Эксперимент: Nested-Cone Latent Dynamics (#395)

{ "worked": false, "confidence": 9, "verdict": "Built a region-valued latent-dynamics MVP with diagonal-radius ellipsoids, sampled boundary inclusion loss, contraction regularization, analytic nested-set checks, and a nonlinear forecasting comparison. The toy math confirmed the predicted radius ratios, perturbation limit eta/(1-rho), and the stability boundary at gain 1. However, the learned region model had negative validation inclusion margin (-0.625), worse one-step RMSE (0.332 vs 0.051), and worse noisy rollout RMSE (0.797 vs 0.038), so the practical mechanism did not produce a win.", "metrics": { "nested_radius_decay": "Observed ratios [0.20, 0.50, 0.80, 0.95] exactly matched predictions.", "perturbation_bound": "Observed steady-state errors [0.0125, 0.0200, 0.0500, 0.19999] matched eta/(1-rho) within 0.004%.", "stability_boundary": "The predicted critical gain gamma*Lambda=1 was supported: gains 1.10 and 1.25 produced final radii 4.10 and 79237, while subcritical gain 0.80 ended at 0.0005.", "baseline": "One-step RMSE 0.0512; noisy rollout RMSE 0.0380.", "idea": "One-step RMSE 0.3323; noisy rollout RMSE 0.7969; learned q 0.0546; validation minimum inclusion margin -0.6246." }, "how_to_run": "/home/maxwelhelp/main/bin/python3 nested_cone_experiment.py", "files": [ "nested_cone_experiment.py", "results.json" ], "limitations": "The forecasting task is a small synthetic stable system rather than pendulum or Lorenz; only diagonal ellipsoids and eight boundary samples were used. The region objective was not extensively tuned, no calibrated uncertainty or FLOP-matched evaluation was performed, and the toy boundary sweep uses a scalar recurrence rather than a learned neural transition." }