spb/wpai0001_uqo

1\section{Results}\label{sec:results}23\begin{sloppypar}4\paragraph{Provenance.} Every number below names its run: the pilot \url{pilot_tier0_opseq_451ef5087182}5(Gates B--C and localization), the exploratory transplant runs \url{graft_tier0_f50a28ca1bf7} (protocol v1)6and \url{graft_tier0_30e3644aa801} (v2), the confirmatory run7\url{graft_tier0_confirmatory_0c2257f6803e} (preregistration v1.0, new seeds), and the Tier-1 runs of8\S\ref{sec:tier1}. Tables and figures are regenerated from the results files by9\url{scripts/build_tables.py} and \url{scripts/build_figures.py}; the confirmatory decision rules are10evaluated by \url{scripts/confirmatory_analysis.py}.11\end{sloppypar}1213\subsection{Gate B: a manufactured, reproducible capability gap}14Three donor seeds trained on all eight operators and three recipient seeds trained with $\Omega$ excluded15reach dev accuracy $1.000$. On the held-out target stratum (programs containing $\Omega$; $n{=}1\,000$ items in16$\approx 900$ programs) final-answer exact match is $1.000$ (sd $0.000$) for donors and $0.092$ (sd $0.053$)17for recipients against a majority-class chance of $0.105$; the token emitted at the first $\Omega$ step is18correct $1.000$ versus $0.062$ of the time. Both roles score $1.000$ on the control stratum. The paired gap on19identical items (seed~0) is $+0.847$ $[+0.825, +0.870]$ (Table~\ref{tab:pilot}, Figure~\ref{fig:gap}). Both20roles fail the length-OOD stratum ($0.086$ vs $0.091$), a limitation of absolute position embeddings that we21treat as a stratum, not a target.2223\begin{table}[t]\centering\small24\caption{Pilot gap qualification (run \url{pilot_tier0_opseq_451ef5087182}): final-answer exact match by25stratum, mean (sd) over three seeds per role; paired gap with cluster-bootstrap 95\% interval over programs.}26\label{tab:pilot}27\input{tables/tab_pilot_gap}28\end{table}2930\begin{figure}[t]\centering31\includegraphics[width=0.62\textwidth]{figures/fig_gap_tier0.pdf}32\caption{Tier-0 pilot: final-answer exact match by evaluation stratum for donor (all operators) and33recipient ($\Omega$ excluded), mean over three seeds (bars) with per-seed values (open markers) and the34majority-class chance level (grey dashes).}35\label{fig:gap}\end{figure}3637\subsection{Gate C: hooks are exact}38For all six pilot models, logits computed with (i) no hooks, (ii) capture hooks on all 27 hook points, and39(iii) a modifying hook registered but disabled are bitwise identical on 256 items, and repeated runs are40bitwise identical on MPS; the same modifying hook, when enabled, changes the output. The MLX backend passes41the same test on Qwen2.5-1.5B and Llama-3.2-3B (\url{tests/integration/test_mlx_noop.py}).4243\subsection{RQ1: where the donor executes $\Omega$}44On 490 clean/corrupted pairs the clean run scores $1.000$ and the sham (corrupted run scored on the clean45answer) $0.000$ in every seed. Patching the clean activation into the corrupted run restores the clean answer46at rate $1.00$ when the residual stream at the \emph{read position} is patched at any layer, and $0.00$ at47every other position including the $\Omega$ token (Figure~\ref{fig:loc}). Within the read position, the48layer-0 attention output is sufficient ($1.00$; layers 1--3: $0.00$) and the layer-0--2 MLP outputs are49partially sufficient ($1.00$, $0.90$, $0.83$; layer 3: $0.17$). Zero-ablation at the read position reduces50accuracy to $0.04$--$0.09$ for the residual stream, $0.13$ for layer-0 attention and $0.21$ for the layer-051MLP, with no effect elsewhere. Head-level patching attributes most of the attention effect to layer-0 head~052($0.62$; heads 1--2: $0.16$, $0.04$). Repeating a sweep changes no entry and the heatmaps correlate across53seeds at $r \geq 0.96$. The candidate organ is therefore the post-layer-0 residual row at the read position.5455\begin{figure}[t]\centering56\includegraphics[width=\textwidth]{figures/fig_localization_patching_tier0.pdf}57\caption{Within-donor interchange interventions (mean of three seeds): restored-answer rate when the clean58activation at (layer, position) is patched into the corrupted run, for the post-block residual stream, the59attention output and the MLP output. The read position $r_1$ predicts $r_2$, the $\Omega$ step. Sham rate $0.00$.