Graph Heavy Light Decomposed Networks: Towards learning scalable long-range graph patterns

Alan Marko, Peter Dominik Ralbovský

Keywords: gnn, graphhldn, graphhldns, long-range patterns, hld, heavy, light, decomposition, scalable, algorithms, aqsol, esol

TL;DR: We introduce Graph Heavy Light Decomposed Networks(GraphHLDs) that enable reasoning about long-range relationships on graphs reducible to trees

Abstract: We present graph heavy light decomposed networks (GraphHLDNs), novel neural network architectures allowing reasoning about long-range relationships on graphs reducible to trees. By decomposing the trees into a set of interconnected chains in a way similar to the heavy-light decomposition algorithm, we rewire a tree with $n$ vertices so that its depth is in order of $O(\log^2 n)$ after building a binary-tree-shaped neural network over each chain. This enables faster propagation and aggregation of information over the whole graph while being able to reason about long-range sequences of nodes and considering their ordering. We show that in this way the method is partially addressing the previous need of message-passing architectures for step-by-step supervision to execute certain algorithms out-of-distribution. Our method is also applicable to real-world datasets, achieving results competitive with other state-of-the-art architectures targeted on learning long-range dependencies or using positional encodings on several molecular datasets.

Type Of Submission: Extended abstract (max 4 main pages).

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Type Of Submission: Extended abstract.