Graph Neural Networks (GNNs) have emerged as effective tools for learning tasks on graph-structured data. Recently, Graph-Informed (GI) layers were introduced to address regression tasks on graph nodes, extending their applicability beyond classic GNNs. However, existing implementations of GI layers lack efficiency due to dense memory allocation. This paper presents a sparse implementation of GI layers, leveraging the sparsity of adjacency matrices to reduce memory usage significantly. Additionally, a versatile general form of GI layers is introduced, enabling their application to subsets of graph nodes. The proposed sparse implementation improves the concrete computational efficiency and scalability of the GI layers, permitting to build deeper Graph-Informed Neural Networks (GINNs) and facilitating their scalability to larger graphs.

翻译：图神经网络（GNN）已成为处理图结构数据学习任务的有效工具。近年来，图信息（GI）层被引入以解决图节点上的回归任务，将其应用范围扩展到经典GNN之外。然而，现有的GI层实现由于密集内存分配而效率低下。本文提出了一种基于稀疏性的GI层实现，利用邻接矩阵的稀疏性显著降低内存使用。此外，引入了一种通用形式的GI层，使其能够应用于图节点的子集。所提出的稀疏实现提高了GI层的具体计算效率和可扩展性，从而允许构建更深的图信息神经网络（GINN），并促进其扩展到更大的图。