Beyond Message Passing: A Symbolic Alternative for Expressive and Interpretable Graph Learning

TL;DR

SymGraph introduces a symbolic graph learning framework that surpasses traditional message-passing limitations, offering enhanced expressiveness, interpretability, and significant training speed improvements, suitable for high-stakes applications.

Contribution

The paper presents SymGraph, a symbolic architecture that overcomes the 1-WL barrier and enhances interpretability without relying on differentiable message passing.

Findings

Achieves state-of-the-art performance on benchmark tasks.

Provides 10x to 100x faster training times on CPU.

Generates semantically rich rules for scientific discovery.

Abstract

Graph Neural Networks (GNNs) have become essential in high-stakes domains such as drug discovery, yet their black-box nature remains a significant barrier to trustworthiness. While self-explainable GNNs attempt to bridge this gap, they often rely on standard message-passing backbones that inherit fundamental limitations, including the 1-Weisfeiler-Lehman (1-WL) expressivity barrier and a lack of fine-grained interpretability. To address these challenges, we propose SymGraph, a symbolic framework designed to transcend these constraints. By replacing continuous message passing with discrete structural hashing and topological role-based aggregation, our architecture theoretically surpasses the 1-WL barrier, achieving superior expressiveness without the overhead of differentiable optimization. Extensive empirical evaluations demonstrate that SymGraph achieves state-of-the-art performance, outperforming existing self-explainable GNNs. Notably, SymGraph delivers 10x to 100x speedups in training time using only CPU execution. Furthermore, SymGraph generates rules with superior semantic granularity compared to existing rule-based methods, offering great potential for scientific discovery and explainable AI.