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Pillar 1: Causal Patching

Causal patching is the fastest faithfulness test and the most commonly reported metric. It answers the question: if we patch back only the circuit nodes to their clean activation values (leaving all other nodes at their corrupted values), does the model's behavior recover?

The Measurement

Setup: 1. Run the model on the corrupted input \(x^*\) — all activations are now "corrupted" 2. Patch circuit nodes back to their clean activation values (from \(x\)) 3. Measure the logit-difference metric \(f\) at the output

If the circuit is faithful, the metric after patching should be close to the full-model clean metric:

\[\text{patching score} = \frac{f(\text{corrupted} + \text{circuit nodes patched}) - f(x^*)}{f(x) - f(x^*)}\]

A score of 1.0 means the circuit alone can fully recover the clean behavior. A score of 0.0 means patching back the circuit has no effect.

Running Pillar 1

# Via Pipeline
pipe.evaluate(pillars=["patching"], n_examples=256)
print(pipe.report.patching_score)

# Via evaluate_circuit
results = evaluate_circuit({
    ...,
    "eval": {"pillars": ["patching"]},
})
print(results.patching_score)  # Pillar 1 patching score

Low-level:

from circuitkit.evaluation.evaluate import evaluate_graph

# Apply circuit to graph
graph.apply_topn(n=30, level="node")  # keep top 30 nodes (default level="edge")

raw_metric = evaluate_graph(
    model,
    graph,
    dataloader,
    metrics=[metric_fn],
    intervention="patching",   # the patching intervention
    quiet=True,
)

evaluate_graph returns the raw metric, not the normalized score

evaluate_graph gives you the raw per-sample metric under the patching intervention — not the 0-1 faithfulness ratio. The normalization against the clean and corrupt baselines happens inside Pillar1_CausalPatching.run, which is what populates report.patching_score. If you call evaluate_graph directly, you still need to normalize yourself: (raw_metric - corrupt_baseline) / (clean_baseline - corrupt_baseline).

Interpreting the Score

Score Interpretation
≥ 0.85 Strong. The circuit accounts for ≥ 85% of the behavior.
0.70 – 0.85 Moderate. The circuit captures the main computation but misses some components.
0.50 – 0.70 Weak. A meaningful portion of the behavior is outside the circuit.
< 0.50 Poor. The circuit does not explain the behavior well.

Typical values in the CircuitKit audit:

Model Task Algorithm Pillar 1 Score
GPT-2 IOI eap-ig 0.83
GPT-2 SVA eap-ig 0.79
Llama-1B MMLU eap-ig 0.71
Gemma-2B IOI eap-ig 0.76

What Causal Patching Tests (and Does Not Test)

Tests: - Whether the circuit nodes are sufficient to reproduce the behavior (sufficiency) - The circuit's ability to carry the relevant information

Does NOT test: - Circuit sufficiency under ablation of out-of-circuit nodes (that's Pillar 2: Ablation) - Whether the circuit is stable across seeds (Pillar 3) - Whether the circuit is better than a random selection of the same size (Pillar 5)

A circuit can pass Pillar 1 and fail Pillar 2 if there are other components outside the circuit that also carry the information: the model has redundancy.

Next Steps