How does over-squashing affect the power of GNNs?

التفاصيل البيبلوغرافية
العنوان: How does over-squashing affect the power of GNNs?
المؤلفون: Di Giovanni, Francesco, Rusch, T. Konstantin, Bronstein, Michael M., Deac, Andreea, Lackenby, Marc, Mishra, Siddhartha, Veličković, Petar
سنة النشر: 2023
المجموعة: Computer Science
Statistics
مصطلحات موضوعية: Computer Science - Machine Learning, Statistics - Machine Learning
الوصف: Graph Neural Networks (GNNs) are the state-of-the-art model for machine learning on graph-structured data. The most popular class of GNNs operate by exchanging information between adjacent nodes, and are known as Message Passing Neural Networks (MPNNs). Given their widespread use, understanding the expressive power of MPNNs is a key question. However, existing results typically consider settings with uninformative node features. In this paper, we provide a rigorous analysis to determine which function classes of node features can be learned by an MPNN of a given capacity. We do so by measuring the level of pairwise interactions between nodes that MPNNs allow for. This measure provides a novel quantitative characterization of the so-called over-squashing effect, which is observed to occur when a large volume of messages is aggregated into fixed-size vectors. Using our measure, we prove that, to guarantee sufficient communication between pairs of nodes, the capacity of the MPNN must be large enough, depending on properties of the input graph structure, such as commute times. For many relevant scenarios, our analysis results in impossibility statements in practice, showing that over-squashing hinders the expressive power of MPNNs. We validate our theoretical findings through extensive controlled experiments and ablation studies.
Comment: 36 pages; Published in Transactions on Machine Learning Research (TMLR)
نوع الوثيقة: Working Paper
URL الوصول: http://arxiv.org/abs/2306.03589
رقم الأكسشن: edsarx.2306.03589
قاعدة البيانات: arXiv