# Эксперимент: Conjugate Bayesian Latent Dynamics Head (#562)

{
  "worked": true,
  "confidence": 9,
  "verdict": "Built a reproducible Matrix Normal-Inverse Wishart conjugate dynamics head in experiment.py with stable posterior and Student-t predictive calculations. The normal-equation residual was 2.7e-15; predictive scale increased by the predicted 2.4402x between near and far regressors, observed exactly 2.4402x; degrees of freedom increased exactly by one per context transition; and posterior coefficient RMSE decreased from 0.0927 at N=1 to 0.0131 at N=80. On a shifted synthetic task, Bayesian predictive NLL was better than the ridge baseline at N=2, 5, and 10, but not clearly at N=20, so the mechanism is real while the practical win is mainly in the low-data regime.",
  "metrics": {
    "baseline": "Ridge adaptation shifted-task NLL: N=2 75.105, N=5 4.499, N=10 0.157, N=20 -0.966",
    "idea": "Conjugate Bayesian Student-t predictive NLL shifted task: N=2 -0.235, N=5 -0.526, N=10 -0.966, N=20 -1.104; leverage scale ratio 2.440 observed vs 2.440 predicted; df exact for N=0,2,5,10,20,40; adaptation RMSE 0.0927 -> 0.0131 from N=1 -> 80"
  },
  "how_to_run": "/home/maxwelhelp/main/bin/python3 experiment.py",
  "files": [
    "experiment.py",
    "results.json"
  ],
  "limitations": "This is a synthetic linear controlled-dynamics regression test, not a learned encoder/world model. It does not test meta-learning across many tasks, multi-step rollout error, CartPole or other physical environments, CUDA behavior, or a carefully compute-matched gradient-adapted MLP. The ridge comparison uses a simple residual variance estimate and is not a full calibrated uncertainty baseline."
}