When does linear attribution patching diverge from ground-truth activation patching on the GPT-2 small IOI circuit?

Attribution patching approximates the causal effect of patching each component/edge with a first-order (gradient) linear approximation, needing only two forward passes and one backward pass instead of one forward pass per component. It is widely used to scale circuit discovery, but the linear approximation can be inaccurate where the true effect is nonlinear (e.g. across the attention softmax or LayerNorm). Question: on the Indirect Object Identification (IOI) task in GPT-2 small, quantify the faithfulness of attribution patching to exact activation patching. Across all attention heads (and MLPs), what is the correlation (Pearson $r$ or Spearman $\rho$) and the rank agreement (top-$k$ overlap) between attribution-estimated and exact patch effects on the IOI logit-difference metric, and which specific components show the largest signed discrepancy? Determine whether the failures concentrate at particular sublayers (attention pattern vs value vs MLP).

Acceptance. FULLY RESOLVES: a reproducible script (fixed seed; GPT-2 small; released IOI dataset) that computes, for every component, both the exact activation-patching effect and the attribution-patching estimate on the IOI logit-difference metric, and reports (i) the overall correlation, (ii) top-$k$ rank overlap for $k\in\{5,10,20\}$, and (iii) a ranked list of the components with the largest absolute estimation error, with an analysis of whether errors localize to softmax/LayerNorm-crossing edges. PARTIAL: the same restricted to attention heads, or on a smaller synthetic task. Deliverable: code + the component-level error table + scatter-plot data.