Rethinking Node Representation Interpretation through Relation Coherence

Understanding node representations in graph-based models is crucial for uncovering biases ,diagnosing errors, and building trust in model decisions. However, previous work on explainable AI for node representations has primarily emphasized explanations (reasons for model predictions) rather than interpretations (mapping representations to understandable concepts). Furthermore, the limited research that focuses on interpretation lacks validation, and thus the reliability of such methods is unclear. We address this gap by proposing a novel interpretation method-Node Coherence Rate for Representation Interpretation (NCI)-which quantifies how well different node relations are captured in node representations. We also propose a novel method (IME) to evaluate the accuracy of different interpretation methods. Our experimental results demonstrate that NCI reduces the error of the previous best approach by an average of 39%. We then apply NCI to derive insights about the node representations produced by several graph-based methods and assess their quality in unsupervised settings.

Node Similarities under Random Projections: Limits and Pathological Cases

Random Projections have been widely used to generate embeddings for various graph tasks due to their computational efficiency. The majority of applications have been justified through the Johnson-Lindenstrauss Lemma. In this paper, we take a step further and investigate how well dot product and cosine similarity are preserved by Random Projections. Our analysis provides new theoretical results, identifies pathological cases, and tests them with numerical experiments. We find that, for nodes of lower or higher degrees, the method produces especially unreliable embeddings for the dot product, regardless of whether the adjacency or the (normalized version) transition is used. With respect to the statistical noise introduced by Random Projections, we show that cosine similarity produces remarkably more precise approximations.