Uncertainty propagation through trained multi-layer perceptrons: Exact analytical results
arXiv:2601.16830v1h-index: 6
Originality Incremental advance
AI Analysis
This provides a precise tool for uncertainty quantification in neural networks, which is incremental but exact compared to prior approximations.
The authors derived exact analytical expressions for the mean and variance of the output of trained multi-layer perceptrons with ReLU activations when the input is Gaussian, eliminating the need for series expansions.
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.