Graph neural networks (GNNs) have led to major breakthroughs in a variety of domains such as drug discovery, social network analysis, and travel time estimation. However, they lack interpretability which hinders human trust and thereby deployment to settings with high-stakes decisions. A line of interpretable methods approach this by discovering a small set of relevant concepts as subgraphs in the last GNN layer that together explain the prediction. This can yield oversimplified explanations, failing to explain the interaction between GNN layers. To address this oversight, we provide HELP (Hierarchical Explainable Latent Pooling), a novel, inherently interpretable graph pooling approach that reveals how concepts from different GNN layers compose to new ones in later steps. HELP is more than 1-WL expressive and is the first non-spectral, end-to-end-learnable, hierarchical graph pooling method that can learn to pool a variable number of arbitrary connected components. We empirically demonstrate that it performs on-par with standard GCNs and popular pooling methods in terms of accuracy while yielding explanations that are aligned with expert knowledge in the domains of chemistry and social networks. In addition to a qualitative analysis, we employ concept completeness scores as well as concept conformity, a novel metric to measure the noise in discovered concepts, quantitatively verifying that the discovered concepts are significantly easier to fully understand than those from previous work. Our work represents a first step towards an understanding of graph neural networks that goes beyond a set of concepts from the final layer and instead explains the complex interplay of concepts on different levels.

Women are underrepresented in the fields of science, technology, engineering, and mathematics (STEM) in most countries, including Germany and the U.S.29,32 This was demonstrated in several surveys investigating the proportion of women in the STEM fields for specific populations. Some of these studies, for example, investigated the number of enrolled students10,30 or the percentage of female professors at universities. Other studies analyzed the disparities in research funding.23 Nearly all these surveys selected a particular population of women in consideration of their university degree or their nationality.11,34 Like many other studies investigating the gender gap and its reasons in science, these surveys are usually based on data records from several kinds of registrations or enrollments, for example, the enrollment as student or doctoral student, the registration of finished doctoral theses or the membership as professor in a certain country.1,14,16,28 However, researchers at the postdoctoral level or industrial researchers are often not registered and unfortunately drop out of the surveys.