When Must All Conditions Hold? Identifiable Conjunctive Explanations for Link Prediction with Multiplicative View-Gated Graph Neural Networks

Abstract

Link predictors that support decisions, such as suggesting a director to a startup, must explain why a link is or is not recommended. We propose the Multiplicative View-Gated GNN (MG-GNN), which scores a pair as the weighted product of gates, each restricted to one view of the evidence: attributes, structural position, neighbourhood overlap and proximity. Its attributions are exact, and a single failing view caps the score, which certifies robustness to the manipulation of any one view. We prove that, under a conjunctive mechanism, each gate recovers its true condition, whereas additive attributions are not identified. We also prove that disjoint view inputs stop one view from absorbing the vetoes of the others, at a measurable cost. An out-of-sample Vuong test tells the analyst whether the conjunctive reading is warranted, and it identifies the mechanism in all ten synthetic graphs. On six benchmarks, a heterogeneous graph and a new national graph of 13,765 Italian innovative firms and 25,918 directors, MG-GNN matches strong GNN baselines. Its explanations reach 0.97–0.99 of oracle fidelity and are far more stable than Shapley values. In the case study, MG-GNN predicts the 2025–2026 appointments from 2024 data and outperforms the platform’s hand-crafted index.