# Correcting Gradient-Based Circuit Localization via Interaction-Aware Backpropagation

arXiv: https://arxiv.org/abs/2505.17630 · HTML: https://mlsanity.com/paper/2505.17630/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 29 of its 34 references that are in the map.
- First posted on arXiv 23 May 2025.

## Builds on (most cited first, 29 of 29)

- [Think you have Solved Question Answering? Try ARC, the AI2 Reasoning Challenge](https://mlsanity.com/paper/1803.05457/) (2018)
- [Axiomatic Attribution for Deep Networks](https://mlsanity.com/paper/1703.01365/) (2017)
- [Locating and Editing Factual Associations in GPT](https://mlsanity.com/paper/2202.05262/) (2022)
- [BoolQ: Exploring the Surprising Difficulty of Natural Yes/No Questions](https://mlsanity.com/paper/1905.10044/) (2019)
- [SuperGLUE: A Stickier Benchmark for General-Purpose Language Understanding Systems](https://mlsanity.com/paper/1905.00537/) (2019)
- [Learning Important Features Through Propagating Activation Differences](https://mlsanity.com/paper/1704.02685/) (2017)
- [FEVER: a large-scale dataset for Fact Extraction and VERification](https://mlsanity.com/paper/1803.05355/) (2018)
- [Interpretability in the Wild: a Circuit for Indirect Object Identification in GPT-2 small](https://mlsanity.com/paper/2211.00593/) (2022)
- [Towards Automated Circuit Discovery for Mechanistic Interpretability](https://mlsanity.com/paper/2304.14997/) (2023)
- [Fact or Fiction: Verifying Scientific Claims](https://mlsanity.com/paper/2004.14974/) (2020)
- [ERASER: A Benchmark to Evaluate Rationalized NLP Models](https://mlsanity.com/paper/1911.03429/) (2019)
- [HateXplain: A Benchmark Dataset for Explainable Hate Speech Detection](https://mlsanity.com/paper/2012.10289/) (2020)
- [The Hydra Effect: Emergent Self-repair in Language Model Computations](https://mlsanity.com/paper/2307.15771/) (2023)
- [Have Faith in Faithfulness: Going Beyond Circuit Overlap When Finding Model Mechanisms](https://mlsanity.com/paper/2403.17806/) (2024)
- [Towards Faithful Model Explanation in NLP: A Survey](https://mlsanity.com/paper/2209.11326/) (2022)
- [AttnLRP: Attention-Aware Layer-Wise Relevance Propagation for Transformers](https://mlsanity.com/paper/2402.05602/) (2024)
- [AtP*: An efficient and scalable method for localizing LLM behaviour to components](https://mlsanity.com/paper/2403.00745/) (2024)
- [Explaining Explanations: Axiomatic Feature Interactions for Deep Networks](https://mlsanity.com/paper/2002.04138/) (2020)
- [XAI for Transformers: Better Explanations through Conservative Propagation](https://mlsanity.com/paper/2202.07304/) (2022)
- [Information Flow Routes: Automatically Interpreting Language Models at Scale](https://mlsanity.com/paper/2403.00824/) (2024)
- [A Mechanistic Interpretation of Arithmetic Reasoning in Language Models using Causal Mediation Analysis](https://mlsanity.com/paper/2305.15054/) (2023)
- [Copy Suppression: Comprehensively Understanding an Attention Head](https://mlsanity.com/paper/2310.04625/) (2023)
- [How does this interaction affect me? Interpretable attribution for feature interactions](https://mlsanity.com/paper/2006.10965/) (2020)
- [MIB: A Mechanistic Interpretability Benchmark](https://mlsanity.com/paper/2504.13151/) (2025)
- [Do Language Models Use Their Depth Efficiently?](https://mlsanity.com/paper/2505.13898/) (2025)
- [Explorations of Self-Repair in Language Models](https://mlsanity.com/paper/2402.15390/) (2024)
- [Answer, Assemble, Ace: Understanding How LMs Answer Multiple Choice Questions](https://mlsanity.com/paper/2407.15018/) (2024)
- [Optimal ablation for interpretability](https://mlsanity.com/paper/2409.09951/) (2024)
- [Normalized AOPC: Fixing Misleading Faithfulness Metrics for Feature Attribution Explainability](https://mlsanity.com/paper/2408.08137/) (2024)

## Built on by (most cited first, 5 of 5)

- [Mechanistic Interpretability as Statistical Estimation: A Variance Analysis](https://mlsanity.com/paper/2510.00845/) (2025)
- [Conditional Co-Ablation: Recovering Self-Repair Backups in Transformer Circuits](https://mlsanity.com/paper/2607.01940/) (2026)
- [PyHealth 2.0: A Comprehensive Open-Source Toolkit for Accessible and Reproducible Clinical Deep Learning](https://mlsanity.com/paper/2601.16414/) (2026)
- [Matryoshka attribution: Learning to attribute language model outputs to representations and weights](https://mlsanity.com/paper/2609.25518/) (2026)
- [A Practical Guide Towards Interpreting Time-Series Deep Clinical Predictive Models: A Reproducibility Study](https://mlsanity.com/paper/2603.24828/) (2026)

## Abstract (arXiv)

Circuit localization methods aim to identify the subset of model components responsible for specific behaviors in large language models, enabling detailed mechanistic analysis. Most existing methods assume components act independently and estimate importance by perturbing each component in isolation. However, components in neural networks interact, and ignoring these interactions leads to systematic misestimation of component importance. We find that one particularly problematic interaction is attention self-repair, in which softmax redistribution causes gradients for influential attention scores to vanish as other positions with similar values compensate. We introduce Gradient Interaction Modifications (GIM), a technique that explicitly accounts for feature interactions during backpropagation. GIM achieves state-of-the-art performance on the circuit localization track of the Mechanistic Interpretability Benchmark and outperforms existing gradient-based methods on feature attribution across diverse tasks. By accounting for interaction effects and explaining why prior methods underestimate component importance, GIM enables more faithful mechanistic analysis of large language models. GIM is available as a Python package at https://github.com/corticph/gim.