}60\label{fig:loc}\end{figure}6162\subsection{Confirmatory test of the primary hypothesis (preregistration v1.0)}63The frozen primary method is the activation graft at the recipient's post-layer-0 residual row at every read64position, $\alpha{=}1$, through an orthogonal Procrustes map (with isotropic scale) fitted on 3\,000 task-free65alignment items; the primary contrast is the control-adjusted effect $\Delta_T^{\mathrm{adj}}$ against the66sham map, paired on identical items, with cluster-bootstrap intervals over programs. On new evaluation and67alignment items (seed base 90\,000) the graft reaches target accuracy $0.966$ (sd $0.037$, min $0.889$ over the68nine donor--recipient pairs) from recipient baselines of $0.101$, $0.056$ and $0.057$ (chance $0.113$), with69control-stratum accuracy $0.992$ (min $0.946$). $\Delta_T^{\mathrm{adj}}$ is $+0.875$ on average70(sd $0.042$, min $+0.776$), and its lower 95\% bound exceeds the smallest effect of interest ($0.25$) in71\textbf{9 of 9} pairs (Table~\ref{tab:confirmatory}). \textbf{H2 (sufficiency) is supported.} H4 (retention72$\geq 0.95$ in every pair) is \textbf{not supported}: one different-initialization pair retains $0.946$ on the73control stratum; the other eight retain $\geq 0.985$. The sham map leaves the target stratum at $0.091$ and74destroys the control stratum ($0.100$); norm-matched random rows and shuffled-item rows behave the same;75shuffled-layer rows ($0.186$) and the unrelated-skill donor ($0.076$) leave the control stratum intact.7677\begin{table}[t]\centering\scriptsize78\caption{Confirmatory run \url{graft_tier0_confirmatory_0c2257f6803e}: target- and control-stratum79accuracy by condition, mean (sd) over same-initialization and different-initialization pairs, and the80control-adjusted effect against the sham map (mean of per-pair cluster-bootstrap estimates and bounds).81Families other than the activation graft are evaluated on the three matched-seed pairs.}82\label{tab:confirmatory}83\resizebox{\textwidth}{!}{\input{tables/tab_confirmatory}}84\end{table}8586\paragraph{Secondary pre-declared families (Holm over four).} Subspace graft with $k{=}8$ versus a random87subspace of the same dimension: $+0.850$ $[+0.837, +0.862]$ ($0.927$ vs $0.077$; control $1.000$). Donor-free88adapter graft versus the unmodified recipient: $+0.472$ $[+0.453, +0.490]$ ($0.544$; control $0.998$); the89saved adapter evaluated in a fresh process on new items reaches $0.344$ $[0.317, 0.372]$ from $0.115$90(control $0.979$). Weight graft of the donor's layer-0 block versus a shuffled-layer weight control:91$+0.556$ $[+0.537, +0.577]$ ($0.642$ vs $0.086$) at a retention cost (control $0.720$, min $0.310$). All three92are rejected at their Holm thresholds (bootstrap $p \leq 0.0003$). Rule versus cache (H5): the primary map93fitted only on $\Omega$ rows with operands in $\{0,\dots,5\}$ gives $\Omega$-step accuracy $0.941$94$[0.919, 0.960]$ on items whose operands are all seen and $0.768$ $[0.727, 0.808]$ on items whose operands are95all unseen (ratio $0.816 \geq 0.8$): \textbf{H5 is supported}; the donor-free adapter gives $0.702$ seen and96$0.000$ unseen, the predicted failure.9798\paragraph{Mechanism and portability (fixed tests, confirmatory items).} Ablating the donor's layer-099attention output at read positions gives $0.113$; rescue from an intact donor of another seed through the100task-free Procrustes map gives $1.000$, through a sham map $0.106$; the reverse graft leaves the donor at101$0.972$. Width mismatch (128 $\to$ 96): $0.901$ (control $1.000$) at layer 0 $\to$ 0 and $1.000$ at1021 $\to$ 1; depth mismatch (4 $\to$ 6): $0.783$ ($0.956$) at 0 $\to$ 0, $0.999$ at 1 $\to$ 1, $1.000$ at 1 $\to$ 2103and 2 $\to$ 2; stride-2: $0.386$, $0.760$, $1.000$, $1.000$ at layers 0--3. Sham maps: $0.08$--$0.13$ with the104control stratum destroyed (Figure~\ref{fig:portability}).105106\paragraph{Conventional learning on the same items.