Scale Analysis and Shape Selection for the Generalized Gaussian Mechanism under Approximate Differential Privacy

What the math gives to ML

The paper provides a constructive way to choose the shape of additive generalized-Gaussian noise rather than treating Laplace and Gaussian noise as the only useful options. Its transferable asset is the combination of privacy calibration through the hockey-stick divergence with a scale-homogeneous utility objective, which makes shape comparison invariant to the absolute sensitivity scale. A direct neural-network application is private gradient or update perturbation: for a fixed privacy budget, numerically calibrate the smallest noise scale for each shape p and select the shape minimizing a gradient-relevant moment. The strongest initial test is one-step or few-step private optimization with exact scalar accounting, followed by a conservative coordinate-wise extension to clipped gradients.