Unveiling the Convergence Dynamics of a Graph Recommender System

Graph Neural Networks (GNN) have shown performance on learning on structured data and found applications in different fields like biology, physics, transportation, e-commerce. However, the convergence dynamic of GNN models, particularly the ones for link prediction tasks, remains a challenge for better design. Existing approaches have shown that some simpler GNN architectures can be effective as complex ones when used for recommender system (recsys). This encourages the need to perceive the advantage of some components towards a model convergence. We built models for link prediction, specially recsys based on a single layer GNN and evaluate their convergence on real and generated graphs data. These recsys are based on a graph convolution layer with added scaling factor or activation function. Our theoretical and numerical results highlight the advantage of a scaling factor over an activation function. It means models which scale down features before the final output converge, compared to others. Besides, the ReLU activation function alone cannot compensate for the missing scaling factor. The takeaway and advantage of a scaling factor resides in its ability to change the direction of the hidden features vector.