# Эксперимент: Fermionic circuit message passing (#578)

{
  "worked": true,
  "confidence": 8,
  "verdict": "Built a degree-2 truncated fermionic message-passing GNN with separate even and odd edge channels, skew-symmetric wedge aggregation, and odd-degree vanishing. The quantitative checks confirmed zero contribution for odd local degree, exact parity transfer across cycle masks, and the predicted wedge-energy scaling 2d(d-1) (observed/predicted ratios 0.984–1.003). On the tiny cycle-versus-path extrapolation task, baseline GIN scored 0.50 and the fermionic model scored 1.00, so the mechanism manifested and also produced a promising toy-task gain; this is not evidence of broad superiority.",
  "metrics": {
    "baseline": "GIN: 0.50 accuracy on 10 longer test graphs (nodes 11-15), trained on nodes 6-10",
    "idea": "Fermionic degree-2 odd-channel GNN: 1.00 accuracy on the same test set; odd-degree residual 0.0; parity max error 0.0 for cycle sizes 1-8; wedge-energy ratios observed/predicted: 1.003, 0.984, 0.998, 0.992 for dimensions 2,4,8,12"
  },
  "how_to_run": "/home/maxwelhelp/main/bin/python3 fast_mvp.py",
  "files": [
    "fast_mvp.py",
    "results_final.json",
    "results.json",
    "run_output.txt",
    "fermionic_mvp.py"
  ],
  "limitations": "Only a synthetic cycle-versus-path task was tested, with one seed and a very small dataset; no molecular benchmarks, multiple seeds, FLOP-matched timing, explicit circuit regrouping, higher exterior degrees, or CUDA comparison was evaluated. The parity sweep uses closed cycle masks and therefore has only two surviving masks per cycle size."
}