Эксперимент: Proximal Spherical Cubic Step (#527)

{ "worked": true, "confidence": 8, "verdict": "Built a readable proximal spherical cubic solver with exact homogeneous tensor construction, tensor contractions, PAM updates, quartic safeguard ratio testing, and deterministic toy verification. The mechanism manifested: representation error was 1.6e-14, maximum proximal block-objective increase was at numerical zero, and all quartic-strength acceptance patterns matched the analytically predicted radius transitions. The secondary comparison did not show a performance win: gradient descent reached -0.59694 versus -0.58612 for the safeguarded method, with 74/80 safeguarded attempts rejected.", "metrics": { "baseline": "Toy quartic objective final value -0.5969433195 after 80 fixed-step gradient updates.", "idea": "Toy quartic objective final value -0.5861162639 after 80 safeguarded cubic-direction attempts; 74/80 rejected. Analytic/observed transition radii: q=0.8, 1.4640/1.4585; q=1.7, 1.1675/1.1570; q=4.0, 0.9044/0.8987. q=0.2 transition was 2.3181, beyond the tested radius maximum 2.0." }, "how_to_run": "/home/maxwelhelp/main/bin/python3 proximal_cubic.py", "files": [ "proximal_cubic.py", "results.json" ], "limitations": "No CIFAR-10, neural-network training, Hessian-vector or third-derivative autodiff, matched-FLOP timing, GPU test, multiple random seeds, or high-dimensional/low-rank tensor benchmark was performed. The implementation materializes a small dense tensor and uses a fixed toy radius rather than a full adaptive trust-region optimizer." }