} A supervised affine adapter (same parameter count as the107adapter graft, 300 gradient steps on the 3\,000 alignment items with labels) and distillation from the donor's108output distributions both reach $1.000$ on both strata. Transplantation is not a cheaper way to learn109this task; it is a way to move the computation without labels or gradient steps.110111\begin{figure}[t]\centering112\includegraphics[width=\textwidth]{figures/fig_pareto_tier0.pdf}113\caption{Target-stratum accuracy versus control-stratum retention for every condition of the confirmatory run,114mean over same-initialization (left) and different-initialization (right) pairs. Green: graft families;115orange: controls; red: conventional-learning references; dotted line: recipient baseline.}116\label{fig:pareto}\end{figure}117118\begin{figure}[t]\centering119\includegraphics[width=\textwidth]{figures/fig_portability_tier0.pdf}120\caption{Donor $\times$ recipient target accuracy for the identity graft, the Procrustes map fitted on121$\Omega$ rows and the Procrustes map fitted on task-free rows (confirmatory items). Diagonal cells share the122initialization seed.}123\label{fig:portability}\end{figure}124125\begin{figure}[t]\centering126\includegraphics[width=0.85\textwidth]{figures/fig_layer_dose_tier0.pdf}127\caption{Left: donor-layer $\times$ recipient-layer grid of target accuracy for the task-free Procrustes128graft (matched seed-0 pair). Right: dose--response of target and control accuracy with graft strength129$\alpha$ at layer 0 $\to$ 0.}130\label{fig:layerdose}\end{figure}131132\begin{figure}[t]\centering133\includegraphics[width=0.5\textwidth]{figures/fig_subspace_tier0.pdf}134\caption{Target accuracy of the subspace graft as a function of its dimensionality $k$ (principal directions135of the mapped $\Omega$-contrast) against random subspaces of the same $k$; mean over matched-seed pairs.}136\label{fig:subspace}\end{figure}137138\begin{figure}[t]\centering139\includegraphics[width=\textwidth]{figures/fig_mechanism_tier0.pdf}140\caption{Left: donor ablation $\to$ loss $\to$ rescue chain (seed 0; rescue from intact donor seed 1 through the141task-free Procrustes map versus a sham map). Right: rule-versus-cache test; maps and adapters fitted on142$\Omega$ rows with operands in $\{0,\dots,5\}$, evaluated on items whose operands are all seen or all unseen143(cluster-bootstrap 95\% intervals).}144\label{fig:mechanism}\end{figure}145146\subsection{Tier 1: open-weight models}\label{sec:tier1}147148\paragraph{Capability gap and within-model localization (development split).} Run149\url{tier1_taskvector_e105e3d91386}. With $k{=}8$ demonstrations the three models solve antonyms150($0.88$--$1.00$), capitals ($1.00$) and ``add three'' ($0.86$--$1.00$) and fail the invented morphology151($0.33$--$0.40$); zero-shot accuracy is $0.16$--$0.25$ for antonyms and $0.00$ for the other tasks152(Table~\ref{tab:tier1loc}). Adding the task vector (few-shot minus zero-shot last-token state, demonstration153items only) to the zero-shot run restores antonyms to $0.84$--$0.88$ (Llama-3.2-3B layer 14, Qwen2.5-1.5B154layer 16, Qwen2.5-3B layers 25--29) and capitals to $0.82$--$1.00$ (layers 14--25); a random vector of equal155norm gives $0.00$--$0.06$ except for antonyms in Qwen2.5-1.5B ($0.47$, where any perturbation of the right156norm elicits single-word answers). ``Add three'' is vectorizable only in Llama-3.2-3B (layer 14, $0.80$) and157nowhere in the Qwen models; the morphology rule is vectorizable nowhere. Removing the vector's direction from158the few-shot state does not reduce few-shot accuracy ($0.91$--$1.00$): the direction is sufficient but not159necessary, i.e.