# Эксперимент: Ordered Diffusion Message Passing (#962)

{
  "worked": true,
  "confidence": 8,
  "verdict": "Built an ordered local Gaussian kernel with row-wise softmax normalization and a controlled 1D forecasting comparison. Observed drift-versus-beta slope was 0.1200 versus predicted 0.1200, drift-versus-epsilon slope was 1.000 versus 1.000, and the quadratic generator error was 0.0. Row sums were 1.0 and the infinity-norm nonexpansion check passed; ordered aggregation reduced toy next-state MSE by 22.8% with nearly unchanged entropy. This is a promising toy signal, not yet evidence for learned ordering on nonlinear SDE trajectories.",
  "metrics": {
    "baseline": "Symmetric Gaussian message passing: MSE 0.0216551, entropy 3.50168",
    "idea": "Ordered Gaussian message passing with oracle s(x)=x and beta=1.8: MSE 0.0167157, 22.81% improvement, entropy 3.48639; drift slope 0.1200 vs 0.1200 predicted; epsilon slope 1.000 vs 1.000 predicted; quadratic-generator max error 0.0"
  },
  "how_to_run": "/home/maxwelhelp/main/bin/python3 ordered_diffusion_experiment.py",
  "files": [
    "ordered_diffusion_experiment.py",
    "results.json"
  ],
  "limitations": "The forecasting test used a 1D smooth sine shift and oracle ordering s(x)=x rather than a learned MLP or hidden-time nonlinear SDE trajectories. It did not compare graph attention, train a next-state model, measure rollout error, or test high-dimensional data and learned bandwidths."
}