A local approximation of neural network output with respect to perturbations in inputs and parameters is exact for perturbations that preserve the network activation pattern

This approximation is exact for perturbations that preserve the network activation pattern, and it allows us to compute analytical expressions for the probability density function and characteristic function of the network output, together with closed-form approximations for its mean and covariance.

http://arxiv.org/abs/2608.20483v1