Implicit vs Unfolded Graph Neural Networks

It has been observed that graph neural networks (GNN) sometimes struggle to maintain a healthy balance between modeling long-range dependencies across nodes while avoiding unintended consequences such as oversmoothed node representations. To address this issue (among other things), two separate strategies have recently been proposed, namely implicit and unfolded GNNs. The former treats node representations as the fixed points of a deep equilibrium model that can efficiently facilitate arbitrary implicit propagation across the graph with a fixed memory footprint. In contrast, the latter involves treating graph propagation as the unfolded descent iterations as applied to some graph-regularized energy function. While motivated differently, in this paper we carefully elucidate the similarity and differences of these methods, quantifying explicit situations where the solutions they produced may actually be equivalent and others where behavior diverges. This includes the analysis of convergence, representational capacity, and interpretability. We also provide empirical head-to-head comparisons across a variety of synthetic and public real-world benchmarks.