Эксперимент: Adaptive Physics-Lifted Koopman State Space (#1215)

{ "worked": true, "confidence": 8, "verdict": "Built an adaptive lifted Koopman-style transition using [x,x^2] observables and forgetting-factor RLS, with numerical stability and adaptation checks. The RLS recursion exactly matched exponentially weighted batch least squares (max error 1.1e-16), and the measured 63% adaptation time was 14 steps versus the predicted 1/(1-lambda)=14.29. After the dynamics shift, adaptive lifting achieved RMSE 0.0235 in the first 20 steps and 8.28e-5 in the last 100, versus 0.0277 and 0.00379 for adaptive linear; its 50-step rollout MSE was 0.000203 versus 0.00438 frozen. This is a clear toy signal for the claimed adaptation/accuracy effect, though not evidence yet for a general neural world-model win.", "metrics": { "baseline": "Adaptive linear lambda=0.95: post-shift RMSE first20=0.027690, last100=0.003789; frozen lifted 50-step post-shift rollout MSE=0.004381", "idea": "Adaptive lifted [x,x^2] lambda=0.95: post-shift RMSE first20=0.023485, last100=0.0000828; 50-step rollout MSE=0.000203; max measured lifted spectral radius=0.928", "math": "RLS-vs-batch max absolute error=1.11e-16; lambda=0.93 predicted adaptation timescale=14.286, measured 63% timescale=14; scalar rho=0.8 power-29=0.001547" }, "how_to_run": "/home/maxwelhelp/main/bin/python3 experiment.py", "files": [ "experiment.py", "results.json" ], "limitations": "Only a deterministic scalar nonlinear synthetic system was tested. The observable map was hand-designed rather than learned, there was no encoder/decoder, GRU or neural SSM baseline, no action-conditioned B matrix evaluation beyond a scalar forcing input, no multi-seed uncertainty estimate, and stability was measured on the fitted lifted matrix without eigenvalue projection or long-duration drifting-regime stress tests." }