Эксперимент: Slow-Mode-Canceling Optimizer Packet (#1081)

{ "worked": true, "confidence": 9, "verdict": "Built and numerically verified the coupled two-replica optimizer on a diagonal quadratic Hessian. Exact slow-mode cancellation was observed, the measured rate matched the discrete prediction across the kappa sweep to numerical precision, saturation occurred at kappa=0.3 as predicted, and the Euler stability boundary was predicted at kappa=19.0 with divergence observed at kappa=19.05. The prepared packet reached 1.05% of the unprepared final loss in this toy case.", "metrics": { "baseline": "Unprepared coupled replicas: final loss 0.0370561 at eta=0.05, kappa=0.35, 100 steps; slow-mode amplitude after 30 steps was 0.860384 of initial target amplitude.", "idea": "Prepared packet: final loss 0.000388824 under identical settings, or 0.01049x baseline; exact initial c1 cancellation and c1=0 after 30 steps. Rate sweep predicted/observed continuous-equivalent rates matched: 0.100251/0.100251, 0.201007/0.201007, 0.404054/0.404054, 0.712544/0.712544, and 0.712544/0.712544 for kappa 0, 0.05, 0.15, 0.3, and 0.6. Stability critical kappa was predicted as 19.0; kappa=19.05 and 19.5 diverged while kappa<=19.0 did not." }, "how_to_run": "/home/maxwelhelp/main/bin/python3 slow_mode_experiment.py", "files": [ "slow_mode_experiment.py", "results.json" ], "limitations": "Only a deterministic diagonal quadratic/local-Hessian model was tested; no MLP, MNIST, stochastic minibatch replenishment, Hessian-vector estimation, nonlinear effects, wall-clock or FLOP comparison, or practical packet-reset schedule was evaluated." }