The $\mu\mathcal{G}$ Language for Programming Graph Neural Networks

TL;DR

The paper introduces $ul$ a domain-specific language for designing graph neural networks, enhancing explainability and trustworthiness through formal semantics, type safety, and visual representation.

Contribution

It presents a novel language with formal semantics and type system for graph neural networks, enabling easier design, understanding, and customization.

Findings

Language can define popular GNN models

Provides graphical visualization of GNN programs

Ensures type soundness and correctness

Abstract

Graph neural networks form a class of deep learning architectures specifically designed to work with graph-structured data. As such, they share the inherent limitations and problems of deep learning, especially regarding the issues of explainability and trustworthiness. We propose $\mu\mathcal{G}$, an original domain-specific language for the specification of graph neural networks that aims to overcome these issues. The language's syntax is introduced, and its meaning is rigorously defined by a denotational semantics. An equivalent characterization in the form of an operational semantics is also provided and, together with a type system, is used to prove the type soundness of $\mu\mathcal{G}$. We show how $\mu\mathcal{G}$ programs can be represented in a more user-friendly graphical visualization, and provide examples of its generality by showing how it can be used to define some of the most popular graph neural network models, or to develop any custom graph processing application.