Uncertainty propagation through trained multi-layer perceptrons: Exact analytical results
Machine Learning
2026-01-26 v1 Artificial Intelligence
Neural and Evolutionary Computing
Statistics Theory
Statistics Theory
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.
Keywords
Cite
@article{arxiv.2601.16830,
title = {Uncertainty propagation through trained multi-layer perceptrons: Exact analytical results},
author = {Andrew Thompson and Miles McCrory},
journal= {arXiv preprint arXiv:2601.16830},
year = {2026}
}