Mechanistic interpretability seeks to recover the internal computations that produce model behavior. Circuit analysis represents a computation as a sparse subgraph of interacting model components. Detailed studies have reconstructed circuits for behaviors such as indirect object identification and numerical comparison, while automated methods aim to find such circuits at scale. Much of this effort follows a natural view: better attribution, more data, or improved search should recover a better account of the computation used by the intact model. But successful recovery also depends on recognizing a better circuit once it has been found.

The usual test is intervention-defined faithfulness: how well a circuit preserves model outputs when computation outside it is ablated or replaced. This test is central to both discovery and evaluation. It can determine which connections are retained during search and which candidate is ultimately presented as an explanation. A high score is therefore more than a description of a circuit; it is a reason to choose that circuit over another. This raises the question this paper studies: can faithfulness prefer an equally sized circuit that reproduces the model's behavior less well?

Executing a circuit requires replacing excluded signals with donor activations, means, or zeros. Retained components then receive inputs that differ from those in the intact model and recompute their activations from these altered inputs. The paper calls this change in computational context context distortion. Different circuits can respond differently to the replacement signals, allowing the score to favor a circuit that works well under the intervention over one that better reproduces the model under a fixed behavioral test.

This is a problem for the objective as well as for discovery. Search may fail to find a high-scoring candidate. But if the score itself prefers a behaviorally worse candidate, searching more effectively does not resolve that preference. The paper refers to this misalignment as an objective-level recovery gap. The authors test it through pairwise misranking: a validation score favors one circuit while independent-test behavior favors the other. Comparing fixed candidates lets examine what the objective rewards separately from how those candidates were obtained. All primary comparisons use circuits of the same size, ruling out differences in the number of retained components as an explanation for misranking. Even under this control, faithfulness can prefer a circuit that reproduces model behavior less well. This failure persists among outputs of established discovery methods on human-studied language-model tasks, making it relevant to practical circuit selection.

Why circuit discovery needs the right yardstick

The paper investigates two complementary settings. InterpBench provides known mechanisms in smaller, semi-synthetic models. The Human suite contains human-studied circuits in pretrained language models, including indirect object identification and docstring completion. The Human suite more closely reflects common applications of circuit discovery. Its higher aggregate candidate–candidate misranking in the main discovery evaluation highlights the importance of assessing faithfulness beyond semi-synthetic benchmarks.

The usual test is intervention-defined faithfulness. For validation prompts, the primary score is negative output-distribution KL divergence. Larger scores are better. Scores are averaged over valid output positions within each prompt and then over prompts. Resampling additionally averages three shared donor draws. Logit difference and probability difference provide additional task-based margin checks. The independent behavioral criterion measures agreement with the intact model's answers on held-out prompts, using ordinary resampling and averaging over the same donor draws. Agreement includes intact-model mistakes. On Greater-Than, the criterion uses semantic accuracy: the fraction of predicted two-digit year endings strictly greater than the prompt's starting ending, rather than exact-token agreement.

A misranking occurs when faithfulness prefers the circuit with lower behavioral quality. For a fixed pair, let the circuit with higher Q have higher behavioral quality and the circuit with lower Q have lower quality. A misranking occurs when faithfulness prefers the lower-Q circuit. The distinction between the two objectives can also be expressed over a family of size-K circuits: if the score-maximizing circuit has lower Q than the true-Q-maximizing circuit, optimizing the score more effectively cannot recover the best circuit under Q. The paper's experiments do not compute these global optima. They test the ranking property that motivates this concern: whether the score can prefer a worse member of a fixed pair.

How faithfulness can misrank equal-size circuits

The authors first remove discovery from the experiment. Starting from a reference circuit, they generate alternatives of the same size and ask how faithfulness ranks them. If a score prefers the worse member of a pair, the failure cannot be attributed to the search procedure: both candidates are already available for evaluation.

For each reference, they replace retained components with the same number of excluded components. The edit bands are one component, 5%, 10%, 20%, 50%, and 75% of reference size, with ten seeds per attainable distinct band. Identical masks and bands resolving to the same edit count are deduplicated. They compare references with candidates (R–C) and candidates with one another (C–C) under resampling, mean, and zero replacement. Candidate masks, prompts, and the test Q ordering remain fixed across evaluations.

