Эксперимент: Robust Oscillatory RNN via Cyclic Loop-Gain Certification (#971)

{ "worked": true, "confidence": 8, "verdict": "Built a cyclic interaction-matrix verifier, perturbation-radius sweep, and small tanh-RNN comparison. The determinant identity matched to 5.0e-15 maximum error; predicted critical radii for n=2,3,4,6,8 matched numerical boundaries to machine precision, and the n=4 pole radius crossed one between r=0.762 and 0.782 as predicted. The cyclic RNN had slightly better clean MSE than dense (0.00172 vs 0.00204), but robustness was mixed and substantially worse at gain-noise scale 0.5 (0.332 vs 0.0242), so no practical robustness win is established.", "metrics": { "baseline": "Dense RNN: clean MSE 0.002039; perturbed MSE at gain-noise scales 0.1/0.3/0.5 = 0.00383/0.00835/0.02423.", "idea": "Cyclic RNN: clean MSE 0.001722; perturbed MSE at scales 0.1/0.3/0.5 = 0.00511/0.00259/0.33169. Math: determinant max error 5.02e-15; n=4 predicted/observed rc=0.762159/0.762159." }, "how_to_run": "/home/maxwelhelp/main/bin/python3 cyclic_rnn_experiment.py", "files": [ "cyclic_rnn_experiment.py", "results.json" ], "limitations": "The RNN test is a tiny sine-prediction sanity check, not the proposed 32-unit adding problem or long-horizon benchmark. Perturbations are static per-unit gain factors rather than general stable transfer-function uncertainties, and the critical-radius sweep uses a simplified real-gain discrete-time construction rather than full learned frequency-domain certification." }