# Эксперимент: Spectral Cross-Block Averaging Layer (#1020)

{
  "worked": true,
  "confidence": 9,
  "verdict": "Built and numerically verified the Spectral Cross-Block Averaging Layer on a reversible synthetic Markov chain. The direct weighted-Frobenius, trace, and chi-squared formulations of F agreed within 5.5e-16; across eight valid spectral regimes, the bottom-P² partition matched the predicted F=alpha² with maximum error 1.6e-16, and random partitions had strictly positive spectral-bound gaps. The block-sum implementation was exactly equivalent to dense Gibbs averaging and was 13.3x faster at n=1200, d=16, although no end-to-end GNN accuracy experiment was run.",
  "metrics": {
    "baseline": "Random partition F mean=0.15697; top nonconstant-mode partition F=0.16000; dense Gibbs averaging=15.264 ms/call.",
    "idea": "Bottom-P² spectral partition F=0.03240 versus spectral eigenvalue 0.03240; F scaling maximum absolute error=1.53e-16; block-sum averaging=1.144 ms/call, 13.34x faster than dense Gibbs averaging; centered feature variance ratio after averaging=0.0100."
  },
  "how_to_run": "/home/maxwelhelp/main/bin/python3 spectral_cross_block.py",
  "files": [
    "spectral_cross_block.py",
    "results.json",
    "run_output.txt"
  ],
  "limitations": "Tested only synthetic reversible chains with uniform stationary distribution and two blocks. The spectral eigensolver used dense NumPy matrices, weighted k-means and multiway partitions were not implemented, and there was no Cora, learned P_theta, end-to-end GNN training, GPU benchmark, memory benchmark, or accuracy comparison."
}