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

2026-03-26

AI Summary

This work investigates the efficient characterization of the evolution of input probability density distributions in neural networks within the framework of probabilistic abstract interpretation. To overcome the representational limitations of traditional grid-based abstractions, the authors introduce two novel abstract domains—distributional approximation and clustering approximation—and design corresponding abstract transformers to formally analyze neural network behavior. This approach represents the first integration of these approximation mechanisms into probabilistic abstract interpretation, offering theoretical soundness guarantees. Empirical evaluations demonstrate its superior precision and expressive power compared to existing methods, thereby establishing a new pathway for the formal verification of neural networks.

Technology Category

• Machine Learning: Probabilistic Circuits and Graphical Models
• Reasoning under Uncertainty: Probabilistic Programming
• Knowledge Representation and Reasoning: Diagnosis and Abductive Reasoning

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Web Mining and Content Analysis: Models for Web evolution
• Social Networks and Social Media: Influence propagation, information diffusion, and the prediction on networks

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.

Problem

• probabilistic abstract interpretation
• neural network analysis
• abstract domains
• density distribution
• approximation methods

Innovation

• distribution approximation
• clusters approximation
• probabilistic abstract interpretation
• abstract domains
• neural network analysis