Criterion C2 — Structural Plausibility

Validity type	Construct
Pass condition	Circuit components are at the layers and positions theory predicts, with weight-space signatures consistent with the claimed computational role
Evidence family	Structural (weight-space)
Minimum reporting	Layer/position of each component; relevant weight-space metric with value; comparison to null (random same-layer heads)
Common failure mode	Reporting only ablation results; never checking whether nominated heads have the right structural properties

What this criterion requires

Structural plausibility asks: if this component were doing what the circuit claim says, what would its weights look like — and do they?

Satisfied when:

1. Layer and position are theoretically expected. Name-mover heads should be late-layer (layers 9–11 in GPT-2 Small). S-inhibition heads should attend to the subject token. An SVA MLP should be downstream of primary syntactic integration heads.
2. Weight-space signatures are consistent. A copying head should have low-rank W_OV (near rank-1, singular value gap ≥ 0.8). An induction head should have predictable W_QK structure. An SVA head should have W_in directions geometrically close to the number-information subspace.
3. The signature is specific to nominated components — not just any same-layer head.

This project’s results

• An SAE direction aligned at cos = 0.82 with L8H6 W_OV — consistent with an output-writing role in IOI. This is a structural plausibility result, not a causal result.
• Another direction aligned at cos = 0.72 with L3H0 — consistent with an early syntactic role.

These findings satisfy structural plausibility for the IOI circuit claim (Finding 25). They do not establish causation; they make the construct coherent.

Primary instruments

• B01 SpectralSVD: spectral gap of W_OV for copying/inhibition heads
• B02 OVQK analysis: eigenvalue analysis for attention pattern detection
• B03 Weight alignment: cosine similarity of W_dec directions to known-circuit templates
• B07 Effective rank: participation ratio of W matrices per head
• B08 Template distance: Frobenius distance to known-circuit W_OV templates

Minimum reporting rule

For each component: layer/position + why theoretically expected + one weight-space metric + comparison to null. If a component is at an unexpected layer or has an unexpected signature, this must be noted — not silently omitted.

Common failures

Ablation-only circuit discovery: Component added because ablating it degrades performance, with no check of whether its weights are consistent with the claimed role.

Layer anomalies ignored: A circuit method nominates a very early-layer head for a late-stage role without explanation.