Unifying Label-inputted Graph Neural Networks with Deep Equilibrium Models
It addresses the dilemma between propagation distance and adaptiveness in graph neural networks for researchers in graph learning, offering a novel integration of two subdomains.
This work unifies Label-inputted Graph Neural Networks (LGNN) and Implicit GNNs (IGNN) by interpreting LGNN within IGNN theory, proposing Label-inputted Implicit GNN (LI-GNN) to combine their advantages, enabling infinite-range label propagation with constant memory and more expressive networks, and demonstrates effectiveness in node classification experiments on eight datasets.
The success of Graph Neural Networks (GNN) in learning on non-Euclidean data arouses many subtopics, such as Label-inputted GNN (LGNN) and Implicit GNN (IGNN). LGNN, explicitly inputting supervising information (a.k.a. labels) in GNN, integrates label propagation to achieve superior performance, but with the dilemma between its propagating distance and adaptiveness. IGNN, outputting an equilibrium point by iterating its network infinite times, exploits information in the entire graph to capture long-range dependencies, but with its network constrained to guarantee the existence of the equilibrium. This work unifies the two subdomains by interpreting LGNN in the theory of IGNN and reducing prevailing LGNNs to the form of IGNN. The unification facilitates the exchange between the two subdomains and inspires more studies. Specifically, implicit differentiation of IGNN is introduced to LGNN to differentiate its infinite-range label propagation with constant memory, making the propagation both distant and adaptive. Besides, the masked label strategy of LGNN is proven able to guarantee the well-posedness of IGNN in a network-agnostic manner, granting its network more complex and thus more expressive. Combining the advantages of LGNN and IGNN, Label-inputted Implicit GNN (LI-GNN) is proposed. It can be widely applied to any specific GNN to boost its performance. Node classification experiments on two synthesized and six real-world datasets demonstrate its effectiveness. Code is available at https://github.com/cf020031308/LI-GNN