# Circuit Claims Depend on What Is Extracted and How It Is Compared

arXiv: https://arxiv.org/abs/2607.18921 · HTML: https://mlsanity.com/paper/2607.18921/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 34 of its 40 references that are in the map.
- First posted on arXiv 21 Jul 2026.

## Builds on (most cited first, 30 of 34)

- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Scaling Laws for Neural Language Models](https://mlsanity.com/paper/2001.08361/) (2020)
- [Training Compute-Optimal Large Language Models](https://mlsanity.com/paper/2203.15556/) (2022)
- [Interpretability in the Wild: a Circuit for Indirect Object Identification in GPT-2 small](https://mlsanity.com/paper/2211.00593/) (2022)
- [Beyond Accuracy: Behavioral Testing of NLP models with CheckList](https://mlsanity.com/paper/2005.04118/) (2020)
- [Towards Automated Circuit Discovery for Mechanistic Interpretability](https://mlsanity.com/paper/2304.14997/) (2023)
- [Sparse Feature Circuits: Discovering and Editing Interpretable Causal Graphs in Language Models](https://mlsanity.com/paper/2403.19647/) (2024)
- [LeanDojo: Theorem Proving with Retrieval-Augmented Language Models](https://mlsanity.com/paper/2306.15626/) (2023)
- [ProofWriter: Generating Implications, Proofs, and Abductive Statements over Natural Language](https://mlsanity.com/paper/2012.13048/) (2020)
- [Measuring Compositional Generalization: A Comprehensive Method on Realistic Data](https://mlsanity.com/paper/1912.09713/) (2019)
- [Transformers as Soft Reasoners over Language](https://mlsanity.com/paper/2002.05867/) (2020)
- [Compositionality decomposed: how do neural networks generalise?](https://mlsanity.com/paper/1908.08351/) (2019)
- [COGS: A Compositional Generalization Challenge Based on Semantic Interpretation](https://mlsanity.com/paper/2010.05465/) (2020)
- [Causal Abstraction: A Theoretical Foundation for Mechanistic Interpretability](https://mlsanity.com/paper/2301.04709/) (2023)
- [Transcoders Find Interpretable LLM Feature Circuits](https://mlsanity.com/paper/2406.11944/) (2024)
- [Localizing Model Behavior with Path Patching](https://mlsanity.com/paper/2304.05969/) (2023)
- [The Disagreement Problem in Explainable Machine Learning: A Practitioner's Perspective](https://mlsanity.com/paper/2202.01602/) (2022)
- [Fine-Tuning Enhances Existing Mechanisms: A Case Study on Entity Tracking](https://mlsanity.com/paper/2402.14811/) (2024)
- [AtP*: An efficient and scalable method for localizing LLM behaviour to components](https://mlsanity.com/paper/2403.00745/) (2024)
- [A Benchmark for Systematic Generalization in Grounded Language Understanding](https://mlsanity.com/paper/2003.05161/) (2020)
- [Tracr: Compiled Transformers as a Laboratory for Interpretability](https://mlsanity.com/paper/2301.05062/) (2023)
- [LLM Circuit Analyses Are Consistent Across Training and Scale](https://mlsanity.com/paper/2407.10827/) (2024)
- [Finding Transformer Circuits with Edge Pruning](https://mlsanity.com/paper/2406.16778/) (2024)
- [MIB: A Mechanistic Interpretability Benchmark](https://mlsanity.com/paper/2504.13151/) (2025)
- [Weight-sparse transformers have interpretable circuits](https://mlsanity.com/paper/2511.13653/) (2025)
- [Sparse Interventions in Language Models with Differentiable Masking](https://mlsanity.com/paper/2112.06837/) (2021)
- [Everything, Everywhere, All at Once: Is Mechanistic Interpretability Identifiable?](https://mlsanity.com/paper/2502.20914/) (2025)
- [Hypothesis Testing the Circuit Hypothesis in LLMs](https://mlsanity.com/paper/2410.13032/) (2024)
- [InterpBench: Semi-Synthetic Transformers for Evaluating Mechanistic Interpretability Techniques](https://mlsanity.com/paper/2407.14494/) (2024)
- [ReCOGS: How Incidental Details of a Logical Form Overshadow an Evaluation of Semantic Interpretation](https://mlsanity.com/paper/2303.13716/) (2023)

## Built on by (most cited first, 2 of 2)

- [Sparse Weight Decomposition for Efficient Circuit Extraction](https://mlsanity.com/paper/2608.03913/) (2026)
- [Inherited Heads: Audio language models track speakers with their text backbone's attention, and an attention-mass ranking retrieves a different set](https://mlsanity.com/paper/2609.14174/) (2026)

## Abstract (arXiv)

Circuit extraction identifies model components whose presence preserves a target behavior under ablation, but preserving behavior does not single out one circuit. We study this in a synthetic Lean tactic-prediction benchmark with fixed proof rules and randomized surface form. Across dense and weight-sparse checkpoints of the same transformer, evaluated on atomic and compositional proofs, we vary which extracted object is reported: a compact prediction-preserving circuit, a broader graph retaining surrounding read, write, and routing structure, or a subgraph extracted with a post-ablation loss budget. First, overlap between groups of component-to-component connections is low, sometimes close to a random baseline. Overlap is much higher for selected attention-head sets under deterministic selection, but falls sharply when selection among equally scored heads is randomized. Second, the normalized graph-size ranking of conditions that differ in which supervised checkpoint initializes reinforcement learning (RL) agrees between repeated extractions of the compact circuit and between joint and separate query/key representations of each of the other two graphs. For the loss-budgeted graph, query/key ordering agreement persists through the budget sweep. Finally, across those same conditions, the largest exact-match accuracy gains from RL on compositional proofs come with the largest proportion of components in the compositional circuit that lie outside the corresponding atomic circuits. Ablating these additional components in the sparse RL model reduces compositional accuracy while largely preserving accuracy on the corresponding atomic tasks. A circuit-level claim therefore requires specifying which circuit is reported and how it is extracted and compared; behavior alone does not determine its interpretation. We distill these requirements into a reporting practice for circuit-extraction studies.