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Pillar 3: Stability

Stability tests whether the discovered circuit is consistent across re-discovery runs with different random seeds. If re-running discovery from the same model and task produces very different circuits each time, the circuit is not a reliable description of the model's computation.

Cost: Expensive — Pillar 3 re-runs the full discovery algorithm n_stability_runs times.

The Measurement

CircuitKit runs discovery \(N\) times with different random seeds and computes the Spearman rank correlation between the importance score vectors across seed pairs:

\[\text{stability} = \text{mean}_{i \neq j} \, \rho_S(\text{scores}_i, \text{scores}_j)\]

where \(\rho_S\) is the Spearman rank correlation. A value of 1.0 means all seeds produce identical score rankings; 0.0 means the rankings are random.

Additionally, CircuitKit measures node overlap as the Jaccard similarity between the selected node sets of two seeds (reported as mean_jaccard), alongside the Dice coefficient (mean_dice):

\[\text{overlap} = \text{Jaccard}(A_i, A_j) = \frac{|A_i \cap A_j|}{|A_i \cup A_j|}\]

Running Pillar 3

# Via Pipeline
pipe.evaluate(pillars=["stability"], n_examples=256, n_stability_runs=5)
print(pipe.report.stability)
# {
#   "mean_spearman": 0.87,   # mean Spearman rho of score vectors across seed pairs
#   "std_spearman": 0.04,
#   "mean_jaccard": 0.82,    # mean top-K node overlap across seed pairs
#   "std_jaccard": 0.05,
#   "mean_dice": 0.90,
#   "n_stable_nodes": 24,    # nodes present in every run
#   "n_runs": 5,
# }

# Full audit with stability
pipe.evaluate(pillars=None, n_stability_runs=5)

Cost Considerations

Pillar 3 is the most expensive pillar. With n_stability_runs=5:

Model Runtime per run Total (5 runs)
GPT-2 (128 examples) ~2 min ~10 min
Llama-1B (128 examples) ~8 min ~40 min
Gemma-4B (128 examples) ~20 min ~100 min

Optimization: Reduce n_examples for the stability runs (they need fewer examples than initial discovery since you're measuring consistency, not accuracy):

pipe.evaluate(
    pillars=["stability"],
    n_examples=64,      # fewer examples OK for stability check
    n_stability_runs=3, # 3 runs is often sufficient
)

Interpreting the Results

Spearman rho Interpretation
≥ 0.90 Highly stable — algorithm consistently finds the same circuit
0.75 – 0.90 Moderately stable — core circuit is consistent; peripheral nodes vary
0.60 – 0.75 Weakly stable — significant variation across seeds
< 0.60 Unstable — circuit is not reliably identifiable

Stability is algorithm-specific: EAP-IG tends to be more stable than ACDC (which is sensitive to the order of edge removal). If stability is low, try increasing n_examples or switching to a more stable algorithm variant.

What Low Stability Means

Low stability (rho < 0.75) can indicate:

  1. Too few examples — attribution scores are noisy; increase n_examples
  2. Task ambiguity — the task does not have a consistent circuit (may be distributed across many paths)
  3. Algorithm sensitivity — some algorithms are inherently more variable; switch to eap-ig
  4. Redundant circuits — the model has multiple equivalent circuits; any of them passes Pillar 1 but they're different per seed

Next Steps