ESSLLI 2026 Course on Verifying graph neural networks

This advanced course is about verifying graph neural networks. We will survey the main results about the expressivity of graph neural networks. We will discuss a methodology to verify the behaviors of GNNs, present their link with counting logics, and describe verification algorithms.

Programme

• Monday 3th of August: motivation and definition of GNN (graph neural networks); color refinement
• Tuesday 4th of August: correspondence between FO with counting with two variables and color refinement. Correspondence between graded modal logic and GNNs.
• Wednesday 5th of August: GNNs and logics with Presburger arithmetics. Idea of tableau method for standard modal logic.
• Thursday 6th of August: Quantifier-free Boolean algebra and Presburger arithmetics and reasoning in a logic with Presburger arithmetics.
• Friday 7th of August: Medley of different topics

Contact

• François Schwarzentruber, francois.schwarzentruber@ens-lyon.fr

Lecture notes

Lecture notes

Other ressources

• Workshop on GNNs and logic
• FLOC 2026 Workshop on Logical Methods for Neural Network Analysis (LogicNN)