SpeqNets: Sparsity-aware Permutation-equivariant Graph Networks

TL;DR

This paper introduces a new class of scalable, permutation-equivariant graph networks that adapt to graph sparsity, balancing expressivity and efficiency, and outperforming existing methods in classification and regression tasks.

Contribution

The authors propose a novel framework for universal, permutation-equivariant graph networks that are scalable and adapt to graph sparsity, improving performance and efficiency.

Findings

Vastly reduced computation times compared to standard higher-order graph networks.

Significant improvements over traditional graph neural networks and kernels in predictive tasks.

Effective control of expressivity and scalability in graph neural network architectures.

Abstract

While (message-passing) graph neural networks have clear limitations in approximating permutation-equivariant functions over graphs or general relational data, more expressive, higher-order graph neural networks do not scale to large graphs. They either operate on $k$-order tensors or consider all $k$-node subgraphs, implying an exponential dependence on $k$ in memory requirements, and do not adapt to the sparsity of the graph. By introducing new heuristics for the graph isomorphism problem, we devise a class of universal, permutation-equivariant graph networks, which, unlike previous architectures, offer a fine-grained control between expressivity and scalability and adapt to the sparsity of the graph. These architectures lead to vastly reduced computation times compared to standard higher-order graph networks in the supervised node- and graph-level classification and regression regime while significantly improving over standard graph neural network and graph kernel architectures in terms of predictive performance.