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arXiv · 2603.25266

Probabilistic Abstract Interpretation on Neural Networks via Grids Approximation

Zhuofan Zhang·Herbert Wiklicky
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Abstract

Probabilistic abstract interpretation is a theory used to extract particular properties of a computer program when it is infeasible to test every single inputs. In this paper we apply the theory on neural networks for the same purpose: to analyse density distribution flow of all possible inputs of a neural network when a network has uncountably many or countable but infinitely many inputs. We show how this theoretical framework works in neural networks and then discuss different abstract domains and corresponding Moore-Penrose pseudo-inverses together with abstract transformers used in the framework. We also present experimental examples to show how this framework helps to analyse real world problems.

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Zhuofan Zhang, Herbert Wiklicky. 2026-03-26. Probabilistic Abstract Interpretation on Neural Networks via Grids Approximation. https://arxiv.org/abs/2603.25266

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