Эксперимент: Transport-PDE Predictor for Delayed Neural State Updates (#1325)

{ "worked": true, "confidence": 9, "verdict": "Built a readable delayed linear-system MVP with a FIFO transport queue, finite-horizon predictor, spectral-radius/Lyapunov verification, and fixed-seed comparisons. The transport identity and predictor formula matched numerically to 0 and 1.1e-16 maximum error; the target closed loop had rho=0.825 and a positive Lyapunov matrix with residual maximum eigenvalue -1.0. Across delays 2-32, the stale-state baseline degraded and diverged dramatically for d>=4, while the predictor remained bounded and converged to approximately zero without noise; under transition noise it stayed bounded with RMS 0.112 and 0.449 for noise scales 0.005 and 0.02. This is a clear win in the intended linear, known-model setting, but not yet evidence for nonlinear learned RNNs.", "metrics": { "baseline": "RMS final-50 state norm: d=1 3.39e-23, d=2 0.883, d=4 1.49e12, d=8 1.56e14, d=16 1.18e12, d=32 1.95e9; at d=16 with noise sigma=0.005/0.02: 1.17e12/1.14e12", "idea": "RMS final-50 state norm: d=1 7.68e-18, d=2 9.38e-18, d=4 1.73e-17, d=8 4.91e-17, d=16 6.69e-17, d=32 4.41e-14; at d=16 with noise sigma=0.005/0.02: 0.112/0.449; target rho(A+BK)=0.8249" }, "how_to_run": "/home/maxwelhelp/main/bin/python3 experiment.py", "files": [ "experiment.py", "results.json" ], "limitations": "Only a small known linear plant was tested; no nonlinear RNN, learned Jacobian estimation, training/accuracy task, gain sweep around the stability boundary, GPU execution, or empirical small-gain threshold was evaluated." }