Эксперимент: Composed Trusted Reachable Families for Recurrent Networks (#1050)

{ "worked": true, "confidence": 9, "verdict": "Built a scalar nonlinear recurrent trusted-reachable-family monitor with affine Jacobian propagation, box probing, tolerance-based horizon checks, and adaptive radius selection. The mechanism manifested exactly: violation scaled as radius^2 (observed slope 2.000 vs predicted 2), measured critical horizons matched the analytical boundary for all tested radii (8/5/2), and trusted radius decayed with observed log slope -0.22314 per step, matching -log(1.25). The monitor reduced H=10 violation from 0.02665 at fixed radius 0.04 to 0.00100 at radius 0.00775; this is a safety/accuracy effect, not evidence of faster task learning.", "metrics": { "baseline": "Fixed affine family radius 0.04 at lambda=1.25, q=0.3, H=10: max one-step violation 0.0266454, exceeding epsilon=0.001.", "idea": "Adaptive trusted radius sqrt(epsilon/(q*lambda^(2(H-1))))=0.007749 at H=10: measured max violation 0.0010000. Radius-scaling slope 2.000; horizon measured/predicted for radii 0.01,0.02,0.04 = 8/8,5/5,2/2; decay slope -0.223144 vs predicted -log(1.25)=-0.223144." }, "how_to_run": "/home/maxwelhelp/main/bin/python3 trusted_reachable_rnn.py", "files": [ "trusted_reachable_rnn.py", "results.json" ], "limitations": "Only a scalar quadratic recurrence with zero nominal input and initial-state uncertainty was tested; input-direction uncertainty, multidimensional polytopes, GRUs, composed block re-centering, adversarial probes, training-time regularization, wall-clock overhead, and downstream forecasting/classification accuracy were not tested." }