CIRCUS: Circuit Consensus under Uncertainty via Stability Ensembles

Abstract: Mechanistic circuit discovery is notoriously sensitive to arbitrary analyst choices, especially pruning thresholds and feature dictionaries, often yielding brittle "one-shot" explanations with no principled notion of uncertainty. We reframe circuit discovery as an uncertainty-quantification problem over these analytic degrees of freedom. Our method, CIRCUS, constructs an ensemble of attribution graphs by pruning a single raw attribution run under multiple configurations, assigns each edge a stability score (the fraction of configurations that retain it), and extracts a strict-consensus circuit consisting only of edges that appear in all views. This produces a threshold-robust "core" circuit while explicitly surfacing contingent alternatives and enabling rejection of low-agreement structure. CIRCUS requires no retraining and adds negligible overhead, since it aggregates structure across already-computed pruned graphs. On Gemma-2-2B and Llama-3.2-1B, strict consensus circuits are ~40x smaller than the union of all configurations while retaining comparable influence-flow explanatory power, and they outperform a same-edge-budget baseline (union pruned to match the consensus size). We further validate causal relevance with activation patching, where consensus-identified nodes consistently beat matched non-consensus controls (p=0.0004). Overall, CIRCUS provides a practical, uncertainty-aware framework for reporting trustworthy, auditable mechanistic circuits with an explicit core/contingent/noise decomposition.