# Эксперимент: Orthogonal-Rank Contextual Memory (#1263)

{
  "worked": true,
  "confidence": 7,
  "verdict": "Built a reproducible orthogonal-rank memory MVP and verified the core graph claim: the 13-vertex graph has chi(G)=4 while an explicit 3D real orthogonal representation exists, with a 3-clique proving xi(G)>=3. The width-3 GRU used 35% fewer parameters than width 4 and matched its toy-task accuracy (72.3%), while the orthogonality penalty reduced edge violation from 0.99 to 0.007. However, the task was weak and the penalty did not improve accuracy or loss, so this is evidence for structural compression rather than a demonstrated neural performance win.",
  "metrics": {
    "baseline": "Width-4 GRU: 177 parameters, long-sequence accuracy 0.7230, loss 0.5884, edge violation 0.9751.",
    "idea": "Width-3 orthogonal GRU: 115 parameters, long-sequence accuracy 0.7230, loss 0.5895, edge violation 0.0071; graph check chi=4, xi=3."
  },
  "how_to_run": "/home/maxwelhelp/main/bin/python3 experiment.py",
  "files": [
    "experiment.py",
    "results.json"
  ],
  "limitations": "Only one 13-vertex graph and one simple compatibility task were tested; the task has class imbalance and observed accuracy is close to the majority-class baseline. No longer sequence sweep, multiple seeds, FLOP-matched training, exact integer-programming coloring, or complex-valued representations were tested."
}