Эксперимент: State-Dependent Metric Projected Optimizer (#381)

{ "worked": true, "confidence": 8, "verdict": "Built a NumPy MVP for state-dependent diagonal metric projected optimization with exact box projection, numerical KKT verification, and ill-conditioned quadratic experiments. The mechanism predictions were confirmed: contraction ratios matched |1-etaalphamh| to numerical precision, the predicted stability boundary 2/(etah)=0.05405 was observed near 0.0561, and fractional decrease scaled linearly with metric m. The optimizer comparison was not a general win: positive beta caused saturation and loss 20000, while inverse-variance beta=-0.5 at alpha=0.01 reached 0.09 versus SGD 0.47 but remained worse than projected Adam 1.56e-5.", "metrics": { "baseline": "Projected SGD final quadratic loss 0.473714 after 180 steps; projected Adam 1.562e-5; all observed box violations were 0.", "idea": "Default state metric beta=+0.5, alpha=0.03 final loss 20000.001; sensitivity found beta=-0.5, alpha=0.01 reached 0.08999 with zero violations, while larger steps often diverged into the box boundary." }, "how_to_run": "/home/maxwelhelp/main/bin/python3 metric_projected_optimizer.py", "files": [ "metric_projected_optimizer.py", "results.json", "sensitivity.json" ], "limitations": "Only a 2D deterministic quadratic and exact box constraints were tested; no neural-network minibatch training, general polytope QP projection, wall-clock or FLOP measurement, stochastic gradients, or broad hyperparameter tuning was performed. The observed stability boundary uses a finite-run divergence threshold and is therefore approximate." }