# Certified Circuits: Stability Guarantees for Mechanistic Circuits

arXiv: https://arxiv.org/abs/2602.22968 · HTML: https://mlsanity.com/paper/2602.22968/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Placed in Circuits and mechanistic analysis, one of 13 directions in Mechanistic interpretability.
- Builds on 33 of its 38 references that are in the map.
- First posted on arXiv 26 Feb 2026.

## Placed in

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

## Builds on (most cited first, 30 of 33)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [ImageNet Large Scale Visual Recognition Challenge](https://mlsanity.com/paper/1409.0575/) (2014)
- [Benchmarking Neural Network Robustness to Common Corruptions and Perturbations](https://mlsanity.com/paper/1903.12261/) (2019)
- [Locating and Editing Factual Associations in GPT](https://mlsanity.com/paper/2202.05262/) (2022)
- [Visualizing and Understanding Convolutional Networks](https://mlsanity.com/paper/1311.2901/) (2013)
- [Natural Adversarial Examples](https://mlsanity.com/paper/1907.07174/) (2019)
- [Certified Adversarial Robustness via Randomized Smoothing](https://mlsanity.com/paper/1902.02918/) (2019)
- [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)
- [Certified Robustness to Adversarial Examples with Differential Privacy](https://mlsanity.com/paper/1802.03471/) (2018)
- [Mechanistic Interpretability for AI Safety -- A Review](https://mlsanity.com/paper/2404.14082/) (2024)
- [Attribution Patching Outperforms Automated Circuit Discovery](https://mlsanity.com/paper/2310.10348/) (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)
- [Have Faith in Faithfulness: Going Beyond Circuit Overlap When Finding Model Mechanisms](https://mlsanity.com/paper/2403.17806/) (2024)
- [OOD-CV: A Benchmark for Robustness to Out-of-Distribution Shifts of Individual Nuisances in Natural Images](https://mlsanity.com/paper/2111.14341/) (2021)
- [Scalable Certified Segmentation via Randomized Smoothing](https://mlsanity.com/paper/2107.00228/) (2021)
- [PURE: Turning Polysemantic Neurons Into Pure Features by Identifying Relevant Circuits](https://mlsanity.com/paper/2404.06453/) (2024)
- [How Well do Feature Visualizations Support Causal Understanding of CNN Activations?](https://mlsanity.com/paper/2106.12447/) (2021)
- [Interpretability Illusions in the Generalization of Simplified Models](https://mlsanity.com/paper/2312.03656/) (2023)
- [Visual Concept Connectome (VCC): Open World Concept Discovery and their Interlayer Connections in Deep Models](https://mlsanity.com/paper/2404.02233/) (2024)
- [Transformer Circuit Faithfulness Metrics are not Robust](https://mlsanity.com/paper/2407.08734/) (2024)
- [Verifying Chain-of-Thought Reasoning via Its Computational Graph](https://mlsanity.com/paper/2510.09312/) (2025)
- [RS-Del: Edit Distance Robustness Certificates for Sequence Classifiers via Randomized Deletion](https://mlsanity.com/paper/2302.01757/) (2023)
- [Mechanistic Interpretability as Statistical Estimation: A Variance Analysis](https://mlsanity.com/paper/2510.00845/) (2025)
- [Automatic Discovery of Visual Circuits](https://mlsanity.com/paper/2404.14349/) (2024)
- [Formal Mechanistic Interpretability: Automated Circuit Discovery with Provable Guarantees](https://mlsanity.com/paper/2602.16823/) (2026)
- [Pruning for Feature-Preserving Circuits in CNNs](https://mlsanity.com/paper/2206.01627/) (2022)
- [Adversarial Circuit Evaluation](https://mlsanity.com/paper/2407.15166/) (2024)

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

- [When Attribution Patching Lies: Diagnosis and a Second-Order Correction](https://mlsanity.com/paper/2606.09899/) (2026)
- [Seeing Through Circuits: Faithful Mechanistic Interpretability for Vision Transformers](https://mlsanity.com/paper/2604.14477/) (2026)
- [Engineering Resource-constrained Software Systems with DNN Components: a Concept-based Pruning Approach](https://mlsanity.com/paper/2604.09988/) (2026)
- [Circuit Condensation: Post-Training that Concentrates a Behavior's Causal Circuit](https://mlsanity.com/paper/2608.27254/) (2026)
- [Certified Mechanistic Edits: Behavioral Guarantees for Skill Removal and Preservation](https://mlsanity.com/paper/2610.03502/) (2026)

## Abstract (arXiv)

Understanding how neural networks arrive at their predictions is essential for debugging, auditing, and deployment. Mechanistic interpretability pursues this goal by identifying circuits--minimal subnetworks responsible for specific behaviors. However, existing circuit discovery methods are brittle: circuits depend strongly on the chosen concept dataset and often fail to transfer out-of-distribution, raising doubts whether they capture the concept or merely dataset-specific artifacts. We introduce Certified Circuits, which provide provable stability guarantees for circuit discovery. Our framework wraps any black-box discovery algorithm with randomized data subsampling to certify that inclusion decisions over circuit components--neurons or edges of the model graph, depending on the base algorithm--are invariant to bounded edit-distance perturbations of the concept dataset. Unstable components are abstained from, yielding circuits that are more compact and more accurate. We validate across three architectures (ResNet, ViT, GPT-2) on vision (ImageNet and four OOD datasets) and language (IOI, IOI-Hard, Greater-Than) tasks. Certified circuits achieve up to 56% higher accuracy and up to 80% fewer components, and remain reliable where baselines degrade. Certified Circuits puts circuit discovery on formal ground by producing mechanistic explanations that are provably stable and better aligned with the target concept. Code: https://github.com/AlaaAnani/certified-circuits.