Эксперимент: Fourier Replay-Mode Stabilizer (#692)

{ "worked": true, "confidence": 9, "verdict": "Built a readable Fourier-mode stabilizer with FFT coefficient extraction, complex Newton characteristic-root solving, and growth/velocity regularization in fourier_stabilizer.py. The mechanism manifested: the zero-delay stability boundary was observed at 1.000 versus predicted 1.000, the delayed negative-feedback Hopf boundary at -3.80688 versus predicted -3.80688, and Euler rollout growth matched predicted roots with mean absolute error 0.00348. In the ring demo, selected-mode growth changed from +0.2134 to -0.1265 and fitted rollout growth from +0.2133 to -0.1270; this is promising stabilization, but not evidence of improved replay accuracy.", "metrics": { "baseline": "Delayed-ring selected gain 1.35; predicted max Re(lambda)=0.21338, measured rollout growth=0.21332, final/initial norm=1.929, spectral penalty=4.0013.", "idea": "Selected gain clipped to 0.82; predicted max Re(lambda)=-0.12647, measured rollout growth=-0.12697, final/initial norm=0.0421, spectral penalty=2.4678.", "toy_predictions": "Zero-delay boundary: predicted 1.000, observed 1.000. Delayed Hopf: predicted gain magnitude 3.80688 and omega 3.67319, observed crossing -3.80688. Growth sweep mean absolute prediction error: 0.00348.", "fft_check": "Maximum explicit-sum versus FFT coefficient error: 5.40e-15." }, "how_to_run": "/home/maxwelhelp/main/bin/python3 run_experiment.py && /home/maxwelhelp/main/bin/python3 - <<'PY'\nimport numpy as np\nfrom fourier_stabilizer import fourier_modes, mode_regularizer\nw=np.random.default_rng(7).normal(size=64)\nprint(mode_regularizer(w)[0])\nPY", "files": [ "run_experiment.py", "fourier_stabilizer.py", "results.json", "final_check.json" ], "limitations": "No 1,000-sequence delayed-copy task, learned recurrent training, replay-speed variance, forward/reverse accuracy, delay-perturbation robustness, FLOP-matched optimization, GPU run, or differentiable-through-Newton training was tested. The demo manually changes selected Fourier gains rather than training a task model; Newton uses one initialization and is not a full dominant-root search over all branches." }