Эксперимент: Spectral subspace initialization for nonlinear teachers (#788)

{ "worked": true, "confidence": 8, "verdict": "Built a bounded supervised spectral covariance estimator and a small MLP initialization experiment. The independent population check confirmed the predicted rank-one signal scaling alpha=2rho across rho=0.125–2.0 with 0.16–0.56% relative error, while the independent-label null was approximately zero (-0.0010). Recovery rose substantially with sample ratio, and spectral initialization reduced test MSE from 2.965 to 1.683 versus Xavier after 180 steps. The exact phase boundary was only coarsely resolved, so the mechanism is supported but the transition estimate is not definitive.", "metrics": { "baseline": "Xavier MLP test MSE: 2.965 +/- 0.378 over 3 trials; null spectral overlap approximately 0.004-0.023 across tested n/d ratios.", "idea": "Spectral MLP test MSE: 1.683 +/- 0.051; rho=0.5 overlap increased from 0.091 at n/d=0.5 to 0.692 at n/d=8; measured population alpha matched 2rho with under 0.6% relative error." }, "how_to_run": "/home/maxwelhelp/main/bin/python3 spectral_experiment.py && /home/maxwelhelp/main/bin/python3 mechanism_checks.py", "files": [ "spectral_experiment.py", "mechanism_checks.py", "results.json", "mechanism_results.json" ], "limitations": "Only scalar responses and a rank-one quadratic teacher were tested. Matrix-valued lifted responses, multi-dimensional r>1 recovery, image inputs, larger dimension sweeps, exact Lanczos, FLOP-matched training, and a finely resolved phase transition were not tested." }