Symbolic Gaussian Smoothing

This work introduces a deterministic variant of randomized smoothing for certifying neural network robustness. Instead of relying on multiple stochastic forward passes with Gaussian noise, the proposed method employs symbolic moment propagation to analytically compute the exact mean and covariance of the output distribution in a single pass. Evaluations on MNIST and Fashion MNIST show that the method yields comparable classification accuracy while achieving, on average, 10% larger certified robustness radii. This deterministic framework offers exact, non-probabilistic guarantees that are particularly attractive for safety-critical applications.