  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
