CIRCUS: Circuit Consensus under Uncertainty via Stability Ensembles

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.

One approach in mechanistic interpretability explains model behavior through circuits: the components and connections that carry it. Frozen discovery often returns hundreds of edges, making them hard to inspect, compare, or verify exhaustively. We introduce Circuit Condensation, which post-trains models to concentrate behaviors into smaller causal graphs. Each round prunes low-attribution edges and trains a low-rank adapter to match the original through what remains. It keeps the cut only if task accuracy and held-out perplexity remain within tolerance. Across four behaviors and eight models, condensed circuits are smaller than the strongest published frozen-weight baseline in 30 of 32 settings, by 8.1x on average and up to 316x. Repeating the search without weight updates produces larger circuits in 29 of 32 settings, showing that weight updates drive the reduction rather than search alone. For 19 small circuits, exhaustive subset tests show that 11 are exactly minimal and identify removable edges in the rest. Pair ablations reveal dependencies that single-edge tests miss. On indirect object identification, condensation isolates 24 heads, including 17 with documented roles, whereas a matched frozen circuit needs 61 heads, 36 without documented roles. The result is a sufficient subcircuit of the published mechanism rather than a reconstruction of it. The resulting circuit tracks the original model's next-token distribution and, at matched edge count, predicts its errors better than a frozen circuit in 10 of 11 evaluable settings.

Circuit extraction identifies model components whose presence preserves a target behavior under ablation, but preserving behavior does not single out one circuit. We study this in a synthetic Lean tactic-prediction benchmark with fixed proof rules and randomized surface form. Across dense and weight-sparse checkpoints of the same transformer, evaluated on atomic and compositional proofs, we vary which extracted object is reported: a compact prediction-preserving circuit, a broader graph retaining surrounding read, write, and routing structure, or a subgraph extracted with a post-ablation loss budget. First, overlap between groups of component-to-component connections is low, sometimes close to a random baseline. Overlap is much higher for selected attention-head sets under deterministic selection, but falls sharply when selection among equally scored heads is randomized. Second, the normalized graph-size ranking of conditions that differ in which supervised checkpoint initializes reinforcement learning (RL) agrees between repeated extractions of the compact circuit and between joint and separate query/key representations of each of the other two graphs. For the loss-budgeted graph, query/key ordering agreement persists through the budget sweep. Finally, across those same conditions, the largest exact-match accuracy gains from RL on compositional proofs come with the largest proportion of components in the compositional circuit that lie outside the corresponding atomic circuits. Ablating these additional components in the sparse RL model reduces compositional accuracy while largely preserving accuracy on the corresponding atomic tasks. A circuit-level claim therefore requires specifying which circuit is reported and how it is extracted and compared; behavior alone does not determine its interpretation. We distill these requirements into a reporting practice for circuit-extraction studies.