Эксперимент: Characteristic-Region Gain Controller (#409)

{ "worked": true, "confidence": 8, "verdict": "Built a finite-delay fractional-memory companion-matrix implementation with q-binomial weights, dominant-root estimation, and the proposed conservative gain controller. The mechanism manifested: the predicted boundary g*=1/sum(w)=0.09021 matched the swept transition 0.09021, rho crossed one between 0.9g* and 1.1g*, and measured gradient log-slope differed from log(rho) by 3.1e-5. Starting 35% above the boundary, control reduced rho from 1.0232 to 0.9533 and reduced final squared state norm from 4.39 uncontrolled to 8.37e-4 controlled.", "metrics": { "baseline": "Uncontrolled g=1.35*gcrit: rho initially 1.02315; final squared state norm after 80 steps = 4.3898.", "idea": "Controller reduced g from 0.12178 to 0.04179 over 50 updates; final rho=0.95326 versus target 0.95; final squared state norm = 0.0008369. Boundary prediction 0.09021087093 versus observed 0.09021087093; stable gradient slope -0.015205 versus predicted log(rho) -0.015174." }, "how_to_run": "/home/maxwelhelp/main/bin/python3 experiment.py", "files": [ "experiment.py", "results.json" ], "limitations": "Only a scalar positive-feedback finite K=30 toy system was tested, not a trained tanh RNN, sequential MNIST, Copy-Memory, SGD, gradient clipping, or spectral normalization. The q-fractional infinite-memory characteristic equation was approximated by a truncated companion matrix; noisy or delayed root estimation was not evaluated." }