Table 2 in the paper reports KL misranking rates and the mean behavioral deficit among failures. The pattern is task-dependent. On Greater-Than, C–C misranking rises from 3.4% under resampling to 54.0% under zero replacement, while R–C misranking rises from zero to 56.7%. IOI shows a different pattern: mean replacement misranks 33.3% of R–C pairs, compared with 3.3% under zero replacement. Because the circuits and Q ordering do not change, these differences show that the intervention can change which candidate the score rewards.

InterpBench exhibits both near-null and high-misranking settings despite reference Q values of 97.33%–100%. Task 97 has no R–C KL misranking under any intervention, whereas task 111 reaches 80.0% R–C and 72.5% C–C under zero replacement. For task 93, zero replacement misranks 70.0% of R–C pairs. Among these pairs, the preferred circuit loses an average of 63.55 percentage points of Q relative to the alternative. The two cases illustrate why the paper reports the size of the behavioral deficit alongside the frequency of misranking.

The failures extend beyond a particular faithfulness metric. KL, logit difference, and probability difference all exhibit misranking. The rates and failed pairs differ, but the objective-level problem is not specific to KL. The result supports a concern across the tested measures of faithfulness, rather than an objection to one formula.

A reference supplies an established circuit against which to test the score, but discovery also requires distinguishing between alternative candidates. InterpBench task 97 illustrates the distinction: it has no R–C KL misranking under any intervention, yet its C–C rates are 5.2%, 14.5%, and 22.0% under resampling, mean, and zero replacement. Recognizing the reference in these comparisons does not ensure reliable ordering of the candidates.

Controlled edits expose misranking across methods

To test practical relevance, the paper evaluates candidates from four established circuit-discovery methods: EAP, EAP-IG, ACDC, and Edge-SP. Each comparison stays within one task and one method. The question is whether faithfulness recognizes the better circuit among the outputs that a method actually returns.

The paper uses ten discovery seeds, with 100 discovery prompts per task and seed shared across methods and disjoint from evaluation prompts. All validation and independent-test prompts from the controlled study are reused, together with their mean banks, valid-position masks, and donor assignments. This keeps the evaluation fixed while changing how candidates are obtained. ACDC and Edge-SP have a 300-second discovery cap per run. Primary comparisons require equal actual executable size.

On the human-reference tasks, resampling KL misranks 20.0% of EAP C–C pairs, 30.4% for EAP-IG, 41.2% for ACDC, and 9.4% for Edge-SP. Misranking therefore occurs under ordinary resampling as well as mean and zero replacement. InterpBench resampling C–C rates range from 2.9% for EAP-IG to 18.7% for Edge-SP. These methods return better candidates, but faithfulness sometimes ranks them below worse alternatives.

On the human-reference tasks, EAP-IG C–C misranking rises from 30.4% under resampling to 53.0% under mean replacement. On InterpBench, ACDC C–C misranking rises from 7.9% under resampling to 46.0% under zero replacement. The scores also sometimes favor candidates with sizable Q deficits: for Human Edge-SP R–C pairs under zero replacement, the mean deficit among misrankings is 34.14 percentage points. By contrast, InterpBench EAP-IG resampling C–C failures average 0.07 pp. These preferences differ sharply in their consequences for behavior, even though both count as misrankings.

Pooling the common discovery pairs within each suite, Human C–C KL misranking is 20.9%, 30.9%, and 38.1% under resampling, mean, and zero replacement, compared with 9.8%, 16.2%, and 26.8% on InterpBench. The Human rates are higher under each intervention. This pattern is not uniform across individual methods, but it shows why the smaller semi-synthetic benchmark is insufficient on its own to assess the reliability of discovery in pretrained language models.

Resampling reveals KL divergence problems

Under resampling alone, KL misranks 9.4%–41.2% of candidate pairs across the four methods on the human-reference tasks. The paper reports these percentages for each method: EAP at 20.0%, EAP-IG at 30.4%, ACDC at 41.2%, and Edge-SP at 9.4%. These comparisons reuse the validation and test prompts from the controlled study, keeping the evaluation fixed while changing how candidates are obtained.

