610/) (2023)
- [Language Models Represent Space and Time](https://mlsanity.com/paper/2310.02207/) (2023)
- [SVD-LLM: Truncation-aware Singular Value Decomposition for Large Language Model Compression](https://mlsanity.com/paper/2403.07378/) (2024)
- [Finding Alignments Between Interpretable Causal Variables and Distributed Neural Representations](https://mlsanity.com/paper/2303.02536/) (2023)
- [How does GPT-2 compute greater-than?: Interpreting mathematical abilities in a pre-trained language model](https://mlsanity.com/paper/2305.00586/) (2023)
- [Localizing Model Behavior with Path Patching](https://mlsanity.com/paper/2304.05969/) (2023)
- [The Hydra Effect: Emergent Self-repair in Language Model Computations](https://mlsanity.com/paper/2307.15771/) (2023)
- [Does Circuit Analysis Interpretability Scale? Evidence from Multiple Choice Capabilities in Chinchilla](https://mlsanity.com/paper/2307.09458/) (2023)
- [The Truth is in There: Improving Reasoning in Language Models with Layer-Selective Rank Reduction](https://mlsanity.com/paper/2312.13558/) (2023)
- [Information Flow Routes: Automatically Interpreting Language Models at Scale](https://mlsanity.com/paper/2403.00824/) (2024)
- [Is This the Subspace You Are Looking for? An Interpretability Illusion for Subspace Activation Patching](https://mlsanity.com/paper/2311.17030/) (2023)
- [Explorations of Self-Repair in Language Models](https://mlsanity.com/paper/2402.15390/) (2024)
- [Missed Causes and Ambiguous Effects: Counterfactuals Pose Challenges for Interpreting Neural Networks](https://mlsanity.com/paper/2407.04690/) (2024)
- [Analyzing and Interpreting Neural Networks for NLP: A Report on the First BlackboxNLP Workshop](https://mlsanity.com/paper/1904.04063/) (2019)

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

- [Measuring Affinity between Attention-Head Weight Subspaces via the Projection Kernel](https://mlsanity.com/paper/2601.10266/) (2026)
- [Towards Single-Source Domain Generalized Object Detection via Causal Visual Prompts](https://mlsanity.com/paper/2510.19487/) (2025)
- [Singular Vectors of Attention Heads Align with Features](https://mlsanity.com/paper/2602.13524/) (2026)
- [Sparse Weight Decomposition for Efficient Circuit Extraction](https://mlsanity.com/paper/2608.03913/) (2026)

## Abstract (arXiv)

Many papers have shown that attention heads work in conjunction with each other to perform complex tasks. It's frequently assumed that communication between attention heads is via the addition of specific features to token residuals. In this work we seek to isolate and identify the features used to effect communication and coordination among attention heads in GPT-2 small. Our key leverage on the problem is to show that these features are very often sparsely coded in the singular vectors of attention head matrices. We characterize the dimensionality and occurrence of these signals across the attention heads in GPT-2 small when used for the Indirect Object Identification (IOI) task. The sparse encoding of signals, as provided by attention head singular vectors, allows for efficient separation of signals from the residual background and straightforward identification of communication paths between attention heads. We explore the effectiveness of this approach by tracing portions of the circuits used in the IOI task. Our traces reveal considerable detail not present in previous studies, shedding light on the nature of redundant paths present in GPT-2. And our traces go beyond previous work by identifying features used to communicate between attention heads when performing IOI.