Эксперимент: Hankel Moment Regularizer (#1251)

{ "worked": false, "confidence": 9, "verdict": "Built a differentiable K=3 Hankel PSD regularizer and a fixed-seed toy response-fitting comparison against no regularization and pairwise log-convexity. The analytic mixture-of-exponentials check confirmed the valid moment sequence has nonnegative Hankel eigenvalues and that a perturbation creates a negative eigenvalue. In the learning experiment, Hankel regularization had worse test MSE than baseline (0.0001163 vs 0.0000871), did not reduce dense PSD violations (29.9% vs 29.9%), and cost 3.15x runtime, so the promised practical win was not observed.", "metrics": { "baseline": "test MSE 8.712e-05; mean absolute second difference 7.086e-05; dense Hankel violation fraction 29.9%; runtime 2.14 s", "idea": "test MSE 1.163e-04; mean absolute second difference 7.004e-05; dense Hankel violation fraction 29.9%; runtime 6.74 s, 3.15x baseline" }, "how_to_run": "/home/maxwelhelp/main/bin/python3 hankel_experiment.py", "files": [ "hankel_experiment.py", "results.json" ], "limitations": "This was a small synthetic scalar-response experiment with 18 noisy training points, one seed, K=3, and 700 optimization steps; no CIFAR, diffusion, calibration, multi-seed, FLOP-normalized, or larger-scale neural-network evaluation was performed." }