Which circuit is correct?

The indirect object identification (IOI) task has been analyzed by at least four independent groups using different methods. Wang et al. (2023) found the circuit manually. Conmy et al. (2023) used ACDC (automated circuit discovery via computational graph pruning). Syed et al. (2023) used attribution patching (gradient-weighted activation differences). Hanna et al. (2023) used a related approach for the greater-than task and found circuits with very different sizes. The circuits don’t agree. The field treats this as a replication problem — which method got the right answer?

The problem is not replication. The problem is that each method asks a different question, and the question determines the answer. Ablation-based methods (ACDC, activation patching) test which components are necessary — remove them and performance degrades. Attribution methods estimate which components contribute most — their gradient-weighted effect on the output. Manual analysis identifies which components fill functional roles — name movers, backup name movers, induction heads. Necessity, contribution, and functional role are three different things, and they give three legitimately different circuit boundaries.

A component can be highly contributory (large attribution) but not necessary (the network compensates when it’s removed). A component can be necessary but fill no identifiable functional role (it’s needed but we can’t say what it does). A component can fill a clear role but contribute little to the output on average (it’s the backup that rarely fires). These are not bugs in the methods. They are different views’ answers to the question “what is this circuit?”

The view confusion

Ablation tests (ACDC, activation patching) operate at the Object view: mechanisms are concrete components, identity is component overlap, evidence is necessity and sufficiency. Attribution methods are closer to the Instrumental view: mechanisms are whatever predicts behavior, no commitment to components being “real.” Manual circuit analysis operates at the Role view: mechanisms are functional roles, identity is role equivalence, evidence is that the same role is filled.

A fourth source of disagreement is the counterfactual distribution. Activation patching replaces activations from one input with those from another — and the choice of “another” is a foil. The Contrastive view makes this explicit: different foils define different contrastive mechanisms, and two groups running activation patching with different counterfactual distributions are studying different contrastive mechanisms, not disagreeing about one. Most circuit discovery papers bury the counterfactual distribution in the methods and state the result as if absolute.

When papers disagree about circuit size or membership, they are often comparing answers from different views without recognizing this. The disagreement is real in the sense that the answers differ, but it is not a conflict — it’s a consequence of asking different questions.

Mechanistic validity impact

Not in the paper

The following content is not in the paper. The paper’s open-problems appendix records each problem’s status and key views and carries no validity criteria; this table reads the same problem against the companion framework’s criteria.

Criterion	The confusion	Resolution
C3 Convergent validity	Different methods “fail to converge” on the same circuit	Convergence should be checked within a view, not across views. ACDC and activation patching should converge (both Object). ACDC and manual role analysis need not
M6 Invariance	Circuit membership changes with method	Method invariance is a within-view criterion. Cross-view variation is expected
I3 Minimality	No principled circuit boundary — threshold-dependent	Each view implies a different natural boundary. Object: necessity threshold. Role: role membership. Subspace: subspace dimension
I5 Rival mechanism exclusion	Can’t exclude that a different circuit is equally valid	The “alternative” is often the same mechanism described at a different view level — not a competing explanation but a complementary one

The key insight: convergent validity (C3) and measurement invariance (M6) should be tested within a view, not across views. Papers that report “failure to replicate” across methods using different views are making a category error.

Resolution status: Clarified

Different methods find different circuits because they ask different questions under different views. Object-view methods (ACDC, activation patching) test necessity. Instrumental methods (attribution) estimate contribution. Role-view methods (manual analysis) identify functional roles. Necessity, contribution, and functional role are three different things. The disagreement is not empirical — it is a consequence of asking different questions. Convergent validity (C3) and measurement invariance (M6) should be tested within a view, not across views.

Sources

• Sharkey et al. (2025) §2.1.4: Validation of descriptions (arXiv:2501.16496)
• Nanda (2022) §2: Circuits in the wild (200 Open Problems)
• Wang et al. (2023): Interpretability in the wild: a circuit for indirect object identification in GPT-2 Small (ICLR 2023)
• Conmy et al. (2023): Towards automated circuit discovery for mechanistic interpretability (ACDC)
• Syed et al. (2023): Attribution patching outperforms automated circuit discovery (EAP)
• Hanna et al. (2023): How does GPT-2 compute greater-than?