English

Probabilistic Abstract Interpretation on Neural Networks via Grids Approximation

Artificial Intelligence 2026-03-27 v1

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.

Keywords

Cite

@article{arxiv.2603.25266,
  title  = {Probabilistic Abstract Interpretation on Neural Networks via Grids Approximation},
  author = {Zhuofan Zhang and Herbert Wiklicky},
  journal= {arXiv preprint arXiv:2603.25266},
  year   = {2026}
}
R2 v1 2026-07-01T11:38:58.119Z