Эксперимент: Bregman-Projection Polyak Optimizer (#948)

{ "worked": true, "confidence": 9, "verdict": "Built an entropy-geometry Bregman-Projection Polyak optimizer for simplex variables with stable analytic mirror mapping and scalar bisection root solving. The mechanism manifested: small-gap lambda/delta matched 1/Var_p(g)=2.782415 within 4e-8 relative error, simultaneous gradient/gap scaling matched the predicted lambda->lambda/a law exactly, fixed-gap local scaling matched 1/a^2 within 1.5e-7, and root feasibility switched at the predicted reachable gap 0.86. In the toy optimization both methods converged to essentially zero loss; Euclidean Polyak was slightly better at step 10, so no practical optimization win was observed.", "metrics": { "baseline": "Euclidean Polyak with simplex projection: loss 1.9971e-08 at step 10 and 4.9111e-32 at step 120.", "idea": "Entropy Bregman Polyak: loss 2.3863e-08 at step 10 and 2.7926e-33 at step 120; root halfspace residual <=1.1e-18. Core predictions: asymptotic lambda/delta observed 2.782415034 vs predicted 2.782415136; scaling ratios 1.0; feasibility succeeded through delta/reachable=0.999999 and failed at 1.001." }, "how_to_run": "/home/maxwelhelp/main/bin/python3 experiment.py", "files": [ "experiment.py", "results.json", "run.txt" ], "limitations": "Only deterministic NumPy simplex optimization was tested, not a neural network, stochastic gradients, AdamW integration, CIFAR-10, wall-clock speed, clipping frequency, router entropy over training, or GPU behavior. The optimization comparison used the exact known optimum and a tiny 8-dimensional quadratic, so it establishes the mechanism rather than a general training advantage." }