IBCircuit: Towards Holistic Circuit Discovery with Information Bottleneck

Circuit study aims to explain how language models (LMs) implement a task by localizing and interpreting a circuit: a computational subgraph responsible for a specific model's behavior. Existing methods for circuit localization are largely hypothesis-driven: they define a task through a dataset, assume that all examples in the task are implemented by the same mechanism, and apply circuit discovery to obtain a single circuit. This workflow does not account for mechanistic diversity within a task, where different examples may rely on different mechanisms. We first show that when a dataset mixes tasks processed through distinct mechanisms, current circuit discovery can combine these mechanisms into a single circuit while retaining faithfulness comparable to circuits discovered on each task separately. Across four tasks and three models, we further provide evidence for such mechanistic diversity within individual tasks. To account for this diversity, we propose Data-driven Circuit Discovery (DCD), which modifies the circuit-discovery workflow by adding a grouping step before the discovery. The grouping step aims to partition the dataset into subsets of examples that rely on similar mechanisms. We instantiate this step with clustering over per-example attribution patterns (DCD-Cluster). Across four tasks and three models, DCD-Cluster decomposes the dataset into multiple subsets whose circuits exhibit distinct faithfulness patterns, providing useful hypotheses about mechanistic differences among examples.

The circuits framework in mechanistic interpretability aims to identify sparse subgraphs of model components that are causally responsible for a behavior, typically evaluated by measuring necessity and sufficiency. But these criteria say little about whether a circuit consistently captures how a model performs a task, or if it is specific to that task. We study these two properties, consistency and specificity, across six tasks and five models, extracting circuits at the component level (attention heads and MLP blocks) and at the level of individual MLP neurons. We find that component-level circuits are highly consistent and causally important for most tasks, but they are not specific: for a given task, ablating its own circuit drops accuracy by about as much as ablating another task's circuit. Neuron-level circuits, on the other hand, exhibit higher specificity across tasks, but far less consistency within tasks. This is explained by circuit overlap: component-level circuits share most of their components across tasks, related or not, while neuron-level circuits overlap only between closely related tasks. In a case study of the components shared by the task circuits of Llama-3.2-3B, we show that they consist mostly of MLP blocks, while the few attention heads within turn out to have general-purpose roles. Overall, our findings raise questions about the degree to which circuits can support targeted understanding of, and intervention on, model behavior.

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.