# Эксперимент: Volume-Mass Diffusion GNN (#459)

{
  "worked": true,
  "confidence": 9,
  "verdict": "Built a seeded MVP for Volume-Mass Diffusion on a 120-node stochastic-block-model graph, including stable Euler propagation, volume sweeps, spectral checks, localization statistics, and a matched two-layer GCN comparison. The mechanism manifested: the measured Euler instability boundary was 0.07828 versus the predicted 0.07808, modal decay matched theory, the similarity-transform eigenvalue error was 1.2e-13, and lognormal ratio heterogeneity correlated with top-mode IPR at 0.80. Classification showed no improvement on this easy graph: both models reached 1.0 test accuracy, with slightly higher intermediate losses for mass diffusion.",
  "metrics": {
    "baseline": "Standard self-loop row-normalized GCN: losses at steps 50/100/250 = 0.04238/0.02324/0.01901; test accuracy = 1.00.",
    "idea": "Volume-mass diffusion with v=k and eta=0.8*(2/lambda_max): losses at steps 50/100/250 = 0.04403/0.02453/0.02003; test accuracy = 1.00. Predicted versus observed stability boundary = 0.07808 versus 0.07828; localization correlation between std(log r) and top-mode IPR = 0.80."
  },
  "how_to_run": "/home/maxwelhelp/main/bin/python3 experiment.py",
  "files": [
    "experiment.py",
    "results.json",
    "results.txt"
  ],
  "limitations": "Only one small dense SBM and one train/test split were tested. Cora, sparse scalability, learned positive gates, metadata volumes, multiple classification seeds, runtime/FLOPs, and harder accuracy benchmarks were not tested. The localization sweep supports the predicted trend but includes a non-monotonic degree-power parameterization and only eight lognormal replicates per level."
}