Эксперимент: Wasserstein-Controlled Gaussian-Mixture Rollouts (#1065)

{ "worked": true, "confidence": 9, "verdict": "Built a readable nonlinear Gaussian-mixture rollout prototype with disturbance-mode branching, analytic chance constraints, moment calculations, and greedy Gaussian-Wasserstein merging. Mode separation matched the predicted 2d exactly, merging transitioned at the measured pair W2 of 1.8, and empirical error rose sharply after merging. The mixture also retained multimodality that the moment-matched Gaussian lost, with chance-probability gaps up to 0.209 and rollout W2 error reaching 1.052 by horizon 8.", "metrics": { "baseline": "Moment-matched single Gaussian: empirical W2 error versus the unmerged mixture was 0.473 at horizon 1, 0.476 at horizon 4, 0.654 at horizon 6, and 1.052 at horizon 8; at d=0.9 its chance estimate was 0.7092.", "idea": "The mixture separation matched 2d for d={0.1,0.3,0.6,0.9,1.2}. Below epsilon=1.8 it retained 2 components with empirical W2 error 0.024-0.084; at epsilon>=1.8 it merged to 1 component with error about 0.472. At d=0.9 its chance estimate was 0.5001." }, "how_to_run": "/home/maxwelhelp/main/bin/python3 gm_rollout_experiment.py", "files": [ "gm_rollout_experiment.py", "results.json" ], "limitations": "This is a one-dimensional toy system, not a trained neural state-space model. The Jacobian is analytic rather than obtained by neural-network autodiff; merging uses pairwise 1D Gaussian W2 rather than exact mixture Wasserstein or Sinkhorn; no FLOP or wall-clock comparison was performed; and exact mixture size grows exponentially with horizon." }