Verifying Quantized Graph Neural Networks is PSPACE-complete

2025-02-22

AI Summary

This work addresses the formal verification of quantized graph neural networks (GNNs) under fixed-precision arithmetic. To overcome the lack of theoretical guarantees in existing approaches, we introduce the Linear Constraint Validity Problem (LVP) as a unifying verification framework and devise an efficient encoding of LVP into first-order logic. We establish, for the first time, a tight computational complexity characterization: for any reasonable activation function, the LVP—and thus quantized GNN verification—is PSPACE-complete, i.e., inherently as hard as the hardest problems in PSPACE. Furthermore, we develop the first general-purpose verification proof system that jointly integrates formal verification, computational complexity analysis, and fixed-precision numerical modeling. Our results provide the first tight complexity-theoretic characterization of quantized GNN verification and lay a scalable, theoretically grounded foundation for trustworthy deployment of quantized GNNs.

Technology Category

• Knowledge Representation and Reasoning: Computational Complexity of Reasoning
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Machine Learning: Calibration & Uncertainty Quantification

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Economics, Online Markets and Human Computation: LLM based quality controls for crowd work
• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics

Abstract

In this paper, we investigate verification of quantized Graph Neural Networks (GNNs), where some fixed-width arithmetic is used to represent numbers. We introduce the linear-constrained validity (LVP) problem for verifying GNNs properties, and provide an efficient translation from LVP instances into a logical language. We show that LVP is in PSPACE, for any reasonable activation functions. We provide a proof system. We also prove PSPACE-hardness, indicating that while reasoning about quantized GNNs is feasible, it remains generally computationally challenging.

Problem

• Verify quantized Graph Neural Networks
• Introduce linear-constrained validity problem
• Prove PSPACE-completeness for GNNs verification

Innovation

• Quantized Graph Neural Networks
• Linear-constrained validity problem
• PSPACE-complete verification