# Эксперимент: Semantic Pushforward Uncertainty Head (#432)

{
  "worked": true,
  "confidence": 8,
  "verdict": "Built a finite-state semantic pushforward and calibrated uncertainty head MVP. The core aggregation identity was exact up to floating-point error, and synonym redistribution preserved state probabilities. Across gamma values 0.5–2.0, fitted calibration slopes satisfied gamma*a approximately 1 (0.916–1.026), while calibration substantially reduced posterior TV and ECE; this confirms the proposed mechanism in the controlled synthetic setting.",
  "metrics": {
    "baseline": "At gamma=2.0: NLL 0.8894, Brier 0.4904, TV 0.1420, ECE 0.1324, 90% set coverage 0.8884.",
    "idea": "At gamma=2.0: calibrated NLL 0.7791, Brier 0.4599, TV 0.0070, ECE 0.0175, 90% set coverage 0.9680; pushforward and synonym-splitting errors were 0.0 and 1.11e-16."
  },
  "how_to_run": "/home/maxwelhelp/main/bin/python3 experiment.py",
  "files": [
    "experiment.py",
    "results.json",
    "README.md"
  ],
  "limitations": "This is a controlled synthetic experiment rather than a transformer integration: candidate response probabilities are generated analytically, not obtained from token log-probabilities. It does not test prompt sensitivity, malformed LM outputs in practice, real semantic-map errors, compute overhead, or calibration transfer under distribution shift; the optimizer reported non-success despite converging to useful parameters for gamma 0.5 and 2.0."
}