Эксперимент: Square-Root Error-Density Timestep Grid (#920)

{ "worked": true, "confidence": 9, "verdict": "Built a NumPy MVP for square-root error-density timestep grids, including quantile-grid construction, dense cost evaluation, pilot-density noise robustness, and a fixed-NFE Euler scheduler comparison. The mechanism manifested: adaptive cost converged to the predicted L²/(2N) bound (1.0003× at N=128), interval widths had 0.99999 log-correlation with a^-1/2, and scaling a by 0.25–16 left the grid unchanged while scaling cost exactly. The toy ODE showed 3.4–18.6× lower error than uniform spacing, but this is not evidence of CIFAR diffusion quality by itself.", "metrics": { "baseline": "Uniform-grid local cost at N=32: 0.18179; toy Euler absolute errors at N={8,16,32,64}: {0.68645, 0.06977, 0.03433, 0.01670}.", "idea": "Adaptive local cost at N=32: 0.08775, a 2.07× reduction; toy Euler absolute errors: {0.03685, 0.01837, 0.00947, 0.00487}, ratios versus baseline {0.054, 0.263, 0.276, 0.292}. Mechanism checks: bound ratio at N=128=1.00029, width log-correlation=0.999994, density-scale grid deviation=0 and cost ratios exactly matched scale." }, "how_to_run": "/home/maxwelhelp/main/bin/python3 adaptive_grid_experiment.py", "files": [ "adaptive_grid_experiment.py", "results.json" ], "limitations": "Only synthetic one-dimensional densities and a variable-stiffness scalar ODE were tested. No trained score network, CIFAR-10 samples, FID, precision/recall, likelihood, GPU timing, Jacobian Hutchinson estimator, cosine/log-SNR/Karras schedules, or end-to-end diffusion sampler was evaluated." }