Эксперимент: Dual-Ensemble Latent Transition Model (#458)

{ "worked": true, "confidence": 8, "verdict": "Built a dual-operator finite-state MVP with equilibrium matrix P and source-sink recycling matrix Q, plus stationary-weighted coarse-graining and MFPT evaluation. Matched operators recovered their respective coarse stationary distributions across lags 1–32 to about 1e-15 error, and the recycling MFPT matched the direct first-passage value to 3.8e-11 while the equilibrium-only estimate had errors around 797–806 steps. Finite-sample dual occupancy error decreased with N, although the fitted slope was -0.368 rather than the predicted -0.5, so that scaling claim is only partially supported.", "metrics": { "baseline": "Equilibrium-only P used for NESS MFPT: absolute errors 805.667, 803.583, 801.500, 799.417, 797.333 across reset-mixture sweep; NESS occupancy RMS errors 0.1344, 0.1192, 0.0937, 0.0795 for N=400,1600,6400,25600.", "idea": "Matched dual P/Q stationary errors <=6.1e-15 across lags 1–32; recycling MFPT error 0.000000 numerically versus direct MFPT 837.5; dual NESS occupancy RMS errors 0.1093, 0.0793, 0.0493, 0.0234, with fitted log-log slope -0.368." }, "how_to_run": "/home/maxwelhelp/main/bin/python3 dual_ensemble_experiment.py", "files": [ "dual_ensemble_experiment.py", "results.txt", "REPORT.md" ], "limitations": "Synthetic eight-state Markov chain only; no learned encoder, soft memberships, neural training, optimization comparison, wall-clock benchmark, grid-world/MuJoCo data, or joint P/Q learning. The recycling operator is specified from exact dynamics rather than learned from raw source-sink rollouts, and the finite-sample scaling sweep is limited by rare-sink effects and four sample sizes." }