Speqnets Sparsityaware Permutationequivariant Graph Networks

# SpeqNets: Sparsity-aware Permutation-equivariant Graph Networks

**arXiv ID:** 2203.13913
**Authors:** Christopher Morris, Gaurav Rattan, Sandra Kiefer, Siamak Ravanbakhsh
**Published:** 2022-03-25T21:17:09Z
**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.

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## References

- [arXiv:2203.13913](http://arxiv.org/abs/2203.13913v3)