Эксперимент: Degree-Calibrated Stable Residual Flow (#1334)

{ "worked": true, "confidence": 8, "verdict": "Built and ran a deterministic toy implementation of the degree-calibrated residual flow with an exactly tangent learned component. The radial identity held to approximately 7e-13, and observed decay slopes were -1.002 for m=0, -0.965 for m=1, and -0.473 for m=2, matching the claimed exponential and algebraic laws. Against the unconstrained residual control, the calibrated flow stayed bounded under tested Euler steps through dt=1.0 while the control grew substantially; this supports the stability claim, though it is not a task-accuracy win.", "metrics": { "baseline": "Unconstrained tanh residual dynamics: final maximum norm 5.64 at dt=0.01, 76.58 at dt=0.1, 407.74 at dt=0.5, and 830.43 at dt=1.0.", "idea": "Degree-calibrated tangent flow: final maximum norm 0.706, 0.258, 0.159, and 0.198 at the same step sizes; maximum radial identity error 6.82e-13, with decay slopes -1.002 for m=0, -0.965 for m=1, and -0.473 for m=2." }, "how_to_run": "/home/maxwelhelp/main/bin/python3 run_experiment.py", "files": [ "run_experiment.py", "results.json" ], "limitations": "Only the toy hidden-state decay and stability phenomenon was tested; no sequence-learning accuracy, sequential MNIST, adaptive ODE solver, spectrally normalized baseline, FLOP comparison, or systematic Euler instability boundary was evaluated. With r=||z||^2/2, the supplied vector field needs a factor-of-two convention adjustment: the implementation uses -(a/2)r^m z so that dr/dt=-a r^(m+1), matching the stated decay claim." }