Uncertainty propagation through trained multi-layer perceptrons: Exact analytical results

TL;DR

This paper derives exact analytical expressions for propagating uncertainty through trained multi-layer perceptrons with a single hidden layer and ReLU activations, providing precise mean and variance calculations for Gaussian inputs.

Contribution

It introduces exact formulas for uncertainty propagation in MLPs with ReLU activations, avoiding approximations used in prior work.

Findings

Exact mean and variance expressions for Gaussian inputs

No series expansion needed for the derivations

Improved accuracy over previous approximate methods

Abstract

We give analytical results for propagation of uncertainty through trained multi-layer perceptrons (MLPs) with a single hidden layer and ReLU activation functions. More precisely, we give expressions for the mean and variance of the output when the input is multivariate Gaussian. In contrast to previous results, we obtain exact expressions without resort to a series expansion.