Эксперимент: Lyapunov-Calibrated Multiplicative Noise (#537)

{ "worked": true, "confidence": 9, "verdict": "Built a compact Lyapunov-calibrated multiplicative-noise controller and verified its mechanism numerically. Autodiff finite-time Lyapunov rates matched the exact log|1+a| prediction with maximum error 5.1e-8, including the r_hat=0 boundary at a=0; the controller slope was 0.14 versus predicted 0.14, and sampled gate variance had fitted slope 0.999 versus predicted 1.0. In the tiny regression test, adaptive noise did not improve loss over fixed noise, so the mechanism is confirmed but no training win was observed.", "metrics": { "baseline": "Fixed q=0.08: final MSE 0.0049883, best MSE 0.0049737, mean Lyapunov rate -0.01398", "idea": "Adaptive q=0.14*[r_hat]_+: final MSE 0.0049937, best MSE 0.0049937, mean Lyapunov rate -0.01412, mean q 0.000632; exact-rate max error 5.1e-8, q slope 0.1400 vs 0.1400 predicted, variance slope 0.9989 vs 1.0 predicted" }, "how_to_run": "/home/maxwelhelp/main/bin/python3 run_experiment.py", "files": [ "run_experiment.py", "results.json" ], "limitations": "The training comparison is only a small synthetic scalar residual regression, not WikiText-2, a Transformer, or a long-horizon copy task. It does not test generalization, wall-clock overhead, hard-ceiling learning-rate intervention, smoothed noisy Jacobian estimates, or multi-layer nonlinear Jacobians." }