Learning Self-Explainable Edge Representations via Compositional Geometry

Representation learning is central to graph machine learning, with link prediction as a central task. However, most graph models represent edges through opaque similarity functions, offering limited insight into how the latent memberships of two nodes combine to produce, or inhibit, a particular interaction. Many networks naturally admit a compositional view, where nodes express soft membership over multiple latent archetypes and edges may arise through different combinations of these memberships. Motivated by this structure, we propose a compositional graph model that learns self-explainable edge representations. Nodes are represented as simplex-valued compositions over learned archetypes, with each archetype defining an edge channel that combines the shared membership of a node pair in that archetype with their Aitchison agreement over the remaining archetypes. The resulting channel values jointly determine the edge probability and, after normalization, form a compositional representation of the edge itself. This yields explanations by construction: the same quantities used for prediction describe how an interaction is allocated across latent archetypes. We establish that these channels retain relational information lost by global membership overlap and full compositional distance, respond predictably to membership perturbations, and support exact counterfactual reasoning through channel restriction. Across link-prediction benchmarks, the model achieves competitive performance against strong graph-learning baselines while enabling new analyses of how latent memberships shape individual interactions. In particular, its compositional structure supports semantic membership interventions and counterfactual studies that probe which latent channels carry individual edge predictions.