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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}
}
R2 v1 2026-07-01T09:17:31.345Z