# Эксперимент: Jacobian-Ranked Simplex Features (#1258)

{
  "worked": true,
  "confidence": 8,
  "verdict": "Built a differentiable Heron area feature and Jacobian-based weighting prototype in experiment.py. The supplied 4×9 Jacobian was verified to numerical precision (maximum error 6.7e-16) under the paper’s squared-edge-length convention, with full rank and smallest singular value 2.70 for the test configuration. In a five-split angle-sensitive invariant triangle regression, distance-only RMSE was 0.0915, area augmentation 0.0591, and Jacobian-weighted area 0.0561, indicating a reproducible but modest improvement over unweighted area features.",
  "metrics": {
    "baseline": "Distance-only mean test RMSE 0.09154 ± 0.01082 across 5 splits",
    "idea": "Distance + Jacobian-weighted Heron area mean test RMSE 0.05613 ± 0.00609; unweighted distance+area was 0.05912 ± 0.00602"
  },
  "how_to_run": "/home/maxwelhelp/main/bin/python3 experiment.py",
  "files": [
    "experiment.py"
  ],
  "limitations": "This is a small triangle-level regression benchmark rather than QM9, ModelNet40, or a full EGNN/hypergraph message-passing model. The weighting uses the scalar Heron-area Jacobian norm for each triangle, not batched multi-output simplex selection, attention, rank loss, FLOP accounting, or a learned end-to-end Jacobian schedule. Rigid-motion invariance was numerically checked for features, but transformed-input prediction equivalence was not separately evaluated."
}