Probabilistic Abstract Interpretation on Neural Networks via Grids Approximation

2026-03-26

AI Summary

This work addresses the challenge of analyzing the propagation of input probability density distributions through neural networks when inputs are uncountable or countably infinite, a setting where exhaustive testing is infeasible. It introduces, for the first time, a systematic application of probabilistic abstract interpretation to neural network analysis. The authors propose a grid-based abstract domain and corresponding abstract transformers, combined with the Moore–Penrose pseudoinverse to construct a computable model of density flow. This approach effectively captures the evolution of input distributions throughout the network. Empirical evaluations on multiple real-world case studies demonstrate the framework’s ability to accurately model input density transformations, highlighting its practical applicability and effectiveness in realistic scenarios.

Technology Category

Reasoning under Uncertainty: Relational Probabilistic ModelsMachine Learning: Probabilistic Circuits and Graphical ModelsNatural Language Processing: Interpretability, Analysis, and Evaluation of NLP Models

Application Category

Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphsSocial Networks and Social Media: Influence propagation, information diffusion, and the prediction on networksWeb Mining and Content Analysis: Large pretrained models with web data

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.

Problem

• Probabilistic Abstract Interpretation
• Neural Networks
• Density Distribution
• Abstract Domains
• Input Space

Innovation

• Probabilistic Abstract Interpretation
• Neural Networks
• Grids Approximation
• Abstract Transformers
• Moore-Penrose Pseudo-inverse