mlsanityData to 7 Oct 2026

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

arXiv 2601.16830 ↗First posted 23 Jan 2026cs.LG cs.AI cs.NEcited by 0

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Abstract (arXiv)

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.

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References · 4

  1. 2024An Analytic Solution to Covariance Propagation in Neural Networkscited by 11
  2. 2018Uncertainty Propagation in Deep Neural Networks Using Extended Kalman Filteringcited by 8
  3. 2024Analytical results for uncertainty propagation through trained machine learning regression modelscited by 3
  4. 2025Uncertainty propagation in feed-forward neural network modelscited by 3

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