Reinventing the Theory of Machine Learning on Graphs

In many scientic domains, graphs are the objects of choice to represent structured data: from molecules to social networks, power grids, the internet, and so on. The exploitation of graph data represents a major scientic and industrial challenge. Graph Machine Learning(GML) is thus a fast-growing eld, with so-called Graph Neural Networks (GNN) at the forefront. However, in sharp contrast with traditional ML, the eld of GML has somewhat jumped from early methods to deep learning, without the decades-long development of well- established notions to compare, analyze and improve algorithms. As a result, 1) GNNs, all based on the so-called message-passing paradigm, have signicant limitations both practical and theoretical, and it is not clear how to address them, and 2) GNNs do not take into account the specicities of graphs coming from domains as dierent as biology or the social sciences. Thus, practical results may vary wildly from one case to the other, with no guidelines on how to design reliable GNNs in each case. Overall, these are the symptoms of an overlooked major issue: GML is hitting a glass ceiling due to its severe lack of a grand, foundational theory.The ambition of project MALAGA is to develop such a theory. Solving the crucial limitations of the current theory is highly challenging: current mathematical tools cannot analyze the learning capabilities of GML methods in a unied way, existing statistical graph models donot faithfully represent the many characteristics of modern graph data, computational complexity becomes problematic on large graphs. MALAGA will develop a radically new understanding of GML problems, and of the strengths and limitations of a large panel of algorithms. Our goal is to signicantly boost the performance, reliability and adaptivity of GNNs, with a signicant impact on three types of graph data that exhibit very dierent but representative behaviors: biological networks, social networks, and online recommender systems.