Эксперимент: KL Mirror-Prox for coupled routing (#775)

{ "worked": true, "confidence": 9, "verdict": "Built a numerically stable KL prox implementation and a coupled three-state cyclic routing proxy comparing entropic mirror descent with KL Mirror-Prox. The three mechanism predictions were confirmed: zero coupling produced exactly zero update, local amplification/contraction factors matched theory with maximum errors 5.60e-7 (MD) and 1.02e-6 (MP), and the predicted MP transition at x=eta*Lambda/3=1 was observed between x=0.667 and 1.333, with factor 1.00000003 at x=1. In the mini-run at x=2/3, MD diverged in radius while MP contracted from 0.04315 to 8.57e-6 and reduced the VI residual from 0.05658 to 1.61e-5.", "metrics": { "baseline": "Entropic mirror descent: local factor matched sqrt(1+x^2); at eta=1, Lambda=2, radius 0.04315 -> 0.81081 and VI residual 0.05658 -> 1.13835 after 60 steps.", "idea": "KL Mirror-Prox: local factor matched sqrt(1-x^2+x^4); at eta=1, Lambda=2, radius 0.04315 -> 8.57e-6 and VI residual 0.05658 -> 1.61e-5 after 60 steps. Maximum local prediction error was 1.02e-6." }, "how_to_run": "/home/maxwelhelp/main/bin/python3 kl_mirror_prox_experiment.py", "files": [ "kl_mirror_prox_experiment.py", "results.json", "README.md" ], "limitations": "Only a deterministic three-state cyclic operator was tested; this is a mechanism-level toy verification rather than a trained MoE, attention, CIFAR, or language-model benchmark. No wall-clock or equal-FLOP neural routing comparison was performed, and behavior outside the local uniform-equilibrium analysis was not systematically swept." }