Graph Neural Networks (GNNs) are a recent extension of the neural network machinery to the graph setting that resolve the challenge of extending deep learning methods the peculiarities of network data by convolving node features across neighbourhoods to embed nodes in Euclidean space. Heralded as the breakthrough for machine learning on graphs that would allow the same “AI renaissance” that standard neural networks have brought to Computer Vision and Natural Language Processing, GNNs have been suggested as a panacea for a wide number of tasks across disciplines. In the biological sciences alone, GNNs have been applied to molecular design, drug-drug interaction predictions, biological networks,
knowledge graphs, and spatial transcriptomics.

Despite their popularity and widespread adoption, the theoretical foundations of GNNs remain underexplored. Fundamental questions about the mathematical principles driving their success, as well as their limitations, biases, and underlying statistical assumptions, are still unresolved. Notably, GNNs diverge significantly from traditional neural networks, with their architecture and function rooted in the unique properties of graph-structured data. These gaps in understanding could have significant implications in real-world applications, where issues revolving around bias and uncertainty must be rigorously addressed.

This workshop seeks to bring together researchers from statistics, computer science and computational biology to explore the theoretical and practical aspects of GNNs. The workshop will focus on topics revolving around three key themes:

• GNN Theory: Investigating foundational topics such as learning rates for classification and regression tasks, understanding the impact of different GNN architectures and the convolution operator.
• Uncertainty Quantification & Interpretability: Understanding the confidence and robustness of GNN predictions.
• Bias and Fairness: Exploring how GNNs may inadvertently propagate or amplify biases and ensuring equitable outcomes in their applications.

This two-day workshop will feature a series of focused deep-dive sessions, each dedicated to a core topic. These sessions will integrate expert talks with interactive discussions and structured brainstorming activities, led by small groups of participants, to foster collaboration and innovative thinking. The anticipated outcome of each session is the formulation of a precise research question and the initial framework of a research plan, providing participants with the opportunity to continue working on these topics beyond the workshop. The
workshop's overarching goal is to produce a collaborative white paper that synthesizes the discussions, highlights key open questions, and outlines promising research directions in the theory and applications of Graph Neural Networks (GNNs).