Эксперимент: Parameter-Dependent Lyapunov Neural Dynamics (#1132)

{ "worked": true, "confidence": 8, "verdict": "Built a compact parameter-conditioned residual dynamics model with a learned positive-definite metric and finite-step generalized-eigenvalue Lyapunov penalty. The exact 2D check satisfied the finite-step LMI (maximum normalized residual eigenvalue -0.083) and the measured energy ratio 0.797 was below the theoretical bound 0.946. In the learned comparison, the penalty reduced violating transitions from 44.5% to 3.9% and reduced the mean residual eigenvalue from 0.634 to -0.247, but prediction MSE worsened from 0.0199 to 0.0233, so the stability effect is real while there was no accuracy win.", "metrics": { "baseline": "MSE 0.01987; Lyapunov violation fraction 0.445; mean generalized residual eigenvalue 0.634; local contraction ratio mean 0.679", "idea": "MSE 0.02332; Lyapunov violation fraction 0.039; mean generalized residual eigenvalue -0.247; local contraction ratio mean 0.681" }, "how_to_run": "/home/maxwelhelp/main/bin/python3 experiment.py", "files": [ "experiment.py", "results.json" ], "limitations": "Only a tiny 2D one-step residual-dynamics task was tested for 120 optimization steps. The parameter transition used for P_{k+1} was a rolled minibatch condition rather than a generated multi-step trajectory, and no GRU, Lorenz-63, spectral-normalization baseline, long-horizon robustness test, or equal-FLOP study was run." }