Эксперимент: Delay-Gain Certified Recurrent Block (#1099)

{ "worked": true, "confidence": 7, "verdict": "Built a self-contained scalar delayed recurrent-block MVP with exact Lambert-W stability analysis, first-order Padé realization, frequency-domain gain measurement, and a bounded-real LMI feasibility surrogate. The mechanism manifested: the predicted exact critical delay was 2.4152, with the observed stability transition bracketed by 2.391 (stable) and 2.439 (unstable), zero-delay gain scaling matched 1/(a+b) with 0% error across five values, and measured gain rose from 0.417 at zero delay to 2.478 near the boundary. The first-order Padé model incorrectly remained stable just beyond the true delay boundary, so the approximation is not a reliable boundary detector without further validation.", "metrics": { "baseline": "Unconstrained near-boundary delayed block: delay=2.2944, stable=true, measured H-infinity gain=2.4777, gain squared=6.1391.", "idea": "Lower-delay certified-style block: delay=0.8453, stable=true, measured gain=0.7338, gain squared=0.5385; bounded-real LMI returned a finite conservative gamma. Exact boundary prediction 2.4152 versus observed bracket [2.391,2.439]; zero-delay gain scaling relative error 0.0 across b in {0.2,0.5,1,2,4}." }, "how_to_run": "/home/maxwelhelp/main/bin/python3 delay_gain_experiment.py", "files": [ "delay_gain_experiment.py", "results.json", "run_output.txt" ], "limitations": "This is a scalar linear toy study, not a trained GRU/SSM or sequential-task experiment. The delay implementation uses first-order Padé approximation, which showed a false-stability region beyond the exact delayed-system boundary. The scipy nonlinear optimizer is only an approximate replacement for a dedicated SDP solver; no CUDA, minibatch Jacobian training, independent dual delays, nonlinear activation-region certification, or robustness over parameter updates was tested." }