# Эксперимент: Symmetry-Quotiented Local Correlation Encoder (#415)

{
  "worked": true,
  "confidence": 9,
  "verdict": "Built the symmetry-quotiented local P2 correlation encoder and numerically verified all three mechanism predictions. Across flip probabilities 0–1 and shell counts 1–4, transformed configurations had zero measured invariant-feature error, while raw-vector RMS differences remained about 0.79–0.87; P2 evenness also had zero error. In the toy phase experiment, the invariant autoencoder had lower reconstruction MSE (0.0233 vs 0.3236) and much stronger correlation with independently computed S (0.998 vs 0.143), although this is a small synthetic MLP-autoencoder test rather than a full Monte Carlo/CNN study.",
  "metrics": {
    "baseline": "Raw-vector AE: reconstruction MSE 0.323576; best absolute latent-S correlation 0.142525; transformed-copy raw RMS distance 0.787–0.872.",
    "idea": "Invariant local-correlation AE: reconstruction MSE 0.023321; best absolute latent-S correlation 0.997695; transformed-copy feature RMS error 0.0 for flip probabilities 0, 0.25, 0.5, 0.75, 1.0 and shells 1–4; P2 evenness maximum error 0.0."
  },
  "how_to_run": "/home/maxwelhelp/main/bin/python3 experiment.py",
  "files": [
    "experiment.py",
    "results.json"
  ],
  "limitations": "The data are synthetic isotropic/nematic orientation clouds, not Lebwohl–Lasher Monte Carlo configurations near a weak first-order transition. The comparison uses a fully connected autoencoder rather than a CNN, has one fixed seed and small sample count, and does not test contrastive training, temperature histograms, FLOPs, or scaling to larger lattices."
}