Эксперимент: Separable Ky-Fan spectral regularization (#1388)

{ "worked": true, "confidence": 8, "verdict": "Built separable PSD Kronecker-factor parameterization with exact factor-spectrum Ky-Fan/R1 bounds, plus a reproducible fitting experiment. The majorization claim held in all 100 trials with zero failures and only 3.2e-12 worst numerical slack; the R1 penalty lowered peak exact norm from 2.68 to 2.17, but final loss worsened from 0.0621 to 0.0748 and runtime rose from 11.0s to 14.6s. Thus the claimed spectral-control effect was observed, but this small task did not show a validation or optimization win.", "metrics": { "baseline": "final loss 0.06210; best loss 0.05583; max exact norm 2.6799; final norm 0.7381; 250/250 steps; 11.00 s", "idea": "R1 penalty: final loss 0.07479; best loss 0.06772; max exact norm 2.1670; final norm 0.7400; final exact norm/R1 0.904; 250/250 steps; 14.60 s. Verification: 0/100 failures, worst cumulative gap 3.18e-12." }, "how_to_run": "/home/maxwelhelp/main/bin/python3 experiment.py", "files": [ "experiment.py", "results.json" ], "limitations": "Only a tiny synthetic 27-dimensional tensorized regression task was tested; no MNIST/CIFAR, large operator, top-k penalty comparison, wall-clock factorization scaling study, or exploding-update regime was evaluated. The controller variant was exploratory and is not used as evidence for the penalty result." }