# Эксперимент: Randomized-QMC gradient batches (#944)

{
  "worked": true,
  "confidence": 8,
  "verdict": "Built randomized-shift Sobol sampling with inverse-normal transformation, toy prediction sweeps, gradient-variance measurement, and equal-step neural training comparison. The mechanism manifested: smooth-integrand RMSE scaled as n^-1.19 for QMC versus n^-0.51 for IID, estimated shift bias was 0.00092, and gradient-component variance was reduced by 85.2%. The dimension sweep showed the expected degradation, while training ended slightly better with QMC (0.0205 vs 0.0237), although IID reached a lower best transient loss, so the optimization win is promising but not conclusive.",
  "metrics": {
    "baseline": "IID: smooth RMSE slope -0.511; gradient variance 0.001516; final training loss 0.02369; best training loss 0.01477.",
    "idea": "Randomized shifted Sobol: smooth RMSE slope -1.187; mean estimate absolute bias error 0.000918; gradient variance 0.000224 (85.2% reduction); final training loss 0.02048; best training loss 0.01929. At dimension 16, QMC/IID RMSE ratio was 0.81, versus 0.06 at dimension 2."
  },
  "how_to_run": "/home/maxwelhelp/main/bin/python3 qmc_experiment.py",
  "files": [
    "qmc_experiment.py",
    "results.json"
  ],
  "limitations": "This is a small synthetic expectation model rather than CIFAR-10, VAE, or diffusion. Only one seed and one neural training trajectory were used; the implementation tests random shifts rather than full Owen-scrambled Sobol, and no wall-clock/FLOP benchmark or multiple independent optimization runs was performed."
}