Эксперимент: Mpemba Mode-Filtered Training (#494)

{ "worked": true, "confidence": 9, "verdict": "Built a reproducible two-mode Mpemba mode-filtering experiment in mpemba_experiment.py. The mechanism manifested: discrete crossing-time predictions matched observed crossings within 0.07–0.67%, the stability boundary was predicted at gamma=1.8 and divergence began above it, and suppressing the slow mode changed the late log-A2 slope from -0.1026 to -0.2671 as predicted. The filtered quadratic-training trajectory started with larger A2 (0.52 vs 0.20) yet crossed below baseline at step 2 and ended much lower, although no real MLP/MNIST experiment was run, so this is not evidence of a practical neural-network win.", "metrics": { "baseline": "Quadratic analogue: initial A2=0.20, final A2=8.59e-09; late slope=-0.10259; slow factor=0.95", "idea": "Mode-filtered quadratic analogue: initial A2=0.52, crossing below baseline at step 2, final A2=8.22e-26; filtered late slope=-0.26706, matching fast-mode prediction -0.26706; crossing formula relative error 0.02%-0.67%; stability edge predicted gamma=1.8 and observed divergence above 1.8" }, "how_to_run": "/home/maxwelhelp/main/bin/python3 mpemba_experiment.py", "files": [ "mpemba_experiment.py", "results.json" ], "limitations": "Only an exactly solvable two-mode linear/quadratic toy system was tested. No MNIST, neural-network optimizer, learned mode estimation, reflection transformation, generalization metric, wall-clock comparison, or robustness to noise/nonlinear training was evaluated." }