Distribution and Clusters Approximations as Abstract Domains in Probabilistic Abstract Interpretation to Neural Network Analysis

TL;DR

This paper introduces two novel approximation methods, distribution and clusters, within the probabilistic abstract interpretation framework to improve neural network analysis by better capturing input distributions.

Contribution

It presents the first theoretical development of distribution and clusters approximation methods as new abstract domains in probabilistic neural network analysis.

Findings

Distribution approximation method demonstrated in simple examples

Clusters approximation method illustrated with theoretical examples

Framework enhances neural network analysis by capturing input distributions more effectively

Abstract

The probabilistic abstract interpretation framework of neural network analysis analyzes a neural network by analyzing its density distribution flow of all possible inputs. The grids approximation is one of abstract domains the framework uses which abstracts concrete space into grids. In this paper, we introduce two novel approximation methods: distribution approximation and clusters approximation. We show how these two methods work in theory with corresponding abstract transformers with help of illustrations of some simple examples.