Эксперимент: Recycled-curvature proximal optimizer (#515)

{ "worked": true, "confidence": 8, "verdict": "Built a self-contained quadratic composite-proximal experiment with exact center-residual transport, secant reuse, inverse-BFGS updating, and frozen modeled rollouts. The mechanism checks passed: transport error was 2.48e-16, secant identity error was 1.42e-14, the observed secant curvature ratio stayed above the predicted lower bound 1, and the H=I stability sweep matched the predicted contractive interval 0 < gammalambda < 2. The recycled method used 31 versus 90 expensive gradient calls, a 65.6% reduction, but had substantially worse final residual (0.109 versus 0.00614) and was slower on this tiny dense problem, so the claimed end-to-end win was not demonstrated.", "metrics": { "baseline": "90 gradient calls; final residual 0.00614; mean residual 0.00780; 0.00219 s", "idea": "31 gradient calls; 65.6% fewer; final residual 0.10894; mean residual 0.18040; 0.13316 s", "math": "transport error 2.48e-16; secant identity error 1.42e-14; minimum secant ratio 1.1685 versus bound 1; stability boundary consistent with gammalambda=2" }, "how_to_run": "/home/maxwelhelp/main/bin/python3 experiment.py", "files": [ "experiment.py", "results.json" ], "limitations": "Only a small convex quadratic toy problem was tested, not a neural network, CIFAR-10, group sparsity, noisy gradients, wall-clock expensive forward loss, or larger-scale L-BFGS memory behavior. The recycled predictor used a dense inverse matrix in the toy implementation and therefore its wall-clock timing is not representative of a production limited-memory implementation." }