Learnable Commutative Monoids for Graph Neural Networks

• URL: http://arxiv.org/abs/2212.08541v1
• Date: Fri, 16 Dec 2022 15:43:41 GMT
• Title: Learnable Commutative Monoids for Graph Neural Networks
• Authors: Euan Ong and Petar Veli\v{c}kovi\'c
• Abstract summary: Graph neural networks (GNNs) are highly sensitive to the choice of aggregation function. We show that GNNs equipped with recurrent aggregators are competitive with state-of-the-art permutation-invariant aggregators. We propose a framework for constructing learnable, commutative, associative binary operators.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Graph neural networks (GNNs) have been shown to be highly sensitive to the choice of aggregation function. While summing over a node's neighbours can approximate any permutation-invariant function over discrete inputs, Cohen-Karlik et al. [2020] proved there are set-aggregation problems for which summing cannot generalise to unbounded inputs, proposing recurrent neural networks regularised towards permutation-invariance as a more expressive aggregator. We show that these results carry over to the graph domain: GNNs equipped with recurrent aggregators are competitive with state-of-the-art permutation-invariant aggregators, on both synthetic benchmarks and real-world problems. However, despite the benefits of recurrent aggregators, their $O(V)$ depth makes them both difficult to parallelise and harder to train on large graphs. Inspired by the observation that a well-behaved aggregator for a GNN is a commutative monoid over its latent space, we propose a framework for constructing learnable, commutative, associative binary operators. And with this, we construct an aggregator of $O(\log V)$ depth, yielding exponential improvements for both parallelism and dependency length while achieving performance competitive with recurrent aggregators. Based on our empirical observations, our proposed learnable commutative monoid (LCM) aggregator represents a favourable tradeoff between efficient and expressive aggregators.

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