Эксперимент: Bifurcation-Aware Adaptive Compute Controller (#922)

{ "worked": true, "confidence": 9, "verdict": "Built a scalar saddle-node toy solver with fixed-step and bifurcation-aware adaptive RK4 controllers, plus numerical checks of the proposed scaling laws. The observed ghost residence slope (-0.512) matched -1/2, adaptive allocation slope (-1.012) matched the predicted -1, and slow-passage delay slope (-0.340) matched -1/3. The controller reduced function evaluations by 60% near mu=1e-4 and about 96% at mu=0.316, while retaining small passage-time error, so the mechanism manifested in this toy setting.", "metrics": { "baseline": "Fixed RK4 h=0.002: mean relative passage-time error 6.73e-8; evaluations ranged from 156080 to 1883 across mu=1e-4..0.316.", "idea": "Adaptive square-root controller: mean relative passage-time error 5.71e-5; evaluations ranged from 62432 to 76, with 60.0% saving at mu=1e-4 and 96.0% saving at mu=0.316. Observed slopes were residence -0.512 vs -0.5, allocation -1.012 vs -1, and slow delay -0.340 vs -0.333." }, "how_to_run": "/home/maxwelhelp/main/bin/python3 experiment.py", "files": [ "experiment.py", "results.json" ], "limitations": "This is a scalar normal-form experiment rather than a neural ODE, RNN, or learned hidden-state controller. The fixed baseline used a deliberately small constant step and the adaptive method used a hand-tuned clipped schedule; no equal-tolerance adaptive baseline, training experiment, noisy mu estimation, multidimensional projection, or wall-clock GPU benchmark was tested." }