Methods and experimental design
A preregistered Stage A comparison in which oracle information, execution depth, data, and optimization were held constant while the organization of procedural parameters changed.
A controlled test of cross-domain parameter sharing
The experiment used a synthetic typed relational world rather than natural language. Three domain renderers—PROGRAM, SCENE, and SET—expressed four operation families—LOOKUP, REVERSE, CHAIN, and LIFT. Every operation and every domain appeared in training, but three valid combinations did not: SET × REVERSE, SCENE × LIFT, and PROGRAM × CHAIN.
The experimental contrast changed where the procedural transition parameters were shared. All neural conditions received the same allowable oracle bindings and operation sequence, used the same fact and query encoder architecture, executed at most two steps, and were trained on the same frozen data with matched seed-specific data order.
PROGRAM · SCENE · SET
LOOKUP · REVERSE · CHAIN · LIFT
4 conditions × 6 settings
4 conditions × 5 seeds
Steps per primary run
Canonical learned tensors
The latent operation stayed fixed while the rendering changed.
Examples were generated from formally specified relational worlds with typed entities, ordered argument roles, and declared operation contracts. Domain-specific renderers changed the surface representation without changing the relevant semantics. This separation allowed the study to test domain–operation recombination, renderer robustness, and larger structural variation independently.
Valid operations in familiar domains, never paired during training.
- 01SET × REVERSE
- 02SCENE × LIFT
- 03PROGRAM × CHAIN
A bounded two-step executor with a restricted primitive interface.
The implementation prevents one module from seeing the whole problem and silently solving it outside the proposed procedure.
Two transformer layers, four attention heads, 192-dimensional fact vectors. Attention never crosses fact boundaries.
Query, domain, and two 64-dimensional role-preserving entity embeddings initialize a 192-dimensional state.
One selected 384-hidden-unit MLP updates the state per active step; maximum depth is two.
The decoder sees only the final normalized state—no oracle token, raw fact, or domain skip connection.
Four active operation-linked modules and four unused sentinels in Stage A.
No mixture, parallel expert aggregation, or learned route revision.
One-step tasks mask the second transition; two-step tasks require both evidence items.
All choices were frozen before sealed evaluation.
A pilot using seed 1101 evaluated all six combinations of learning rate {0.0001, 0.0003, 0.0006} and dropout {0.0, 0.1} for all four conditions, producing 24 equal-budget runs. The preregistered tie rule selected learning rate 0.0006 and dropout 0.0. Pilot runs did not enter claim statistics.
The primary matrix contained seeds 1101, 2202, 3303, 4404, and 5505 for each condition. Training used AdamW with batch size 256, 2,000 warmup steps, weight decay 0.01, gradient clipping at 1.0, and a 50,000-step fixed budget. Validation and checkpoint records were produced every 500 steps. Each run’s frozen checkpoint maximized observed-cell macro-validation accuracy.
Predictions were generated before labels entered the authorized aggregate stage.
The study separated model execution, sealed aggregation, and claim decisions to prevent evaluation data from influencing training or threshold selection.
- Stage 1Label-blind execution
Frozen checkpoints generated predictions, interventions, and neural-probe artifacts without sealed labels.
- Aggregate v4Authorized label join
Frozen outputs were joined to 51,600 sealed target rows without loading or executing models.
- Claim stageFrozen thresholds
Decision rules were applied after metrics were sealed; no threshold or status was changed during closeout.
Paired inference across both seeds and latent worlds
The primary effect was Δgeneralist = Acc(OPM_SHARED) − Acc(DOMAIN_GENERALIST) on the three withheld cells. Predictions were paired by model seed and external example key. A two-level bootstrap resampled model seeds, then world IDs within each selected seed, for 10,000 replicates using PCG64DXSM seed 99117.
H1 was supported only if the lower endpoint of the percentile 95% interval exceeded +0.02 and OPM interpolation accuracy was no more than 0.01 below both DOMAIN_GENERALIST and PROC_UNTIED. Low model quality was not an exclusion reason; all five declared seeds entered the analysis.