Implicit Subgraph Neural Network

Subgraph neural networks have recently gained prominence for various subgraph-level predictive tasks. However, existing methods either 1) apply simple standard pooling over graph convolutional networks, failing to capture essential subgraph properties, or 2) rely on rigid subgraph definitions, leading to suboptimal performance. Moreover, these approaches fail to model longrange dependencies both between and within subgraphs-a critical limitation, as many realworld networks contain subgraphs of varying sizes and connectivity patterns. In this paper, we propose a novel implicit subgraph neural network, the first of its kind, designed to capture dependencies across subgraphs. Our approach also integrates label-aware subgraph-level information. We formulate implicit subgraph learning as a bilevel optimization problem and develop a provably convergent algorithm that requires fewer gradient estimations than standard bilevel optimization methods. We evaluate our approach on real-world networks against state-ofthe-art baselines, demonstrating its effectiveness and superiority. Our code is avaliable https: //github.com/MLonGraph/ISNN