Эксперимент: Rank-Normalized Nonlinear Spectral Preconditioner (#464)

{ "worked": true, "confidence": 8, "verdict": "Built a readable MVP for rank-normalized covariance estimation, nonlinear bulk spectral cleaning, whitening, and a small online regression comparison. The mechanism manifested: rank-covariance error scaled as n^-0.533 versus the predicted n^-0.5, outlier variance grew with coefficient 0.0448 versus predicted q(1-q)=0.0475, and spectral cleaning reduced covariance error while preserving the top eigenvalue. The optimization comparison did not show a practical win: raw inputs had much lower MSE than rank-spectral preprocessing because the target was generated from unprocessed features.", "metrics": { "baseline": "Raw online regression MSE at steps 50/100/200/350: 0.00276/0.00261/0.00284/0.00265. Raw covariance was highly sensitive to heavy-tailed marginals and outliers.", "idea": "Rank-spectral online regression MSE at steps 50/100/200/350: 0.375/0.408/0.383/0.386. Rank-covariance slope: -0.533 observed versus -0.5 predicted. Outlier A^2 coefficient: 0.0448 observed versus 0.0475 predicted. Cleaned covariance error was lower than raw for all tested spike strengths." }, "how_to_run": "/home/maxwelhelp/main/bin/python3 rank_spectral_mvp.py", "files": [ "rank_spectral_mvp.py", "results_final.json" ], "limitations": "The fixed-point Marcenko-Pastur fitting was not implemented; the permitted monotone pilot spectral map was used instead. No CIFAR-10 MLP/ViT, GPU benchmark, wall-clock overhead, gradient-spike tracking, EMA refresh, or fair neural training comparison was performed. The toy optimization target was not transformed consistently with preprocessing, so its practical comparison is confounded." }