SpeqNets: Sparsity-aware Permutation-equivariant Graph Networks
This addresses a key bottleneck in graph machine learning for applications requiring scalable and expressive models, though it is incremental in refining existing higher-order approaches.
The paper tackles the trade-off between expressivity and scalability in graph neural networks by introducing SpeqNets, a class of permutation-equivariant networks that adapt to graph sparsity, resulting in vastly reduced computation times and significant improvements in predictive performance over standard methods.
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.