Эксперимент: Robust Instability Radius Monitor (#973)

{ "worked": false, "confidence": 10, "verdict": "Built a reproducible Robust Instability Radius Monitor toy implementation with exact diagonal-radius checks, a coarse 2x2 coupled-matrix search, and a scalar recurrent training comparison. The math predictions passed: diagonal radius error was 0, the decay/growth transition occurred at |g|=1.0 exactly, and radius scaled as |g|-1. However, the proposed max(0, margin-rho_hat)^2 penalty has the wrong optimization direction: when active it drove g to 1.2066, rho_hat to 0.2066, and hidden growth to 2.12, versus baseline g=1.0, rho_hat=0, growth=1.0 and task loss 0.0. The radius estimator is numerically valid, but the stated regularizer does not penalize instability.", "metrics": { "baseline": "Final g=1.0000, rho_hat=0.0000, task_loss=0.0000, |g|^T=1.0000", "idea": "Final g=1.2066, rho_hat=0.2066, task_loss=1.2537, |g|^T=2.1197; diagonal prediction 1.5 observed exactly, stability boundary predicted/observed 1.0, and rho_hat scaled as |g|-1" }, "how_to_run": "/home/maxwelhelp/main/bin/python3 rir_experiment.py", "files": [ "rir_experiment.py", "results.json" ], "limitations": "Not tested on sequential MNIST, GRUs, larger RNNs, continuous-time SSMs, or automatic-differentiation Jacobian estimation. The coupled 2x2 radius values use a coarse brute-force grid rather than projected optimization, and a corrected penalty such as lambda*max(0,rho_hat-m)^2 was not evaluated.", "tool": "finish" }