Uncertainty propagation through trained multi-layer perceptrons: Exact analytical results
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866911394002108416 |
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| author | Thompson, Andrew McCrory, Miles |
| author_facet | Thompson, Andrew McCrory, Miles |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_16830 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Uncertainty propagation through trained multi-layer perceptrons: Exact analytical results Thompson, Andrew McCrory, Miles Machine Learning Artificial Intelligence Neural and Evolutionary Computing Statistics Theory 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. |
| title | Uncertainty propagation through trained multi-layer perceptrons: Exact analytical results |
| topic | Machine Learning Artificial Intelligence Neural and Evolutionary Computing Statistics Theory |
| url | https://arxiv.org/abs/2601.16830 |