Demystifying Variance in Circuit Discovery of LLMs

Circuit discovery aims to explain how language models (LMs) implement a specific task by localizing and interpreting a circuit, a computational subgraph responsible for the LM's behavior. Existing circuit discovery methods are hypothesis-driven; they first informally define a task with a dataset, and then apply a circuit discovery algorithm over that dataset to obtain a single circuit. This imposes two strong assumptions: that the LM implements the task with a single circuit, and that the dataset adequately represents the task as humans understand it. We systematically test these assumptions across four previously studied tasks and find that even minor dataset variations that preserve task semantics can produce circuits with low edge overlap and cross-dataset faithfulness. More strikingly, when applied to a mixed dataset with two distinct tasks whose separately discovered circuits have near-zero cross-faithfulness, existing methods still return a single circuit with high faithfulness across both tasks. This indicates that current methods discover dataset-specific circuits, rather than general task circuits. We propose Data-driven Circuit Discovery (DCD), a new discovery framework that drops both assumptions: instead of returning a single circuit for a dataset, DCD first clusters examples in the dataset by how similarly the model processes them and discovers a separate circuit for each group. This allows distinct mechanisms to appear separately rather than merged into a single circuit; each circuit explains its group, not the full task. Experiments show that DCD discovers multiple circuits per dataset, each more faithful to its group than a single circuit discovered by existing methods. Broadly, DCD lets the data reveal mechanistic structure within LMs, rather than relying on human-defined task boundaries that may not align with how models organize their computation.

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 on most tasks, but they are not specific: ablating one task's circuit damages another task's performance about as much as that task's own circuit does. Neuron-level circuits, on the other hand, exhibit higher task-specificity but are far less consistent within tasks. This is explained by circuit overlap: component-level circuits share most of their components across all task pairs, 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 be generic attention-sink heads. Overall, our findings raise questions about the degree to which circuits can support targeted understanding of, and intervention on, model behavior.

A prominent research direction in mechanistic interpretability is learning sparse circuits over LLM components to reveal how they jointly produce model behavior. However, raw neurons are polysemantic, making learned circuits hard to interpret. Sparse autoencoder (SAE) features alleviate this, but their high dimensionality makes existing intervention-based circuit learning methods computationally prohibitive. We propose CircuitLasso, a scalable circuit-learning approach based on sparse linear regression. CircuitLasso recovers circuits whose structural accuracy matches that of state-of-the-art intervention-based methods on the benchmark data, at a fraction of the computational cost. For interpretability, CircuitLasso efficiently uncovers relationships among SAE features, showing how human-interpretable semantic features propagate through the model and influence its predictions. Finally, we validate the utility of our learned circuits by leveraging their insights to achieve comparable performance at substantially lower cost on a domain-generalization task.