Эксперимент: Bernstein resolvent activation (#1302)

{ "worked": false, "confidence": 9, "verdict": "Built a drop-in finite Bernstein resolvent activation with positive softplus-constrained coefficients, fixed positive poles, epsilon stabilization, and configurable τ. The 500-step digits MLP comparison gave GELU 98.44% test accuracy versus 97.11% for the proposed τ=0.5 activation, with mean gradient norm 0.131 versus 5.26 and maximum 1.38 versus 60.29. The core math check was positive: the 500-pole fractional-Bessel partial-fraction approximation had 0.094% maximum relative error, and the τ=0.5 activation had nonnegative first derivative and nonpositive second derivative on the tested grid; however, this did not translate into a training win.", "metrics": { "baseline": "GELU: test accuracy 0.9844, final train loss 0.000236, mean gradient norm 0.1307, gradient std 0.2370, max gradient 1.3781", "idea": "Bernstein resolvent τ=0.5: test accuracy 0.9711, final train loss 0.05247, mean gradient norm 5.2641, gradient std 5.2259, max gradient 60.2857; τ=0.75 ablation reached 0.9844 accuracy but was not a valid improvement over GELU" }, "how_to_run": "/home/maxwelhelp/main/bin/python3 experiment.py", "files": [ "experiment.py" ], "limitations": "Only one fixed-seed, small digits classification MLP experiment was run rather than CIFAR-10. Pole ranges, output normalization, K ablations, multiple seeds, calibration, FLOP-normalized timing, and a rigorous higher-order Bernstein-sign test were not evaluated. The τ=0.75 check measured second-derivative concavity only; concavity alone does not test the full sharp Bernstein restriction." }