When Do Shared Training Trajectories Help a New Model?

The system trains small two-hidden-layer parity MLPs with 16 input bits, width 64, two output classes, AdamW learning rate 0.01, weight decay 1e-4, batch size 64, and a 400-step maximum horizon. Model-zoo trajectories share the exact initialization at seed 12345. A rank-32 SVD basis represents centered final parameter changes; ridge heads predict both remaining displacement and time. Candidate weight jumps are scaled, norm-clipped, and gated by validation loss and counterfactual geometry. Results charge observer, validation, and inference work to online example-equivalents, and report model-zoo training separately.

Frozen v4 used 60 successful parity trajectories (orders 2 and 3), a rank-16 time gate, and a single proposal at step 100 if at least 125 steps were predicted to remain. It evaluated 90 new episodes at offset 800. The nested-majority zero-shot gate reused this parity-only controller without retraining and evaluated 90 tasks at offset 1000. The final multi-family evaluation added 60 nested-majority trajectories to the 60 parity trajectories, calibrated separately, then froze a rank-64 displacement model and rank-32 time gate. It proposed at step 150 only when at least 90 steps remained, used 32 labeled validation examples plus 16 metamorphic probes as guards, required no validation-loss increase and at most 0.10 residual increase, and used episodes 3000–3089.

The publication date is 2026-10-18; experiments are documented in local reports from earlier dates. No trained model checkpoint files were located in the scoped source folders; result JSON files contain metrics and denoiser diagnostics, not deployable weights.

The drivers require Python, PyTorch, and NumPy. Example commands from the repository root are `python projects/geometric-meta-optimization/experiments/geometric_trajectory_denoiser.py --model-zoo-episodes 60 --evaluation-episodes-per-family 45 --evaluation-offset 800 --input-bits 16 --width 64 --base-seed 12345 --learning-rate 0.01 --train-size 2048 --validation-size 128 --horizon 400 --interval 50 --proposal-step 100 --minimum-predicted-remaining-steps 125 --rank 32 --gate-rank 16 --prediction-scale 0.40 --output /tmp/parity-v4.json` for the parity driver, and `python projects/geometric-meta-optimization/experiments/geometric_nested_majority_transfer.py --model-zoo-episodes 60 --majority-model-zoo-episodes 60 --evaluation-episodes 90 --evaluation-offset 3000 --input-bits 16 --width 64 --base-seed 12345 --learning-rate 0.01 --train-size 1024 --validation-size 128 --horizon 400 --interval 50 --proposal-step 150 --rank 64 --gate-rank 32 --minimum-predicted-remaining-steps 90 --prediction-scale 0.30 --maximum-validation-loss-ratio 1.0 --guard-validation-size 32 --guard-probe-size 16 --output /tmp/multifamily.json` for multi-family evaluation. The zero-shot report used the transfer driver’s parity-only configuration and episode offset 1000, as specified in the protocol. Commands rerun the experiments; none were run for this article.

The parity result is a useful gain for models sharing architecture and initialization. The zero-shot failure demonstrates that a guard can protect individual candidate updates without making the overall controller worthwhile: frequent probes and rejected proposals still cost compute, and parity-derived directions were mismatched to nested-majority trajectories.

The multi-family result supports a narrower transfer claim. Including examples of the target structure recovered a positive online saving, but the 2.02% gain is smaller than the parity-only gain and far from paying back the offline corpus over a small number of uses. Optimizer-state clearing after accepted updates and a post-jump training interval were part of the calibrated repair, not evidence that the original zero-shot controller worked.

These experiments use synthetic tasks, a small MLP, and exact shared-base initialization. Weight-space alignment is a major assumption; arbitrary independently initialized or downloaded networks can have functionally equivalent but differently arranged parameters.

Example-equivalents are an accounting proxy, not measured latency or energy. Amortization assumes future runs achieve the same saving and can reuse the compatible model zoo. The final nested-majority cohort passed its predefined rule, but the bootstrap interval and single frozen cohort do not guarantee broader transfer. No trained weights were found in the inspected source folders; diagnostic JSON records results rather than model checkpoints.