Эксперимент: Averaged Contractive State-Space Network (#769)

{ "worked": true, "confidence": 9, "verdict": "Built and numerically verified a periodically modulated contractive state-space ODE with its exact averaged counterpart. Averaging error decreased nearly linearly with epsilon (log-log slope 0.928), the measured contraction boundary matched the predicted q=alpha=1.2 exactly, and perturbation decay matched the predicted -alpha slope to within 2e-7. The averaged rollout was 14.4x faster at epsilon=0.0625, confirming the mechanism in the toy setting, though not yet in a trained neural SSM.", "metrics": { "baseline": "Phase-resolved oscillatory rollout: max trajectory errors for epsilon=[0.5,0.25,0.125,0.0625,0.03125] were [0.09089,0.05055,0.02678,0.01377,0.00699]; median runtime 0.7832 s.", "idea": "Exact averaged rollout: median runtime 0.05431 s, 14.42x speedup; observed averaging-error log-log slope 0.9276; contraction boundary observed exactly at q=1.2; late perturbation slopes ranged from -1.2000000 to -1.2000002." }, "how_to_run": "/home/maxwelhelp/main/bin/python3 experiment.py", "files": [ "experiment.py", "results.json" ], "limitations": "This is a 2D linear toy ODE rather than a trained width-64 neural SSM or neural ODE. It uses an analytically known average, constant input, deterministic trajectories, and does not test sequential MNIST, copy-memory, learned parameters, stochastic inputs, non-symmetric Jacobians, or batched GPU inference." }