Эксперимент: Delay-Budget Controller for Coupled Training (#1261)

{ "worked": true, "confidence": 7, "verdict": "Built a readable four-pole delayed-feedback MVP with the stated characteristic equation, controller branch logic, numerical root estimation, and Euler DDE simulation. The magnitude and phase equations matched numerically to approximately 5e-13 relative magnitude error and zero phase error; the dominant root crossed from -0.0061 at 0.8 tau_crit to +0.0033 at 1.2 tau_crit, and reducing delay lowered tail RMS from 0.01357 to 0.00749. In the filter-margin case, increasing filter rates reduced tail RMS from 1.84e-9 to 2.10e-22 at zero delay, while delay-only intervention did nothing; this is a promising toy-level confirmation, not evidence of a neural-training win.", "metrics": { "baseline": "Delay-induced case at tau=1.2 tau_crit: dominant real root 0.003275, tail RMS 0.013568; filter-margin case with unchanged filters: tail RMS 1.844e-9 at tau=0.", "idea": "Delay reduced to 0.8 tau_crit: dominant real root -0.006119, tail RMS 0.007489. Faster filters in the margin case: tail RMS 2.10e-22; at tau=20 and G=0.8, dominant root remained stable at -0.010732, consistent with no finite Hopf crossing from the formula." }, "how_to_run": "/home/maxwelhelp/main/bin/python3 delay_controller.py", "files": [ "delay_controller.py", "results.json" ], "limitations": "Only a scalar linear toy DDE was tested; no GAN, neural network, parameter or gradient trace estimator, Hutchinson Jacobian estimation, noisy measurements, wall-clock comparison, FID, mode coverage, or divergence-rate study was performed. The implementation uses a four-factor magnitude equation consistent with the characteristic polynomial; the idea text's displayed magnitude formula appears to omit one filter factor. Filter-rate changes hold G fixed, so they do not model every physical dependence of G on kappa." }