\ the few-shot context encodes the task redundantly. Localization is therefore task- and160model-dependent, and the candidate organ exists only where the within-model test passes.161162\begin{table}[t]\centering\scriptsize163\caption{Tier-1 within-model localization (development split): zero-shot and few-shot accuracy, best layer,164accuracy with the task vector added to the zero-shot run, with a random vector of equal norm, and few-shot165accuracy with the vector's direction removed.}166\label{tab:tier1loc}167\resizebox{\textwidth}{!}{\input{tables/tab_tier1_localization_e105e3}}\\[4pt]168\resizebox{0.7\textwidth}{!}{\input{tables/tab_tier1_localization_eb5d09}}169\end{table}170171\paragraph{Alignment maps.} Fitted on 700 format-matched task-free prompts, Procrustes maps reach held-out172$R^2$ $0.29$--$0.59$ and ridge maps $0.18$--$0.81$ between last-token states of different models (in-sample173$0.65$--$0.82$ and $0.93$--$1.00$); random orthogonal maps are negative. Cross-model alignment of these states is174far weaker than in the micro-world.175176\paragraph{Cross-model transfer (development split; selection data).} Antonyms transfer in all four pairs:177the best development condition reaches $0.72$ (Qwen-3B $\to$ Qwen-1.5B, donor few-shot state replaced through178Procrustes at layer 16), $0.75$ (Qwen-1.5B $\to$ Qwen-3B, norm-rescaled Procrustes vector at layer 21),179$0.81$ (Llama-3B $\to$ Qwen-3B, CCA vector at layer 25) and $0.66$ (Qwen-3B $\to$ Llama-3B, Procrustes vector180at layer 14), against best null controls of $0.44$, $0.56$, $0.50$ and $0.38$ and own-vector ceilings of181$0.84$--$0.88$. The controls are not at chance for antonyms: an unrelated-task vector or a sham-mapped vector182raises antonym accuracy from $\approx 0.2$ to $0.4$--$0.6$, so part of the antonym effect is a non-specific183``answer with one word'' push. Capitals transfer in two pairs ($0.73$ Qwen-1.5B $\to$ Qwen-3B, Procrustes at184layer 28; $0.50$ Llama-3B $\to$ Qwen-3B, CCA at layer 18; controls $0.14$ and $0.27$) and not in the other two185($0.18$ and $0.05$). The donor few-shot state of a \emph{shuffled} query transfers antonyms as well as the186matched state ($0.72$ vs $0.72$; $0.81$ vs $0.81$): what moves is the task identity, not query content187(amendment A1). Transferred vectors leave the held-out next-token NLL within $\pm 0.1$ nats for antonyms and188raise it by $0.4$--$0.6$ nats for the capital vectors in the Qwen pairs; they do not change accuracy on the other189tasks (all $0.00$).190191\paragraph{Tier 2 (Qwen2.5-7B, development split).} Run \url{tier1_taskvector_eb5d091bf5ed} on a 96\,GB node.192Qwen2.5-7B-Instruct (28 layers, $d{=}3584$) localizes antonyms at layer 16 ($0.91$) and capitals at layer 11193($1.00$); the morphology rule and ``add three'' are not vectorizable in it. Within the Qwen family, antonyms194transfer in both directions at $0.84$ (7B $\to$ 3B: donor few-shot state through ridge at layer 25; 3B $\to$ 7B:195through Procrustes at layer 19) against null controls of $0.53$ and $0.59$; capitals transfer upward ($0.91$,1963B $\to$ 7B, ridge vector at layer 11; but the unrelated-task control already gives $0.77$ because the 7B197model's zero-shot capital accuracy, $0.23$, responds to any push) and not downward ($0.14$). Across families198(7B $\to$ Llama-3B) nothing transfers: antonyms $0.38$ against a control of $0.34$, capitals $0.05$199(Figure~\ref{fig:tier1}).200201\begin{figure}[t]\centering202\includegraphics[width=\textwidth]{figures/fig_tier1_transfer_e105e3.pdf}\\[3pt]203\includegraphics[width=0.78\textwidth]{figures/fig_tier1_transfer_eb5d09.pdf}204\caption{Open-weight models, development split: per pair and task, recipient zero-shot, few-shot (prompting205ceiling), recipient's own task vector (within-model ceiling), best transferred donor condition and best null206control. Top: Tier-1 pairs (laptop); bottom: Tier-2 pairs with Qwen2.5-7B (M3U96b).