Эксперимент: Integral Master-Stability Coupling for Heterogeneous RNN Copies (#1341)

{ "worked": true, "confidence": 8, "verdict": "Built a scalar two-copy explicit-Euler MVP of proportional-integral coupling and numerically verified its core claims. Proportional coupling left steady disagreement of 0.333333 under a constant replica bias, while stable PI coupling reduced the mean absolute tail disagreement to 0.000486; increasing kI crossed the predicted Euler spectral-radius boundary between 149 and 150 and caused divergence. This validates the toy phenomenon, but not an RNN accuracy or training win.", "metrics": { "baseline": "Proportional-only: mean absolute final-500 disagreement = 0.333333; Euler spectral radius = 1.000000.", "idea": "PI with kP=1, kI=0.2: mean absolute final-500 disagreement = 0.000486; Euler spectral radius = 0.998601. At kI=200, spectral radius = 1.004988 and maximum disagreement = 3.08e9; scan boundary was kI=149 stable to kI=150 unstable." }, "how_to_run": "/home/maxwelhelp/main/bin/python3 pi_coupling_experiment.py", "files": [ "pi_coupling_experiment.py", "pi_results.json" ], "limitations": "Only the smallest scalar linear difference system was tested. No heterogeneous GRU, sequential-MNIST task, backpropagation, validation accuracy, Lyapunov QR estimate, directed hyperedge implementation, or wall-clock comparison was run; the instability boundary is specific to explicit Euler with h=0.01 and the selected parameters." }