To Share or Not to Share: Investigating Weight Sharing in Variational Graph Autoencoders
This work investigates the theoretical justification of weight sharing (WS) in Variational Graph Autoencoders (VGAEs). Through rigorous theoretical analysis and systematic experiments across multiple graph benchmarks—including Cora and Citeseer—we establish, for the first time, the universal benefits of WS in VGAEs: it substantially reduces model complexity, improves generalization, and preserves near-identical performance in link prediction and node classification. We reveal that WS serves a dual role—simplifying optimization and acting as an implicit regularizer—thereby enhancing embedding stability and robustness. Our findings demonstrate that WS is not merely an empirical heuristic but a principled design choice grounded in both theoretical analysis and empirical validation. This work establishes WS as a default architectural recommendation for VGAEs and related variational graph representation learning frameworks.