InterpBench resampling C–C rates range from 2.9% for EAP-IG to 18.7% for Edge-SP. The lower rates on InterpBench may reflect the semi-synthetic nature of those tasks, but the paper notes that lower rates on synthetic benchmarks alone cannot establish reliability in pretrained models.

The paper also considers logit difference and probability difference alongside KL. Every metric exhibits misranking. The rates and failed pairs differ, but the objective-level problem is not specific to one formula. Changing the metric alters the failures but does not eliminate them.

Context distortion as the engine behind misrankings

The paper investigates context distortion as an explanation for the observed misrankings. If the replacement signals contribute to the wrong preference, restoring some of the original signals should be able to correct it. The paper tests this prediction on existing KL misrankings, keeping the two circuits and their original Q values fixed throughout.

The restoration experiment selects 100 equal-size circuit-pair/intervention cases from the discovery pool: 50 Human and 50 InterpBench cases, spanning 50 resampling, 25 mean, and 25 zero cases. Each has a Q deficit of at least 0.5 pp and a strict KL misranking on both validation and independent-test prompts.

At selected excluded incoming connections, the paper replaces intervention signals with activations cached from the recipient prompt's intact-model execution. Retained connections compute normally. Masks, weights, unrestored donor assignments, mean banks, prompts, and the original Q ordering remain fixed. Only selected replacement signals change, isolating whether context restoration can correct the preference.

The search groups excluded incoming connections by receiving node and searches at 80%, 40%, 20%, and 10% of the original eligible group count, with up to five predetermined attempts per level. The first validation-successful subset becomes the sampling parent for the next level; a failed level resets sampling to the original universe. Each qualifying subset is tested on independent prompts using their own intact signals and original donors. Test outcomes never guide the search. A repair requires at least one subset to correct both rankings beyond the predefined tolerance; later failures do not cancel earlier success. Search ends after the 10% level, within 20 attempts.

Table 6 reports independently confirmed repairs, including 50/50 Human cases and 46/50 InterpBench cases. At the nominal 10% level alone, 82 cases have a confirmed repair. The any-level result counts each repaired case once. The mean behavioral deficit before repair across all 100 baseline failures is +10.33 percentage points. Among the 96 repaired cases, the mean deficit after repair is −9.30 percentage points; those same 96 cases have a baseline mean of +9.30 pp. The four unconfirmed cases remain in repair-rate denominators and have no after-repair value.

At the any-level result, 96 of 100 persistent KL misrankings from the discovery pool are repaired on both validation and held-out prompts. The circuits and their original behavioral scores remain unchanged. The preference is corrected by restoring selected signals from the recipient's intact-model execution.

What this means for anyone building or evaluating circuits

The findings show why better discovery alone is insufficient when its objective rewards the wrong candidate. The paper's main findings are:

  • Faithfulness can misrank circuits without a discovery algorithm. Equal-size modifications of reference circuits produce misrankings under resampling, mean, and zero replacement. The failures occur both against references and between candidates, and some score preferences select circuits with substantially worse held-out behavior.
  • The same failure occurs in actual discovery outputs. Candidate pools from EAP, EAP-IG, ACDC, and Edge-SP all contain misranked pairs. Under resampling alone, candidate–candidate KL misranking ranges from 9.4% to 41.2% across the four methods on the human-reference tasks.
  • Restoring part of the intact context can repair the preference. For 100 persistent KL misrankings selected from the discovery pool, at least one partial restoration corrects both validation and independent-test rankings in 96 cases. This supports context distortion as a contributor to the observed failures.

For practitioners, the key takeaway is that a high faithfulness score does not guarantee that a circuit reproduces the model's behavior well under fixed resampling. The evaluation objective and the discovery objective can misalign, and the misalignment arises from changes in computational context when excluded signals are replaced. Restoring signals from the intact model can recover the ranking, which suggests that the problem is not that the search fails to find good circuits but that the yardstick used to select among them rewards the wrong candidate.

Future work could explore whether other intervention choices or restoration strategies reduce misranking further. The paper also raises the question of whether evaluation protocols should incorporate behavioral tests on held-out prompts alongside faithfulness scores, rather than relying on intervention-defined faithfulness alone.