Эксперимент: Positive Mellin Mixture Gate (#1252)

{ "worked": false, "confidence": 9, "verdict": "Built a Positive Mellin Mixture Gate with nonnegative learned weights and rates, plus numerical checks for the gamma-normalization identity, complete monotonicity, log-convexity, and Hankel PSD structure. The mathematical claims were reproduced strongly: gamma identity error was 4.6e-13, all checked signed derivatives were positive, the minimum Hankel eigenvalue was 4.5e-6, and log-convexity slack was positive. However, in the equal-parameter toy regression the Mellin gate had worse extrapolation MSE than the free order MLP (2.10e-4 vs 5.84e-5), so the proposed practical generalization win was not observed.", "metrics": { "baseline": "Free order MLP, 37 parameters: train MSE 1.384e-4; held-out order extrapolation MSE 5.837e-5.", "idea": "Positive Mellin mixture, 37 parameters: train MSE 1.620e-4; held-out order extrapolation MSE 2.098e-4. Mathematical checks: gamma identity max error 4.552e-13; minimum signed derivative through order 4 = 6.530e-4; minimum 4x4 Hankel eigenvalue = 4.547e-6; minimum log-convexity slack = 3.650e-3." }, "how_to_run": "/home/maxwelhelp/main/bin/python3 experiment.py", "files": [ "experiment.py", "results.json" ], "limitations": "Only a small synthetic scalar gate-fitting experiment was tested; no CIFAR-10 diffusion U-Net, FID, denoising loss, timestep gradient variance, sampling speed, or larger-scale training evaluation was performed. The toy used one fixed random seed and one train/extrapolation split." }