[Submitted on 22 May 2026 (v1), last revised 19 Jul 2026 (this version, v2)]

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Abstract:Mechanistic interpretability of transformers requires identifying not just which components matter but how they compose into the computational route that produced a prediction. Both attention and MLP follow a shared key-value template $\phi(S)U$. We exploit this structure to develop Unpack, a backward recursion that decomposes credit through both sublayers, producing interaction strengths between any two components, named end-to-end paths with K/Q/V composition labels, and per-token attribution, all from a single forward pass, without intervention, gradients, or auxiliary training. The interaction scores are causally grounded: across the Pythia-deduped family from 160M to 6.9B parameters, a component's score predicts the perplexity increase when its communication is ablated (within-layer Spearman $\rho = 0.72$ to $0.96$). The composition paths surface all three connections of the indirect-object-identification circuit of Wang et al. (2023), including the mode-specific routing of each: rerooting at the Name Mover heads, S-Inhibition is the strongest query-side input and falls to rank 10 on the key side, a distinction no single per-token or per-component score can express. The same procedure applied to the greater-than circuit of Hanna et al. (2023), a differently shaped circuit, places the named connections among the top contributors, once layer-0 writers, which carry large credit whatever they feed, are set aside. The decomposition reads out contribution under the realized computation; it complements, rather than performs, causal circuit discovery. The per-token readout is faithful under input perturbation, on par with dedicated attribution methods, and distinguishes circuit mechanism from surface identity: two occurrences of the same name receive radically different credit when only one drives the circuit. Code is available at this https URL.

Submission history

From: Po-Kai Chen [view email]
[v1] Fri, 22 May 2026 09:03:01 UTC (1,310 KB)
[v2] Sun, 19 Jul 2026 23:47:44 UTC (1,316 KB)