PRECOG — Can Pre-Training Signals Predict Trainability?

A research prototype testing whether "zero-cost" signals computed on an untrained network (before a single optimizer step) can predict which hyperparameters will actually train well. Full spec in docs.md.

This is a curated subset of a larger project. It exists to show three things honestly, in order: a real positive finding, a headline number that turned out to be wrong and how we caught it, and a mechanistic bug we found but could not fix. If you work in NAS / zero-cost proxies / meta-learning, the last two sections are where we'd like your help.

TL;DR

• Best method found: jacob_cov (NASWOT, Mellor et al. 2021), used directly as a decision rule with zero training, zero learned model — beats 4 RandomForest variants, a Gaussian Process, KNN, and 3 different ways of combining proxies. 47% top-1 accuracy picking the best of 3 init methods (baseline: 38%), and a much lower decision-regret than every alternative (+14.6 mean steps vs +32.9 for the best learned model).
• Our own headline ranking-correlation number (ρ=0.670) was a small-sample overestimate. Rechecked at 26x the sample size: ρ=0.395-0.540. We kept both results and the script that found the discrepancy — see below.
• jacob_cov (and 2 other proxies) can provably never recommend one of our 3 candidate init methods, for a reason that's mathematical, not a data problem. We could not fix it. Details below.

1. What actually works

precog/trainability.py implements 11 zero-cost proxies (SynFlow, SNIP, GraSP, Jacob-Cov/NASWOT, effective rank, Hessian trace, Jacobian conditioning, gradient statistics, ZiCo). scripts/compare_meta_predictors.py evaluates every method — RandomForest (full/reduced features, log-target), Gaussian Process, k-NN, raw proxy heuristics, learned/rank/naive proxy combinations — on one locked test split (60 tasks never touched during development), reporting both top-1 accuracy and regret (steps(predicted) - steps(true_best), since a wrong call that costs 5 extra steps and one that costs 700 are not the same mistake).

Full comparison table: results/reports/...compare_meta_predictors.md

The winner, every time we've re-run this, is the simplest thing on the list: rank the 3 candidates by their raw jacob_cov score, no model at all. Every attempt to do better with more sophistication failed:

Combination method	Ranking correlation (ρ)
naive z-score average	0.365
AZ-NAS-style rank aggregation (CVPR 2024)	0.410
learned linear combination (Ridge, proper Leave-One-Task-Out CV)	0.504
best single proxy alone	0.540

The Ridge result is the one we think is most worth a second pair of eyes: in-sample (no held-out task) it reaches ρ=0.845 — a textbook illustration of overfitting with 11 features on a dozen tasks — which is exactly why we insist on Leave-One-Task-Out grouping, not row-level CV (each task contributes 3 correlated rows, one per candidate). Full writeup: results/reports/...explore_learned_combination.md

2. The number we got wrong, and how we caught it

Our first controlled experiment (scripts/gate1_ranking.py, n=36: 12 tasks x 3 init methods) found gradient_norm_variance correlating with real convergence speed at ρ=+0.670 (report). We used this number in design decisions and reported it as the project's strongest result.

It didn't hold. scripts/gate1_ranking_at_scale.py reruns the identical correlation on the full meta-dataset (n=936: 312 tasks, same controlled design, zero new training runs — the data already existed) and finds ρ=0.395 for that same proxy. The actual best individual proxy at this scale is gradient_norm (ρ=0.540, down modestly from 0.607). Every proxy shrinks by some amount; two combination methods shrink too. Full correction.

We saw the same pattern independently for learning-rate prediction: a screen at n=12 found gradient_norm correlating with optimal LR at ρ=-0.726 (p=0.0076); scaled to n=40, it dropped to ρ=-0.343 (still significant, far weaker). Report.

We're flagging this loudly because we don't think we're unusual — a lot of n=12-36 zero-cost-proxy correlation numbers get published and cited without ever being rechecked at 10-30x the sample size. Ours didn't survive that check unscathed and we'd rather say so than not.

