# Эксперимент: Path-Holonomy Attention (#1240)

{
  "worked": true,
  "confidence": 8,
  "verdict": "Built a PyTorch MVP of Path-Holonomy Attention with ordered matrix products, learned reversal/color maps, and a soft color-switch involution penalty, plus a commutative additive baseline. The numerical check reproduced noncommutativity (||AB-BA||_F=1.4142), exact ordered composition (error 0), and additive order collision (0 difference). On the synthetic order-sensitive task, holonomy achieved 1.000 test accuracy versus 0.749 for the additive baseline, reproduced with an independent seed.",
  "metrics": {
    "baseline": "test accuracy 0.7485; train accuracy 0.7544",
    "idea": "test accuracy 1.0000; train accuracy 1.0000; math ||AB-BA||_F=1.4142, composition error=0"
  },
  "how_to_run": "/home/maxwelhelp/main/bin/python3 holonomy_experiment.py",
  "files": [
    "holonomy_experiment.py",
    "results.json",
    "results_seed235.json"
  ],
  "limitations": "Only a small synthetic length-3 binary task was tested; no real graph, molecular, knowledge-graph, GAT, Graphormer, throughput, parameter/FLOP matching, cycle-consistency loss, or robustness-to-orientation benchmark was evaluated. The observed win demonstrates the proposed order-preserving mechanism, not broad real-world superiority."
}