Stochastic Sample Approximations of (Local) Moduli of Continuity

Modulus of local continuity is used to evaluate the robustness of neural networks and fairness of their repeated uses in closed-loop models. Here, we revisit a connection between generalized derivatives and moduli of local continuity, and present a non-uniform stochastic sample approximation for moduli of local continuity. This is of importance in studying robustness of neural networks and fairness of their repeated uses.