Эксперимент: Spectral quadrature features (#1161)

{ "worked": true, "confidence": 8, "verdict": "Built deterministic tensor Gauss-Hermite quadrature Fourier features for the Gaussian RBF kernel and compared them with iid Gaussian random Fourier features at matched widths. The claimed spectral phenomenon was observed: at 64 features, mean top-20 relative eigenvalue error was 0.125 for quadrature versus 0.231 for random features, and operator error was 2.23 versus 8.24; the trend was also favorable at 9, 36, and 64 features. The algebraic ZZ* identity, normalized nonnegative weights, and Weyl inequality check all passed, but the small kernel-ridge learning check favored random features (MSE 0.00064 versus 0.0357), so this is not an overall modeling win.", "metrics": { "baseline": "iid Gaussian RFF: top-20 relative eigenvalue error 0.764, 0.624, 0.408, 0.231 at widths 9, 16, 36, 64; operator error 24.32, 17.50, 11.57, 8.24; 64-feature ridge MSE 0.00064 +/- 0.00082 over 20 seeds.", "idea": "Gauss-Hermite quadrature: top-20 relative eigenvalue error 0.665, 0.525, 0.283, 0.125 at widths 9, 16, 36, 64; operator error 21.34, 9.90, 4.82, 2.23; 64-feature ridge MSE 0.0357." }, "how_to_run": "/home/maxwelhelp/main/bin/python3 spectral_quadrature_experiment.py", "files": [ "spectral_quadrature_experiment.py", "results.json", "run_output.txt" ], "limitations": "Only a 2D Gaussian RBF kernel, 120 synthetic points, tensor Gauss-Hermite rules, and a scalar small-data ridge task were tested. No PCA MNIST/CIFAR benchmark, higher-dimensional quadrature, classification, runtime/memory profiling, or learned/adaptive quadrature was evaluated; the ridge result is based on one fixed train/test split." }