用雅可比多项式改进点云分类的动态图网络，提升精度与速度。
Dynamic Graph CNN with Jacobi Kolmogorov-Arnold Networks for 3D Classification of Point Sets
- 用雅可比多项式替代MLP，实现可学习的一维多项式变换
- 在ModelNet40上准确率更高，收敛更快，参数更少
- 揭示高次多项式不必然提升性能，启发后续理论研究
我们提出Jacobi-KAN-DGCNN框架，将动态图卷积神经网络（DGCNN）与雅可比柯尔莫戈洛夫-阿诺德网络（KAN）结合，用于三维点云分类。该方法在精简的DGCNN架构中，以可适应的一维多项式展开替换多层感知机（MLP）层，避免了MLP与KAN的深层堆叠，便于逐层对比。在ModelNet40数据集上的对比实验表明，采用雅可比多项式的KAN层在准确率和收敛速度上均优于传统线性层的DGCNN基线，同时保持参数效率。结果还显示，更高的多项式次数并不自动带来性能提升，凸显了进一步研究多项式基、次数与图学习机制之间相互作用的必要性。
原文摘要 · Abstract (English)
We introduce Jacobi-KAN-DGCNN, a framework that integrates Dynamic Graph Convolutional Neural Network (DGCNN) with Jacobi Kolmogorov-Arnold Networks (KAN) for the classification of three-dimensional point clouds. This method replaces Multi-Layer Perceptron (MLP) layers with adaptable univariate polynomial expansions within a streamlined DGCNN architecture, circumventing deep levels for both MLP and KAN to facilitate a layer-by-layer comparison. In comparative experiments on the ModelNet40 dataset, KAN layers employing Jacobi polynomials outperform the traditional linear layer-based DGCNN baseline in terms of accuracy and convergence speed, while maintaining parameter efficiency. Our results demonstrate that higher polynomial degrees do not automatically improve performance, highlighting the need for further theoretical and empirical investigation to fully understand the interactions between polynomial bases, degrees, and the mechanisms of graph-based learning.
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