Эксперимент: Contact-Splitting Momentum Optimizer (#523)

{ "worked": true, "confidence": 9, "verdict": "Built a deterministic contact-splitting optimizer toy implementation and numerically verified the mechanism. Exact certificate decay matched -gamma to 2.7e-10, state error under step halving decreased by 4.0006x, and certificate-rate residual decreased by 4.0003x; the observed stability boundary was 1.9995 versus the predicted h*sqrt(lambda)=2. The mechanism manifested, although the matched-gradient quadratic comparison did not show an optimization win: contact splitting ended at 1.87e-3 loss versus 1.75e-5 for momentum.", "metrics": { "baseline": "Standard momentum at h=0.28 for 120 steps / 240 gradient-equivalent updates: final loss 1.7538e-05, minimum 2.6959e-06.", "idea": "Contact splitting with gamma=0.2 at h=0.28 for 120 steps / 240 gradient evaluations: final and minimum loss 1.8661e-03. Exact-rate absolute error 2.68e-10; state-error halving ratio 4.0006; certificate-residual halving ratio 4.0003; stability boundary 1.9995 versus predicted 2.0." }, "how_to_run": "/home/maxwelhelp/main/bin/python3 experiment.py", "files": [ "experiment.py", "results.json", "run_output.txt" ], "limitations": "Only a separable quadratic toy problem was tested; no MLP/MNIST experiment, learned diagonal preconditioner, wall-clock benchmark, or broad hyperparameter tuning was performed. The positive result supports second-order splitting and certificate behavior, not practical superiority over tuned momentum." }