Probabilistic Abstract Interpretation on Neural Networks via Grids Approximation

TL;DR

This paper applies probabilistic abstract interpretation to neural networks to analyze the distribution of all possible inputs, providing a theoretical framework and experimental validation for understanding neural network behavior over infinite input spaces.

Contribution

It introduces a novel application of probabilistic abstract interpretation to neural networks, including the use of abstract domains and Moore-Penrose pseudo-inverses for input distribution analysis.

Findings

Framework effectively analyzes input density distributions.

Experimental results demonstrate practical applicability.

Provides insights into neural network input space behavior.

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.