Deep Graph Wavelet Neural Networks Using Heat Kernel for Semi-supervised Node Classification

Graph convolutional neural networks have demonstrated promising solutions for processing non-Euclidean data in tasks such as node classification. While existing graph convolution models aim to develop deeper architectures, balancing performance gains with computational efficiency remains challenging. In this work, we propose a Deep Graph Wavelet Neural Networks Using Heat Kernel (DHK), built upon the deep framework of Graph Convolutional Network via Initial Residual and Identity Mapping (GCNII). Motivated by the mathematical properties of heat kernels, we design a novel graph filtering kernel by composing heat kernel components and truncating its first two terms to derive an efficient graph convolution operator. To address computational complexity, we further integrate a Chebyshev polynomial approximation strategy, originally developed for fast graph wavelet transforms, to enable scalable spectral filtering. Our DHK framework consistently outperforms GCNII across multiple benchmark datasets at varying network depths (2–64 layers), demonstrating superior stability in deep architectures. This work advances deep graph representation learning by synergizing heat kernel-inspired operators with efficient wavelet approximation techniques.