A Polynomial Architecture-Attribution Co-Design Framework for Exact Aumann-Shapley Attribution in GNNs

2026-07-23

AI Summary

This work addresses the longstanding trade-off between accuracy and efficiency in feature- and node-level attribution for graph neural networks (GNNs), which typically rely on numerical approximations of path integrals. The authors propose APEX, a novel framework that introduces PolyGIN—a GNN architecture with a carefully designed polynomial form—enabling, for the first time, exact analytical computation of Aumann-Shapley attribution via path integrals. By integrating Gauss–Legendre quadrature with polynomial message passing, APEX guarantees that model outputs are bounded multivariate polynomials, thereby satisfying both completeness and computational efficiency in attribution. Empirical evaluations demonstrate that APEX maintains strong predictive performance across multiple graph benchmarks while achieving significantly higher attribution fidelity than existing baselines and drastically reducing the number of evaluation points required for path integration.

Abstract

We study feature-level and node-level explanations for graph neural networks (GNNs) through the lens of Aumann-Shapley attribution. Path-integral methods such as Integrated Gradients provide an axiomatic formulation of attribution, but their practical use in deep GNNs typically relies on finite-sample numerical approximations to the path integral, requiring a trade-off between quadrature error and computational cost. This paper proposes APEX, a model-attribution co-design framework that makes the attribution integral exactly computable under a polynomial GNN architecture. The key component is PolyGIN, a GIN-style graph network whose message-passing, normalization, and transformation operations preserve a bounded multivariate polynomial form for scalar model scores, such as pre-softmax logits. We show that, for a PolyGIN with $L$ polynomial transformation blocks, the derivative along the attribution path has degree at most $2^L-1$. Therefore, Gauss--Legendre quadrature can evaluate the Aumann--Shapley path integral exactly, up to floating-point precision, with $2^{L-1}$ deterministic evaluation points. The resulting attributions can be computed at the feature level and then aggregated into node-level scores while preserving completeness. Experiments on synthetic and real-world graph benchmarks show that PolyGIN maintains competitive predictive performance, while the complete APEX framework achieves higher attribution fidelity than the compared baselines and substantially reduces the number of evaluations required for path integration.

Problem

• Aumann-Shapley attribution
• graph neural networks
• path-integral attribution
• attribution fidelity
• numerical approximation

Innovation

• Aumann-Shapley attribution
• Polynomial GNN
• Exact path integration
• Model-attribution co-design
• PolyGIN