spb/wpai0001_uqo

1\section{Discussion}\label{sec:discussion}23\paragraph{What the results establish.} In a controlled micro-world, a capability that a recipient4transformer demonstrably lacks can be installed at inference time by replacing one residual row, at the read5position, with the donor's row through an orthogonal map fitted on data that never exercises the capability.6The effect is large (control-adjusted $+0.88$ on average, lower bound above the smallest effect of interest in7every pair), selective (control stratum intact in eight of nine pairs, $0.946$ in the ninth), reproducible8across donor and recipient seeds and across different initializations, low-dimensional (eight directions),9rule-carrying (unseen operands), causally anchored (ablation, rescue, sham) and portable across width, depth10and a harder composition regime. This answers the central question positively \emph{for a bounded, causally11localized computation}.1213\paragraph{What they do not establish.} They do not establish that the same holds for open-ended skills,14for large models, or without the donor in the loop. The donor-free variants are weaker and qualitatively15different: the adapter caches, the weight grafts damage the control stratum, the steering vector transfers16nothing. And conventional learning on the same items is perfect here; the value of transplantation is that no17label and no gradient step is needed, which matters when the capability has no labelled data or when the18recipient must not be trained, not when it is cheap to train.1920\paragraph{Why regression-fitted maps fail, and why it matters for prior work.} The annihilation proposition21is elementary but consequential: any map fitted to predict the recipient from the donor on inputs where the22donor computes something the recipient cannot will remove that computation, in proportion to how23unpredictable it is from the recipient. This is a plausible, testable account of the negative result of24\citet{zhang2026negative}, whose bridge was fitted by regression on hidden states of the very prompts whose25reasoning state it was meant to carry; it also suggests that the success of affine stitching for26\emph{features both models already represent} \citep{chen2025transferring,kim2026one} and its failure for27\emph{capabilities one model lacks} are two faces of the same fitting criterion. The remedy we tested is cheap:28fit on task-free rows, or constrain the map to be orthogonal.2930\paragraph{Initialization.} The identity graft works only between models that share their initial weights.31This recovers, in a transfer setting, the permutation-symmetry picture of model merging32\citep{ainsworth2022git}: differently initialized models compute in rotated coordinates, and a rotation fitted33on unrelated data suffices to undo the difference for this capability.3435\paragraph{Alternative explanations.} (i) \emph{Answer leakage}: the donor row at the read position is36computed from the same token ids and contains the operand and the operator identity but not the answer token;37the shuffled-item control shows that rows from other items do nothing, and the reverse graft shows that the38recipient's own row already contains the operand and operator. (ii) \emph{Trivial map}: the sham map and the39norm-matched random rows destroy both strata, so success is not a property of ``any row of the right norm''.40(iii) \emph{Selection on the test set}: the method, layer and dose were fixed before the confirmatory items41were generated; the one preregistered criterion that failed (retention $\geq 0.95$ in every pair) is42reported as failed. (iv) \emph{Task triviality}: granted for learning (the supervised baselines), not for43transfer (every control fails).4445\paragraph{Open-weight models.} Three facts carry over from the micro-world and three do not. Carried over:46a task-conditioned state exists and is causally sufficient within a model for some tasks (antonyms, capitals)47at specific layers; its mapped form transfers between models above null controls in several pairs; and what48transfers is the task identity, not query content. Not carried over: the separation from controls is modest49(the best null controls reach $0.3$--$0.5$ on antonyms because the recipient's zero-shot behaviour responds to50any push of the right norm), the effect depends on the pair and direction (upward within the Qwen family and51from Llama into Qwen-3B work best; into Llama-3B and from 7B into Llama-3B do not), and tasks that are not52vectorizable in the recipient (the invented morphology everywhere, ``add three'' in Qwen) cannot be installed by53this route at all. The frozen rule returns ``partial'' or ``not supported'' per pair; we report it as such. The54micro-world result therefore does not license claims about capability transfer between large models; it55isolates the conditions under which transfer is identifiable, and shows that in open-weight models the first of56those conditions---a bounded, causally sufficient organ for the capability---holds only for some tasks and the57second---an alignment map that places it where the recipient reads it---holds only for some pairs.58