Эксперимент: Scrambled Sobol Diffusion Ensembles (#851)

{ "worked": true, "confidence": 9, "verdict": "Built a self-contained toy scrambled-Sobol diffusion-transport MVP with exact change-of-variables weighting. The Jacobian check had absolute error 3.7e-11; observed unweighted bias matched the analytic quadratic prediction across lambda=0, 0.25, 0.5, 1.0, while weighting reduced bias at N=1024 to below 8e-5. Scrambled Sobol standard deviation scaled approximately N^-0.98 versus iid N^-0.43 at lambda=0.5, confirming the intended RQMC mechanism in this smooth toy setting.", "metrics": { "baseline": "IID Gaussian seeds: SD slope -0.427; at N=1024, SD 0.06957 and unweighted bias 0.70418 for lambda=0.5.", "idea": "Owen-scrambled Sobol seeds: unweighted SD slope -0.980 and N=1024 SD 0.003148; exact weighted estimator SD 0.000196 and bias -1.07e-5 at lambda=0.5. Predicted versus observed unweighted biases at lambda 0.25/0.5/1.0 were 0.32750/0.32680, 0.70428/0.70418, and 1.60571/1.60520." }, "how_to_run": "/home/maxwelhelp/main/bin/python3 sobol_diffusion_mvp.py", "files": [ "sobol_diffusion_mvp.py", "results.json" ], "limitations": "Only a smooth 2D analytic transport surrogate was tested, not a learned neural diffusion score or high-dimensional image sampler. The Jacobian and importance weight were available analytically; Hutchinson trace estimation, finite-step ODE error with a learned model, GPU performance, and wall-clock batching costs were not evaluated." }