Probabilistic Abstract Interpretation on Neural Networks via Grids Approximation
This work addresses the challenge of verifying neural network properties for safety-critical applications, but it is incremental as it adapts an existing theory to neural networks.
The paper tackles the problem of analyzing neural networks with infinitely many inputs by applying probabilistic abstract interpretation to study input density distributions, and demonstrates its utility through experimental examples.
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.