Grammatical Path Network : You want cycles, paths is all you need.

Jason Piquenot, Louisa Bouzidi, Maxime Berar, Pierre Héroux, Romain Raveaux, Jean-Yves RAMEL, Sébastien Adam

Keywords: Graph Neural Network, Graph Learning

TL;DR: This work introduces the Grammatical Path Network, a novel Graph Neural Network that efficiently captures cycles in graph structures using Context-Free Grammar, achieving high performance on cycle-related tasks without explicit cycle precomputation.

Abstract:

In this work, we address the challenge of learning from structured data by proposing the Grammatical Path Network (GPN), a novel Graph Neural Network (GNN) designed to efficiently capture cycles in graph structures. Building on recent advancements in GNN expressiveness and substructure counting, GPN combines methodologies from Graph Substructure Networks (GSN) and a framework that translates Context Free Grammars (CFG) into GNNs. The key innovation lies in using CFG to count cycles of length $l+1$ by precomputing paths of length $l$ at the edge level, maintaining the computational complexity of standard Message Passing Neural Networks (MPNNs). Our experiments demonstrate that GPN achieves comparable performance to GSN on datasets requiring cycle information, without the need for explicit cycle precomputation. This approach offers a promising direction for developing efficient and expressive GNNs for structured data analysis.

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

Submission Number: 100