Эксперимент: Shape-Optimized Private Gradient Noise (#1149)

{ "worked": false, "confidence": 9, "verdict": "Built generalized-Gaussian sampling, hockey-stick divergence calibration, grid-based shape selection, scaling checks, and a clipped scalar mean-estimation experiment. Quadrature calibration reached delta accurately, Monte Carlo moments matched the analytic formula, and b scaled proportionally with sensitivity while p*=1 remained invariant. However, p=1 was optimal in all tested privacy regimes; the optimized arm is therefore Laplace and its small MSE difference is not evidence of a shape-optimization gain.", "metrics": { "baseline": "Laplace p=1: U2=1.999920 at epsilon=1, delta=1e-5; mean-estimation MSE=0.4461 ± 0.0476", "idea": "Selected p=1, b=0.999980: U2=1.999920; mean-estimation MSE=0.4318 ± 0.0383. Gaussian p=2 had U2=13.9176 and MSE=6.6056 ± 0.7046." }, "how_to_run": "/home/maxwelhelp/main/bin/python3 shape_private_noise.py && /home/maxwelhelp/main/bin/python3 verify_and_sweep.py", "files": [ "shape_private_noise.py", "verify_and_sweep.py", "results.json", "sweep_results.json" ], "limitations": "Only a scalar clipped mean-estimation task was tested, not logistic regression or MNIST MLP. The task prototype uses a sensitivity-calibrated scalar mechanism but does not implement a full DP-SGD accountant or composition across iterations; no wall-clock/FLOP comparison was performed." }