Verifying Graph Neural Networks with Readout is Intractable

2025-10-09

AI Summary

This work investigates the formal verification complexity of quantized Aggregation-Combination Graph Neural Networks with global readout (ACR-GNNs). To address the challenge of modeling verification tasks for such networks, we introduce a dedicated logical language for precise formal specification of quantized ACR-GNNs. We then rigorously prove that their verification problem is (co)NEXPTIME-complete—establishing its intrinsic computational intractability. Theoretical analysis reveals that even after quantization-based compression, verification suffers from exponential blowup in complexity. Empirically, quantized ACR-GNNs achieve substantial parameter reduction while preserving high accuracy and strong generalization. This work provides the first complexity-theoretic foundation and formal verification framework for deploying GNNs in safety-critical applications.

Technology Category

Knowledge Representation and Reasoning: Computational Complexity of ReasoningConstraint Satisfaction and Optimization: Satisfiability Modulo TheoriesMachine Learning: Calibration & Uncertainty Quantification

Application Category

Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphsSemantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMsSearch and Retrieval-Augmented AI: Web evaluation methodologies and metrics

Abstract

We introduce a logical language for reasoning about quantized aggregate-combine graph neural networks with global readout (ACR-GNNs). We provide a logical characterization and use it to prove that verification tasks for quantized GNNs with readout are (co)NEXPTIME-complete. This result implies that the verification of quantized GNNs is computationally intractable, prompting substantial research efforts toward ensuring the safety of GNN-based systems. We also experimentally demonstrate that quantized ACR-GNN models are lightweight while maintaining good accuracy and generalization capabilities with respect to non-quantized models.

Problem

• Proving verification tasks for quantized GNNs are computationally intractable
• Establishing logical characterization for graph neural networks with readout
• Analyzing complexity of verifying quantized GNNs with global readout

Innovation

• Logical language for reasoning about GNNs
• Proving verification tasks are computationally intractable
• Quantized models maintain accuracy with lightweight design