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

Summary

This paper, authored by Zhuofan Zhang and Herbert Wiklicky and posted to arXiv (2603.25273), contributes to the field of machine learning and static analysis. It addresses a stochastic abstract interpretation framework for analyzing neural networks, which works by tracking the flow of density distributions over all possible inputs. Within this framework, grid approximation is one existing abstract domain that abstracts the concrete space into a grid structure. The authors introduce two novel approximation methods: distribution approximations and clusters approximations. They show how both methods operate in theory via corresponding abstraction transformers, illustrated with several simple examples. This work extends the toolkit of abstract domains available for probabilistic analysis of neural network behavior, offering alternatives to grid-based abstraction that may better capture distributional properties of the concrete state space.