Scalable Graph Compressed Convolutions

TL;DR

This paper introduces CoCN, a scalable graph neural network that generalizes Euclidean convolution to graphs through a permutation-based calibration, enabling hierarchical learning and achieving superior results on benchmarks.

Contribution

It proposes a novel permutation-based calibration method to adapt Euclidean convolution for graphs and introduces the CoCN model for hierarchical graph representation learning.

Findings

CoCN outperforms baseline GNNs on node and graph benchmarks.

The permutation calibration enables flexible Euclidean convolution on irregular graphs.

End-to-end training with residual and inception mechanisms enhances performance.

Abstract

Designing effective graph neural networks (GNNs) with message passing has two fundamental challenges, i.e., determining optimal message-passing pathways and designing local aggregators. Previous methods of designing optimal pathways are limited with information loss on the input features. On the other hand, existing local aggregators generally fail to extract multi-scale features and approximate diverse operators under limited parameter scales. In contrast to these methods, Euclidean convolution has been proven as an expressive aggregator, making it a perfect candidate for GNN construction. However, the challenges of generalizing Euclidean convolution to graphs arise from the irregular structure of graphs. To bridge the gap between Euclidean space and graph topology, we propose a differentiable method that applies permutations to calibrate input graphs for Euclidean convolution. The permutations constrain all nodes in a row regardless of their input order and therefore enable the flexible generalization of Euclidean convolution to graphs. Based on the graph calibration, we propose the Compressed Convolution Network (CoCN) for hierarchical graph representation learning. CoCN follows local feature-learning and global parameter-sharing mechanisms of convolution neural networks. The whole model can be trained end-to-end, with compressed convolution applied to learn individual node features and their corresponding structure features. CoCN can further borrow successful practices from Euclidean convolution, including residual connection and inception mechanism. We validate CoCN on both node-level and graph-level benchmarks. CoCN achieves superior performance over competitive GNN baselines. Codes are available at https://github.com/sunjss/CoCN.