Эксперимент: Moment-Sharp Spectral-Norm Control (#1391)

{ "worked": true, "confidence": 8, "verdict": "Built a readable K=2 moment-sharp spectral bound using the closed-form extremizer, plus exact/Hutchinson moment utilities and a reproducible digits MLP control experiment. Numerical checks showed the bound was always above the true spectral norm and exactly recovered a two-cluster spectrum (9.0); in training, moment rescaling reduced the maximum true singular value from 3.127 to 1.544 but reduced validation accuracy from 96.7% to 94.0% and increased runtime from 0.657s to 0.860s. Thus the claimed sharp-bound phenomenon is real, but this small control experiment does not show a practical optimization or accuracy win.", "metrics": { "baseline": "Digits MLP: loss 0.0413 mean-last-20, validation accuracy 0.9667, max gradient norm 0.830, max true sigma 3.127, runtime 0.657s.", "idea": "K=2 rescaling: loss 0.2791 mean-last-20, validation accuracy 0.9400, max gradient norm 0.779, max true sigma 1.544, K=2 bound max sigma 2.000, runtime 0.860s; sanity checks had no upper-bound violations and exact clustered recovery at 9.0." }, "how_to_run": "/home/maxwelhelp/main/bin/python3 moment_sharp.py", "files": [ "moment_sharp.py", "results.json" ], "limitations": "Only K=2 with exact matrix SVD moments was used in the controller; K=3, actual Hutchinson-noisy control, convolutional layers, CIFAR-10, power-iteration baseline, matched FLOPs, robustness, and multi-seed testing were not evaluated. The Hutchinson check used a diagonal matrix and many probes, so it does not characterize estimator variance for dense layers." }