3. A bug we found but can't fix

While digging into why our best method (jacob_cov) never once recommends "He init" across 60 test tasks — even the 10 where He genuinely is fastest — we found the cause is not statistical, it's structural:

jacob_cov (NASWOT) scores a network by the binary activation-sign pattern it produces on a batch (sign(activation) > 0). Xavier and He initialization, for a network with zero-initialized biases, draw from the same underlying Gaussian random values (same shape, same global RNG state under the hood) and only differ in the positive scalar they scale those values by. Scaling every layer's weights by a positive constant does not change the sign of any activation. So:

jacob_cov(He-init network)  ==  jacob_cov(Xavier-init network)

exactly, for the same random seed. We checked: max difference across all 312 tasks in our meta-dataset is 0.0. Not close to zero — exactly zero. Two other proxies we use (effective_rank, entropy of normalized singular values; jacobian_condition_mean, a singular-value ratio) turn out to have the same property for the same reason — any proxy built from a scale-invariant statistic cannot see this distinction. Full audit of all 11 proxies.

We tried two fixes:

1. Break jacob_cov ties with gradient_norm (which does differ by init). Failed — gradient_norm(He) turned out to be higher than gradient_norm(Xavier) on all 312/312 tasks (a fixed ~2.3x scale ratio from He's larger init std), so the tiebreak picks Xavier deterministically too, just for a different reason.
2. Z-score gradient_norm against each init family's own population statistics before comparing (removing that fixed offset). This made things worse (33% accuracy vs 47%), suggesting there's close to no real task-dependent signal left in gradient_norm once you remove the scale confound.

We don't have a third idea from the zero-cost literature we haven't already tried. If your first thought is "why not proxy X" — there's a real chance we tried it; check the full report first. If it's a proxy family we haven't touched (something sensitive to task-dependent absolute scale, not just a fixed per-init offset), that's exactly the kind of comment we're hoping for.

4. Generalization: does it know anything, or does it just remember?

We held out one entire synthetic task family from training and tested only on it (3 folds). The learned RandomForest's regret on its worst held-out fold is 2.2x its in-distribution regret (+73.6 vs +32.9 mean steps) — concrete evidence it's partly memorizing per-family patterns, not learning a family-independent notion of trainability. The training-free jacob_cov heuristic degrades far more gently across every fold. Report.

Reproduce it

pip install -r requirements.txt
python scripts/gate1_ranking.py              # the original (overestimated) result
python scripts/gate1_ranking_at_scale.py     # the correction, on data already in data/meta_dataset.db
python scripts/explore_scale_invariance_blindspot.py   # the Xavier/He proof
python scripts/compare_meta_predictors.py    # full method comparison + regret

data/meta_dataset.db ships with the repo (2.5MB, 312 tasks / 936 controlled experiments) so the scale-corrected results reproduce without rerunning any training.

What this is not

Not a finished system. No gate in the full spec's success criteria is met yet (see docs.md §17, §26). This is a snapshot of an ongoing, openly-documented research effort — the full project (40+ dated reports, every negative result kept) lives at github.com/NEURAX-canvas/PRECOG.

Repository layout

docs.md / stack.md / source.md   full spec, tech-stack rationale, bibliography
precog/                          the engine: encoders, Trainability Engine,
                                  Meta-Predictor, Search Engine (see docs.md §9)
scripts/                         every experiment referenced above, runnable as-is
results/reports/                 the dated, evidence-first writeup for each finding
data/meta_dataset.db             312 tasks x 936 controlled experiments (SQLite)
.github/workflows/reproduce.yml  CI: reruns every script above on each push

Contributing

main is protected — every change goes through a reviewed PR with CI green. See CONTRIBUTING.md for what that means in practice here (short version: no claim without a script and a number behind it, negative results welcome).

Citing this work

See CITATION.cff. This is an active research snapshot, not a peer-reviewed publication — cite accordingly.

License

MIT.