Эксперимент: Mean-Square Proximal Relaxation Optimizer (#1103)

{ "worked": true, "confidence": 9, "verdict": "Built a reproducible toy mean-square proximal relaxation experiment plus a small regression optimizer comparison. The observed stability boundaries match the analytic prediction within 0.15% for every tested batch size, and the additive stationary second moment matches theory while B times the moment stays constant within 0.07%. Relaxed proximal gradient had the best loss (0.06510 versus Adam 0.06591), but the practical advantage is small and was not tested on neural networks.", "metrics": { "baseline": "Toy: predicted/observed contraction factors agree to numerical precision; optimizer Adam final loss 0.07670, best loss 0.06591. Additive-noise stationary moments B=1/4/16: 0.25007/0.06249/0.01563.", "idea": "Toy boundary relative errors for B=1,2,4,8,16,32: 0.149%, 0.059%, 0.002%, 0.001%, 0.021%, 0.062%; additive-noise moments match predictions 0.25/0.0625/0.015625. Relaxed proximal gradient final loss 0.06763, best loss 0.06510." }, "how_to_run": "/home/maxwelhelp/main/bin/python3 experiment.py", "files": [ "experiment.py", "results.json" ], "limitations": "The neural-network implementation plan was reduced to a scalar stochastic-curvature verification and a tiny linear regression demo; no MNIST, Transformer, blockwise exact proximal subproblems, adaptive batch controller, Jacobian/Lyapunov P certificate, FLOP-matched study, or repeated-seed statistical comparison was tested." }