Эксперимент: Variable-Projection Adaptive Fourier Layer (#969)

{ "worked": false, "confidence": 9, "verdict": "Built a NumPy/SciPy variable-projection Fourier MVP with complex ridge solves, direction optimization, Gramian inspection, and a fixed-random-feature comparison. Two quantitative mechanism checks passed: ridge objectives increased monotonically with lambda, and the near-duplicate Gramian eigenvalue scaled quadratically with angular separation (observed exponent 1.982 versus predicted 2.0). Direction recovery failed and the optimized model did not beat the fixed random baseline, so the full mechanism was not demonstrated.", "metrics": { "baseline": "Fixed random 3-feature dictionary: mean relative field error 0.8861 +/- 0.2149; one draw 0.7657; coefficient-fit time 0.00034 s.", "idea": "Variable projection: relative field error 0.9767; 3/3 features retained by the 1e-3 Gramian cutoff; optimization time 0.0697 s. Ridge objective increased from 0.2901 at lambda=0 to 2.2291 at lambda=1.0, while coefficient norm decreased from 1.9498 to 1.9282. Duplicate-direction eigenvalue log-log exponent was 1.9824. Direction-recovery errors for 30, 60, 120, and 240 samples were 3.286, 3.044, 3.763, and 4.147 radians." }, "how_to_run": "/home/maxwelhelp/main/bin/python3 vp_fourier_mvp.py", "files": [ "vp_fourier_mvp.py", "results.json" ], "limitations": "Only a small 2D synthetic regression was tested; no PINN/PDE residual training, MLP integration, adaptive feature birth or pruning during optimization, weighted nonuniform samples, L-BFGS/Adam comparison, or GPU implementation was tested. The direction optimizer was derivative-free and multimodal, so failed recovery may reflect optimization difficulty as well as method limitations." }