Эксперимент: Resolution-adaptive spectral front end (#1418)

{ "worked": false, "confidence": 8, "verdict": "Built a dyadic FFT resolution-adaptive spectral front end with the supplied risk terms, cutoff formula, noise-floor screening, and ridge-regression comparison in experiment.py. The math check showed the common-grid risk and grid floor decrease with increasing m, as expected. In repeated noisy-curve trials, adaptive screening helped at m=16 and 32 but fixed modes were better at m=64 and 128; the no-hint estimator also overestimated alpha and retained only 2 modes, so the promised general accuracy/resolution win was not established.", "metrics": { "baseline": "Fixed Fourier ridge regression MSE means at m=16/32/64/128: 0.01603/0.01157/0.00894/0.00831; retained modes: 8/12/12/12.", "idea": "Adaptive Fourier ridge regression with alpha=1.2 and s=0.8 hints MSE means at m=16/32/64/128: 0.01556/0.01138/0.00912/0.00856; retained modes: 3/3/3/3. Without hints, estimated alpha was approximately 2.96 and the selector retained 2 modes." }, "how_to_run": "/home/maxwelhelp/main/bin/python3 experiment.py", "files": [ "experiment.py", "results.json" ], "limitations": "This is a small synthetic scalar functional-regression proxy, not a neural operator or transformer. The main MSE comparison used supplied oracle alpha and s hints rather than fully estimated exponents; only five repetitions were run, no FLOP timing was measured, and independent train/test curves rather than paired physical trajectories were used across resolutions." }