}207\label{fig:tier1}\end{figure}208209\paragraph{Confirmatory test (frozen rule, disjoint queries).} The rule (preregistration, D11 with amendments210A1--A2) fixes, per pair and task eligible by within-recipient sufficiency $\geq 0.5$, the development-selected211condition (map family, recipient layer, $\alpha$, add or replace) and tests it on the disjoint confirmatory212queries against the \emph{best} null control (norm-matched random, unrelated-task vector, sham map, mapped donor213zero-shot state), paired on items with an exact item bootstrap; H6 is supported for a pair if the lower bound214exceeds $0.10$ for at least two tasks. Run \url{tier1_taskvector_confirmatory_625c54bd186f}215(Table~\ref{tab:tier1conf}): antonyms transfer above the best control in all four pairs ($+0.16$, $+0.28$,216$+0.50$, $+0.25$; lower bounds $0.00$, $0.09$, $0.31$, $0.09$), capitals in two ($+0.36$ $[+0.14, +0.59]$217Qwen-1.5B $\to$ Qwen-3B; $+0.18$ $[+0.05, +0.36]$ Llama-3B $\to$ Qwen-3B) and not in the other two218($+0.09$, $-0.05$); ``add three'' does not transfer into Llama-3B although it is vectorizable there ($0.69$ own219vector, $0.00$ transferred). Under the frozen rule \textbf{H6 is partially supported} for Qwen-1.5B $\to$220Qwen-3B and Llama-3B $\to$ Qwen-3B (one task each with lower bound above $0.10$) and \textbf{not supported}221for Qwen-3B $\to$ Qwen-1.5B and Qwen-3B $\to$ Llama-3B. Transferred vectors never reach the recipient's own222vector ($0.82$--$0.91$) and the best transfers (antonyms into Qwen-3B from Llama-3B, $0.81$) equal the shuffled-query223diagnostic, confirming that what moves is the task identity. The null controls are far from chance for224antonyms ($0.31$--$0.44$), which is why the micro-world's unambiguous separation does not carry over: in these225models, part of ``doing the task zero-shot'' is a non-specific disposition that any vector of the right norm226elicits.227228\begin{table}[t]\centering\scriptsize229\caption{Tier-1 confirmatory test under the frozen rule (run \url{tier1_taskvector_confirmatory_625c54bd186f};230development selection from \url{tier1_taskvector_e105e3d91386}). ``own'' = recipient's own task vector at its231development-selected layer; ``selected'' = development-selected transfer condition; best null control = maximum232over norm-matched random, unrelated-task, sham-map and donor zero-shot conditions; shuffled-query diagnostic =233mapped donor few-shot state of a different query. Exact paired item bootstrap, 2\,000 draws.}234\label{tab:tier1conf}235\resizebox{\textwidth}{!}{\input{tables/tab_tier1_confirmatory_625c54}}236\end{table}237238\paragraph{Tier-2 confirmatory test.} Run \url{tier1_taskvector_confirmatory_532eb68bd5e2}. With Qwen2.5-7B239the pattern is the same (Table~\ref{tab:tier2conf}): antonyms transfer downward into Qwen-3B at $0.84$ against a240best null control of $0.31$ ($+0.53$ $[+0.34, +0.72]$; the recipient's own vector gives $0.91$) and upward into2417B at $0.75$ against $0.56$ ($+0.19$ $[+0.03, +0.34]$); capitals transfer upward at $0.86$ but the mapped donor242\emph{zero-shot} state already gives $0.73$ ($+0.14$ $[+0.00, +0.27]$) and downward only at $0.32$ against243$0.23$; across families (7B $\to$ Llama-3B) nothing transfers (antonyms $0.34$ vs $0.34$; capitals $0.00$ vs244$0.14$; ``add three'' $0.00$ against an own-vector ceiling of $0.71$). Under the frozen rule H6 is245\textbf{partially supported} for 7B $\to$ 3B and \textbf{not supported} for 3B $\to$ 7B and 7B $\to$ Llama-3B.246Scale does not rescue cross-family transfer in this design.247248\begin{table}[t]\centering\scriptsize249\caption{Tier-2 confirmatory test under the frozen rule (Qwen2.5-7B pairs on M3U96b; run250\url{tier1_taskvector_confirmatory_532eb68bd5e2}, development selection from \url{tier1_taskvector_eb5d091bf5ed}).251Columns as in Table~\ref{tab:tier1conf}.}252\label{tab:tier2conf}253\resizebox{\textwidth}{!}{\input{tables/tab_tier1_confirmatory_532eb6}}254\end{table}255