Эксперимент: Zero-Crossing Reset Integral Optimizer (#406)

{ "worked": true, "confidence": 8, "verdict": "Built a deterministic quadratic PI/reset-PI prototype with continuous-flow and discrete-time simulations. The critical-damping boundary R=kP²λ/(4kI)=1 was confirmed at every sweep point: R<1 produced complex roots and R≥1 real roots. Resetting the integral state reduced the post-crossing peak from 0.2984 to 3.0e-5, while increasing dwell from 0 to 500 steps reduced resets from 100 to 5; the mechanism manifested clearly, although this is not evidence of a general neural-network win.", "metrics": { "baseline": "On the scalar quadratic, SGD reached loss <1e-6 in 652 steps and final loss 7.50e-23; continuous PI without reset had final loss 8.78e-9.", "idea": "Reset PI reached loss <1e-6 in 47 steps and final loss 9.35e-314; continuous post-crossing peak was 3.0e-5 versus 0.2984 without reset. Dwell sweep reset counts were 100, 100, 34, 20, 12, and 5 for dwell 0, 20, 50, 100, 200, and 500." }, "how_to_run": "/home/maxwelhelp/main/bin/python3 experiment.py", "files": [ "experiment.py", "results.json", "run_output.txt" ], "limitations": "Only deterministic scalar quadratic dynamics were tested; no MNIST/MLP, minibatch noise, tensor-wise block residuals, Adam or momentum comparisons, wall-clock/FLOP measurements, or GPU execution. The decay-rate fit was only numerically usable for the lowest underdamped sweep point because non-oscillatory trajectories do not provide local peaks." }