Эксперимент: Caratheodory-kernel passivity regularizer (#1299)

{ "worked": false, "confidence": 9, "verdict": "Built a differentiable Caratheodory-kernel regularizer using resolvent solves, sampled passivity margins, and a symmetrized kernel Gram matrix, plus a reproducible linear-SSM comparison. The numerical check confirmed that a non-passive scalar response has negative H and kernel eigenvalue margins and that optimization can repair them. However, the learned toy SSM was already strongly passive without regularization, so CK produced essentially unchanged long-horizon MSE (2.958e-5 baseline vs 3.080e-5 idea) while adding about 2.58x runtime overhead; therefore no practical win was observed.", "metrics": { "baseline": "train MSE 6.912e-6; long-horizon MSE 2.958e-5; H minimum 1.0480; kernel minimum 1.8868; runtime 9.93 s", "idea": "train MSE 6.719e-6; long-horizon MSE 3.080e-5; H minimum 1.0481; kernel minimum 1.8867; runtime 25.64 s; overhead 2.58x", "math_check": "good response H min 2.0 and kernel min 3.553; bad response H min -0.4 and kernel min -7.198; gradient repair reached H min 64.56 and kernel min 114.70" }, "how_to_run": "/home/maxwelhelp/main/bin/python3 experiment.py", "files": [ "experiment.py", "results.json" ], "limitations": "Only a small scalar-output, 8-state linear SSM and three fixed seeds were tested. The comparison omitted spectral-radius clipping and the proposed copy, adding, and ListOps tasks; the training fixture did not begin from substantially non-passive systems, so it cannot establish whether CK helps in genuinely unstable or non-passive regimes." }