Эксперимент: Pole-safe rational neural layer (#1257)

{ "worked": true, "confidence": 8, "verdict": "Built a pole-safe order-two rational layer using psi(z,x)=(z-beta)^2 h_theta(x)/||h_theta(x)|| and compared it with unconstrained and gradient-clipped controls. The math check reproduced the expected inverse-square divergence for the unsafe product and a bounded, near-constant safe product converging to Q_-2 v. In the synthetic regression, the safe branch achieved validation MSE 0.0227 versus 7.996e11 unconstrained and 1.337e11 with clipping, with output norm about 1.49 versus roughly 1.8e7–2.0e7. This is a clear stability and optimization signal, but only on a synthetic one-seed benchmark.", "metrics": { "baseline": "Unconstrained: validation MSE 7.996e11, maximum output norm 1.837e7, near-pole norm 5.304e7; gradient-clipped control: validation MSE 1.337e11, maximum output norm 2.049e7, near-pole norm 2.239e7.", "idea": "Pole-safe: validation MSE 2.273e-2, maximum output norm 1.491, near-pole norm 1.327; direct math unsafe slope -1.9995, safe slope 0.00046, safe limit error 1.22e-5 at |z-beta|=1e-5." }, "how_to_run": "/home/maxwelhelp/main/bin/python3 pole_safe_experiment.py", "files": [ "pole_safe_experiment.py", "results.json", "README.md" ], "limitations": "Only a synthetic 32-dimensional order-two operator, one fixed random seed, and one short regression setup were tested. No real state-space model, sequential benchmark, learned pole, lower-order nullspace parameterization, ablation over pole orders, or repeated-seed statistical evaluation was performed." }