Certified Circuits: Stability Guarantees for Mechanistic Circuits

Alaa Anani, Tobias Lorenz, Bernt Schiele, Mario Fritz, Jonas Fischer
Proceedings of the 43rd International Conference on Machine Learning, PMLR 306:2650-2676, 2026.

Abstract

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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v306-anani26a, title = {Certified Circuits: Stability Guarantees for Mechanistic Circuits}, author = {Anani, Alaa and Lorenz, Tobias and Schiele, Bernt and Fritz, Mario and Fischer, Jonas}, booktitle = {Proceedings of the 43rd International Conference on Machine Learning}, pages = {2650--2676}, year = {2026}, editor = {Zhang, Tong and Dudik, Miroslav and Jaggi, Martin and Agarwal, Alekh and Li, Sharon and Schuurmans, Dale and Zhu, Jerry and Berkenkamp, Felix and Dong, Hanze and Bietti, Alberto}, volume = {306}, series = {Proceedings of Machine Learning Research}, month = {06--11 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v306/main/assets/anani26a/anani26a.pdf}, url = {https://proceedings.mlr.press/v306/anani26a.html}, abstract = {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.} }
Endnote
%0 Conference Paper %T Certified Circuits: Stability Guarantees for Mechanistic Circuits %A Alaa Anani %A Tobias Lorenz %A Bernt Schiele %A Mario Fritz %A Jonas Fischer %B Proceedings of the 43rd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2026 %E Tong Zhang %E Miroslav Dudik %E Martin Jaggi %E Alekh Agarwal %E Sharon Li %E Dale Schuurmans %E Jerry Zhu %E Felix Berkenkamp %E Hanze Dong %E Alberto Bietti %F pmlr-v306-anani26a %I PMLR %P 2650--2676 %U https://proceedings.mlr.press/v306/anani26a.html %V 306 %X 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.
APA
Anani, A., Lorenz, T., Schiele, B., Fritz, M. & Fischer, J.. (2026). Certified Circuits: Stability Guarantees for Mechanistic Circuits. Proceedings of the 43rd International Conference on Machine Learning, in Proceedings of Machine Learning Research 306:2650-2676 Available from https://proceedings.mlr.press/v306/anani26a.html.

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