Convex Order Comparisons for Sub-Gamma Random Variables

What the math gives to ML

The paper develops sharp convex-order majorants for centered random variables whose moment generating functions satisfy finite-range Bernstein/sub-Gamma bounds. Its transferable asset is not Laplace noise itself, which is standard, but a principled calibration constant that guarantees every convex test loss under an admissible perturbation is bounded by the corresponding loss under a scaled Laplace perturbation; the extremal law is an asymmetric two-point distribution. A practical neural-network use is certified scalar perturbation regularization: estimate local sub-Gamma parameters of activations, gradients, or logit noise, compute the sharp majorant scale numerically from the convex-order condition, and train with the resulting scaled Laplace perturbation as a distributionally robust surrogate.