Graph Neural Networks (GNNs) are powerful tools for handling graph-type data. Recently, GNNs have been widely applied in various domains, but they also face some issues, such as overfitting, over-smoothing and non-robustness. The existing research indicates that random dropout methods are an effective way to address these issues. However, random dropout methods in GNNs still face unresolved problems. Currently, the choice of dropout rate, often determined by heuristic or grid search methods, can increase the generalization error, contradicting the principal aims of dropout. In this paper, we propose a novel random dropout method for GNNs called FlexiDrop. First, we conduct a theoretical analysis of dropout in GNNs using rademacher complexity and demonstrate that the generalization error of traditional random dropout methods is constrained by a function related to the dropout rate. Subsequently, we use this function as a regularizer to unify the dropout rate and empirical loss within a single loss function, optimizing them simultaneously. Therefore, our method enables adaptive adjustment of the dropout rate and theoretically balances the trade-off between model complexity and generalization ability. Furthermore, extensive experimental results on benchmark datasets show that FlexiDrop outperforms traditional random dropout methods in GNNs.

翻译：图神经网络（GNNs）是处理图结构数据的强大工具。近年来，GNNs 已在多个领域得到广泛应用，但也面临过拟合、过度平滑及鲁棒性不足等问题。现有研究表明，随机丢弃方法是解决这些问题的有效途径。然而，GNNs 中的随机丢弃方法仍存在未解决的难题。当前丢弃率的选择通常依赖启发式或网格搜索方法，这可能增加泛化误差，与丢弃方法的核心目标相悖。本文提出一种名为 FlexiDrop 的新型 GNN 随机丢弃方法。首先，我们基于 Rademacher 复杂度对 GNN 中的丢弃机制进行理论分析，证明传统随机丢弃方法的泛化误差受限于一个与丢弃率相关的函数。随后，我们将该函数作为正则项，将丢弃率与经验损失统一至单个损失函数中同步优化。因此，本方法能够自适应调整丢弃率，并从理论上平衡模型复杂度与泛化能力之间的权衡。此外，在基准数据集上的大量实验结果表明，FlexiDrop 在 GNNs 中优于传统随机丢弃方法。