# Circuit Stability Characterizes Language Model Generalization

arXiv: https://arxiv.org/abs/2505.24731 · HTML: https://mlsanity.com/paper/2505.24731/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Placed in Circuits and mechanistic analysis, one of 13 directions in Mechanistic interpretability.
- Builds on 40 of its 63 references that are in the map.
- First posted on arXiv 30 May 2025.

## Placed in

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

## Builds on (most cited first, 30 of 40)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [SWE-bench: Can Language Models Resolve Real-World GitHub Issues?](https://mlsanity.com/paper/2310.06770/) (2023)
- [Locating and Editing Factual Associations in GPT](https://mlsanity.com/paper/2202.05262/) (2022)
- [Beyond the Imitation Game: Quantifying and extrapolating the capabilities of language models](https://mlsanity.com/paper/2206.04615/) (2022)
- [Gemma 2: Improving Open Language Models at a Practical Size](https://mlsanity.com/paper/2408.00118/) (2024)
- [Challenging BIG-Bench Tasks and Whether Chain-of-Thought Can Solve Them](https://mlsanity.com/paper/2210.09261/) (2022)
- [Interpretability in the Wild: a Circuit for Indirect Object Identification in GPT-2 small](https://mlsanity.com/paper/2211.00593/) (2022)
- [Refusal in Language Models Is Mediated by a Single Direction](https://mlsanity.com/paper/2406.11717/) (2024)
- [In-context Learning and Induction Heads](https://mlsanity.com/paper/2209.11895/) (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)
- [Combining Recurrent, Convolutional, and Continuous-time Models with Linear State-Space Layers](https://mlsanity.com/paper/2110.13985/) (2021)
- [Textbooks Are All You Need II: phi-1.5 technical report](https://mlsanity.com/paper/2309.05463/) (2023)
- [Causal Abstractions of Neural Networks](https://mlsanity.com/paper/2106.02997/) (2021)
- [FrontierMath: A Benchmark for Evaluating Advanced Mathematical Reasoning in AI](https://mlsanity.com/paper/2411.04872/) (2024)
- [How to use and interpret activation patching](https://mlsanity.com/paper/2404.15255/) (2024)
- [Attribution Patching Outperforms Automated Circuit Discovery](https://mlsanity.com/paper/2310.10348/) (2023)
- [A Mechanistic Understanding of Alignment Algorithms: A Case Study on DPO and Toxicity](https://mlsanity.com/paper/2401.01967/) (2024)
- [An Introduction to Vision-Language Modeling](https://mlsanity.com/paper/2405.17247/) (2024)
- [The Clock and the Pizza: Two Stories in Mechanistic Explanation of Neural Networks](https://mlsanity.com/paper/2306.17844/) (2023)
- [Does Circuit Analysis Interpretability Scale? Evidence from Multiple Choice Capabilities in Chinchilla](https://mlsanity.com/paper/2307.09458/) (2023)
- [Have Faith in Faithfulness: Going Beyond Circuit Overlap When Finding Model Mechanisms](https://mlsanity.com/paper/2403.17806/) (2024)
- [A Toy Model of Universality: Reverse Engineering How Networks Learn Group Operations](https://mlsanity.com/paper/2302.03025/) (2023)
- [A Theory for Emergence of Complex Skills in Language Models](https://mlsanity.com/paper/2307.15936/) (2023)
- [AtP*: An efficient and scalable method for localizing LLM behaviour to components](https://mlsanity.com/paper/2403.00745/) (2024)
- [Arithmetic Without Algorithms: Language Models Solve Math With a Bag of Heuristics](https://mlsanity.com/paper/2410.21272/) (2024)
- [Towards a Theoretical Framework of Out-of-Distribution Generalization](https://mlsanity.com/paper/2106.04496/) (2021)
- [Compositional Generalization from First Principles](https://mlsanity.com/paper/2307.05596/) (2023)
- [Skill-Mix: a Flexible and Expandable Family of Evaluations for AI models](https://mlsanity.com/paper/2310.17567/) (2023)
- [LLM Circuit Analyses Are Consistent Across Training and Scale](https://mlsanity.com/paper/2407.10827/) (2024)

## Built on by (most cited first, 6 of 6)

- [AutoSOTA: An End-to-End Automated Research System for State-of-the-Art AI Model Discovery](https://mlsanity.com/paper/2604.05550/) (2026)
- [CorrSteer: Generation-Time LLM Steering via Correlated Sparse Autoencoder Features](https://mlsanity.com/paper/2508.12535/) (2025)
- [Navigating by Old Maps: The Pitfalls of Static Mechanistic Localization in LLM Post-Training](https://mlsanity.com/paper/2605.06076/) (2026)
- [Reforming the Mechanism: Editing Reasoning Patterns in LLMs with Circuit Reshaping](https://mlsanity.com/paper/2603.06923/) (2026)
- [CircuitKIT : Circuit Discovery, Evaluation, and Application Toolkit for Mechanistic Interpretability](https://mlsanity.com/paper/2607.19317/) (2026)
- [Shared circuits predict whether LLMs generalize across formats in arithmetic reasoning](https://mlsanity.com/paper/2609.04463/) (2026)

## Abstract (arXiv)

Extensively evaluating the capabilities of (large) language models is difficult. Rapid development of state-of-the-art models induce benchmark saturation, while creating more challenging datasets is labor-intensive. Inspired by the recent developments in mechanistic interpretability, we introduce circuit stability as a new way to assess model performance. Circuit stability refers to a model's ability to apply a consistent reasoning process-its circuit-across various inputs. We mathematically formalize circuit stability and circuit equivalence. Then, through three case studies, we empirically show that circuit stability and the lack thereof can characterize and predict different aspects of generalization. Our proposed methods offer a step towards rigorously relating the generality of models to their interpretability.