Non-convolutional Graph Neural Networks
This work addresses graph learning challenges for researchers and practitioners by offering a robust and efficient alternative to convolutional GNNs, though it is incremental as it builds on existing random walk and RNN concepts.
The paper tackles the limitations of convolution-based graph neural networks, such as limited expressiveness and computational inefficiency, by introducing a non-convolutional method called RUM neural network, which achieves competitive performance and is faster than simple convolutional GNNs on various tasks.
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.