On the Spectral Differences Between NTK and CNTK and Their Implications for Point Cloud Recognition

The Convolutional Neural Tangent Kernel (CNTK) offers a principled framework for understanding convolutional architectures in the infinite-width regime. However, a comprehensive spectral comparison between CNTK and the classical Neural Tangent Kernel (NTK) remains underexplored. In this work, we present a detailed analysis of the spectral properties of CNTK and NTK, revealing that point cloud data exhibits a stronger alignment with the spectral bias of CNTK than images. This finding suggests that convolutional structures are inherently more suited to such geometric and irregular data formats. Based on this insight, we implement CNTK-based kernel regression for point cloud recognition tasks and demonstrate that it significantly outperforms NTK and other kernel baselines, especially in low-data settings. Furthermore, we derive a closed-form expression that connects CNTK with NTK in hybrid architectures. In addition, we introduce a closed-form of CNTK followed by NTK, while not the main focus, achieves strong empirical performance when applied to point-cloud tasks. Our study not only provides new theoretical understanding of spectral behaviors in neural tangent kernels but also shows that these insights can guide the practical design of CNTK-based regression for structured data such as point clouds.