# Эксперимент: Maximum-Entropy Relational Block Kernel (#510)

{
  "worked": true,
  "confidence": 9,
  "verdict": "Built a finite stochastic-block relational kernel with exact edge, wedge, and triangle motif statistics, entropy-constrained fitting, and factorized message propagation. The mechanism manifested: sampled triangle RMSE scaled as n^-0.492 versus the predicted n^-0.5, entropy increased monotonically as triangle constraints moved away from the homogeneous solution, and heterogeneity increased monotonically. Block propagation matched dense propagation to 7.1e-15 relative error while using 666x less kernel storage and running 14.9x faster in this NumPy benchmark.",
  "metrics": {
    "baseline": "Dense relational kernel: 77,760,000 bytes and 0.4408 seconds propagation at n=1800, r=3, hidden size 32.",
    "idea": "Factorized block kernel: 116,736 bytes and 0.0297 seconds propagation, yielding 666.1x memory reduction and 14.9x speedup; maximum relative numerical error 7.1e-15. Motif RMSE log-log slope was -0.492 versus predicted -0.5; maximum edge and triangle constraint errors were 3.3e-15 and 4.3e-14."
  },
  "how_to_run": "/home/maxwelhelp/main/bin/python3 experiment.py",
  "files": [
    "experiment.py",
    "results.json"
  ],
  "limitations": "Only a NumPy toy benchmark was tested; no Cora or ogbn-arxiv dataset, learned node assignments, task accuracy, CUDA benchmark, multi-relation motif constraints, or end-to-end GNN training was evaluated. Entropy optimization used small m and SLSQP, so global optimality was not established."
}