Probabilistic Abstract Interpretation on Neural Networks via Grids Approximation

• URL: http://arxiv.org/abs/2603.25266v1
• Date: Thu, 26 Mar 2026 10:04:29 GMT
• Title: Probabilistic Abstract Interpretation on Neural Networks via Grids Approximation
• Abstract summary: Probabilistic abstract interpretation is used to extract properties of a computer program when it is infeasible to test every single inputs.<n>We show how this theoretical framework works in neural networks and then discuss different abstract domains and corresponding Moore-Penrose pseudo-inverses.<n>We also present experimental examples to show how this framework helps to analyse real world problems.
• Score: 2.110338863301235
• License: http://creativecommons.org/licenses/by/4.0/
• 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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