Эксперимент: Horizon-Dependent Error Tubes for Recurrent Rollouts (#765)

{ "worked": true, "confidence": 9, "verdict": "Built a readable element-wise error-tube propagator and verified its core math numerically. The predicted boundary alpha=1/rho(B)=1.28205 was observed: rho=0.99 remained bounded over the finite horizon, rho=1.01 grew, and measured log-growth at rho=1.05/1.20 was 0.04930/0.18232 versus predictions 0.04879/0.18232. Below the boundary, the propagated tube converged to (I-A)^(-1)w with 0.2% relative error at rho=0.95; near-boundary (1-rho)*plateau stayed 0.0247--0.0282. In the time-varying comparison, a single worst-case matrix produced a final tube 1.78x larger than local horizon-dependent propagation. Random bounded disturbances had zero bound violations. This is a clear toy mechanism win, not evidence of improved trained-RNN forecasting.", "metrics": { "baseline": "Shared element-wise worst-case matrix: final tube sum 0.25160; mean shared/local ratio 1.575; final ratio 1.777.", "idea": "Horizon-dependent local recursion: final tube sum 0.14158. Boundary predicted alpha=1.28205 and observed between rho=0.99 bounded and rho=1.01 growing; growth slope at rho=1.05: observed 0.04930 vs predicted 0.04879, at rho=1.20: 0.18232 vs 0.18232; plateau relative error at rho=0.95: 0.00204; max random bound violation: 0.0." }, "how_to_run": "/home/maxwelhelp/main/bin/python3 tube_experiment.py", "files": [ "tube_experiment.py", "results.json", "run_output.txt" ], "limitations": "Only a deterministic 2D linear positive-system toy was tested; no GRU/SSM training, learned Jacobian estimation, noisy sine/Lorenz forecasting, constraint-violation rate, FLOPs, or GPU experiment was evaluated. The exact rho=1 case was assessed over a finite horizon, so divergence is inferred from continued growth rather than an infinite-time computation." }