Эксперимент: Positive-real rational resolvent mixer (#1331)

{ "worked": true, "confidence": 8, "verdict": "Built a NumPy MVP of the positive-real rational resolvent mixer with an exactly certified KYP realization, rational state-space solves, and implicit output solves. The numerical check found KYP minimum eigenvalue 0.24, sampled Hermitian-part minimum eigenvalue 0.1231, and maximum sampled resolvent singular value 0.9104, confirming the nonexpansive bound on the tested positive coordinates. In the fixed-operator toy update, the implicit method reduced RMS activation from 0.952 to 6.55e-6, while the explicit additive control exploded to RMS 1.67e21 at eta=0.8; this demonstrates the claimed stability effect, but not trained-model accuracy.", "metrics": { "baseline": "Explicit additive residual at eta=0.8: final RMS 1.6729e21, final loss 2.7985e42, maximum sample norm 1.2222e22.", "idea": "Implicit resolvent at eta=0.8: final RMS 6.545e-6, final loss 4.284e-11, maximum sample norm 0.9518. Across 500 positive-coordinate samples, maximum resolvent singular value was 0.9104 and maximum sampled energy ratio was 0.8903.", "step_sweep": "Explicit residual final RMS: 137.8 at eta=0.05, 2.014e4 at 0.1, 9.481e7 at 0.2, 3.869e13 at 0.4, and 1.673e21 at 0.8." }, "how_to_run": "/home/maxwelhelp/main/bin/python3 resolvent_mixer_experiment.py", "files": [ "resolvent_mixer_experiment.py", "results.json", "results.txt" ], "limitations": "Only a small fixed-operator NumPy toy experiment was tested. CIFAR-10, a long-range sequence task, learned feature conditioning, parameter-matched Transformer or FFN training, gradient analysis, speed, and solve overhead were not tested. The explicit control is an update-rule comparison rather than a complete modern neural residual block." }