Эксперимент: Finite-Horizon Lyapunov Risk Monitor (#575)

{ "worked": true, "confidence": 9, "verdict": "Built a differentiable finite-horizon FTLE monitor for a noisy tanh RNN, including mean and one-sided UCB risk variants, plus an exact scalar stochastic-map verification. In the toy sweep, observed standard deviations matched sigma/sqrt(T) within about 0.1%, tail probabilities matched the Gaussian prediction closely, and the UCB crossed zero at sigma=0.195 versus the predicted 0.1945. The mechanism is therefore numerically manifested, although the RNN comparison is not evidence of a practical task-performance win because the unregularized baseline was already highly contractive.", "metrics": { "baseline": "RNN MSE 0.1655; FTLE mean -0.6946; positive fraction 0.000; UCB -0.5491", "idea": "UCB RNN MSE 0.1679; FTLE mean -0.3960; positive fraction 0.000; UCB -0.2678. Mean-only variant: MSE 0.1722, FTLE mean -0.0340, positive fraction 0.359, UCB 0.1116. Toy: sd scaling and p+ predictions matched; UCB boundary observed 0.195 vs predicted 0.1945." }, "how_to_run": "/home/maxwelhelp/main/bin/python3 experiment.py", "files": [ "experiment.py", "results.json" ], "limitations": "The scalar verification is an analytically Gaussian construction, so it validates the formulas but not Gaussianity for nonlinear RNN dynamics. The RNN study used a tiny adding-style task, one noise level, short training, K=4 monitor samples, and did not test sequential MNIST, FLOPs, long-horizon generalization, or multiple random seeds." }