Эксперимент: Jacobian-Frozen Stable Rollouts (#1326)

{ "worked": true, "confidence": 8, "verdict": "Built Jacobian-frozen affine rollouts with analytic Jacobians, spectral-radius monitoring/clipping, and reproducible toy checks. The Taylor remainder had log-log slope 1.97 with approximately 4x error reduction when perturbations were halved, confirming quadratic local mismatch; the scalar stability boundary matched rho=1. On a bounded locally unstable map, rho=1.024 caused the unclipped frozen rollout to reach norm 1.03 by horizon 100, while clipping to 0.98 kept it at norm 0.011, demonstrating the promised stabilization effect. The effect is real in this toy setting, though clipping can reduce fidelity to nonlinear dynamics.", "metrics": { "baseline": "Nonlinear rollout final norms at radii 0.03, 0.10, 0.25, 0.50, 0.90: 0.0764, 0.0689, 0.0578, 0.0586, 0.0924. Scalar stability decayed for rho<1 and grew for rho>1.", "idea": "Frozen-rollout RMSE versus nonlinear truth at those radii: 0.00114, 0.00296, 0.0161, 0.0675, 0.1618. In the unstable-map check, raw rho=1.0235 produced final norm 1.0306; clipping to rho=0.98 produced final norm 0.0110 and maximum norm 0.1032." }, "how_to_run": "/home/maxwelhelp/main/bin/python3 experiment.py && /home/maxwelhelp/main/bin/python3 unstable_check.py", "files": [ "experiment.py", "unstable_check.py", "results.json", "unstable_results.json", "run_output.txt" ], "limitations": "No learned GRU or world-model training, CUDA benchmark, wall-clock speed measurement, multi-seed sweep, or high-dimensional Jacobian-vector-product approximation was tested. The clipping rule was simple radial rescaling of a 2D matrix, and the unstable example was hand-designed." }