Grothendieck Graph Neural Networks Framework: An Algebraic Platform for Crafting Topology-Aware GNNs

Amirreza Shiralinasab Langari, Leila Yeganeh, Kim Khoa Nguyen

Keywords: Graph Neural Networks, Categorical Deep Learning, Algebraic Deep Learning, Graph Isomorphism, Graph Classification

TL;DR: This paper proposes a novel approach by generalizing the concept of neighborhoods through algebraic covers to overcome these limitations.

Abstract:

Due to the structural limitations of Graph Neural Networks (GNNs), particularly those relying on conventional neighborhoods, alternative aggregation strategies have been explored to enhance expressive power. This paper proposes a novel approach by generalizing the concept of neighborhoods through algebraic covers to overcome these limitations.
We introduce the Grothendieck Graph Neural Networks (GGNN) framework, providing an algebraic platform for systematically defining and refining diverse covers for graphs. The GGNN framework translates these covers into matrix representations, extending the scope of designing GNN models by incorporating desired message-passing strategies.
Based on the GGNN framework, we propose Sieve Neural Networks (SNN), a new GNN model that leverages the notion of sieves from category theory. SNN demonstrates competitive performance in experiments, particularly in differentiating between strongly regular graphs, and exemplifies the versatility of GGNN in generating novel architectures.
In conclusion, our work advances the design of GNNs by introducing algebraic structures that empower more expressive message-passing mechanisms, addressing the limitations of traditional neighborhood-based methods.

Primary Area: learning on graphs and other geometries & topologies

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Submission Number: 8675