Non-convolutional Graph Neural Networks

TL;DR

This paper introduces RUM, a convolution-free graph neural network that leverages RNNs along random walks to enhance expressiveness and mitigate common GNN issues like over-smoothing, demonstrating competitive and scalable performance.

Contribution

The paper proposes a novel convolution-free GNN model called RUM that combines RNNs with random walks, improving expressiveness and efficiency over traditional convolution-based GNNs.

Findings

RUM is more expressive than the Weisfeiler-Lehman test.

RUM achieves competitive performance on various tasks.

RUM is robust, scalable, and faster than simple convolutional GNNs.

Abstract

Rethink convolution-based graph neural networks (GNN) -- they characteristically suffer from limited expressiveness, over-smoothing, and over-squashing, and require specialized sparse kernels for efficient computation. Here, we design a simple graph learning module entirely free of convolution operators, coined random walk with unifying memory (RUM) neural network, where an RNN merges the topological and semantic graph features along the random walks terminating at each node. Relating the rich literature on RNN behavior and graph topology, we theoretically show and experimentally verify that RUM attenuates the aforementioned symptoms and is more expressive than the Weisfeiler-Lehman (WL) isomorphism test. On a variety of node- and graph-level classification and regression tasks, RUM not only achieves competitive performance, but is also robust, memory-efficient, scalable, and faster than the simplest convolutional GNNs.