Simplifying Graph Neural Kernels: from Stacking Layers to Collapsed Structure

The Graph Neural Tangent Kernel (GNTK) successfully bridges the gap between kernel methods and Graph Neural Networks (GNNs), addressing key challenges such as the difficulty of training deep networks and the limitations of traditional kernel methods. However, the existing layer-stacking strategy in GNTK introduces redundant computations, significantly increasing computational complexity and limiting scalability for practical applications. To address these issues, this paper proposes the Simplified Graph Neural Tangent Kernel (SGTK), which replaces the traditional multi-layer stacking mechanism with a continuous $K$-step aggregation operation. This novel approach streamlines the iterative kernel computation process, effectively eliminating redundant calculations while preserving the kernel's expressiveness. By reducing the dependency on layer stacking, SGTK achieves both computational simplicity and efficiency. Furthermore, we introduce the Simplified Graph Neural Kernel (SGNK), which models infinitely wide Graph Neural Networks as Gaussian Processes. This allows kernel values to be directly determined from the expected outputs of activation functions in the infinite-width regime, bypassing the need for explicit layer-by-layer computation. SGNK further reduces computational complexity while maintaining the capacity to capture intricate structural patterns in graphs. Extensive experiments on node and graph classification tasks demonstrate that the proposed SGTK and SGNK achieve performance comparable to existing approaches while improving computational efficiency. Implementation details are available at https://anonymous.4open.science/r/SGNK-1CE4/.