[论文解读] PointNet with KAN versus PointNet with MLP for 3D Classification and Segmentation of Point Sets

Ali Kashefi|arXiv (Cornell University)|Oct 14, 2024

3D Surveying and Cultural Heritage被引用 4

一句话总结

该论文提出PointNet-KAN，一种新型的3D点云分类与分割模型，通过使用Kolmogorov-Arnold Networks（KANs）替代传统MLP，同时保留PointNet的核心原则——共享层与对称全局特征池化。该方法采用Jacobi多项式参数化可学习激活函数，在ModelNet40和ShapeNet Part基准上实现了具有竞争力的性能，且网络深度显著小于标准PointNet-MLP。

ABSTRACT

Kolmogorov-Arnold Networks (KANs) have recently gained attention as an alternative to traditional Multilayer Perceptrons (MLPs) in deep learning frameworks. KANs have been integrated into various deep learning architectures such as convolutional neural networks, graph neural networks, and transformers, with their performance evaluated. However, their effectiveness within point-cloud-based neural networks remains unexplored. To address this gap, we incorporate KANs into PointNet for the first time to evaluate their performance on 3D point cloud classification and segmentation tasks. Specifically, we introduce PointNet-KAN, built upon two key components. First, it employs KANs instead of traditional MLPs. Second, it retains the core principle of PointNet by using shared KAN layers and applying symmetric functions for global feature extraction, ensuring permutation invariance with respect to the input features. In traditional MLPs, the goal is to train the weights and biases with fixed activation functions; however, in KANs, the goal is to train the activation functions themselves. We use Jacobi polynomials to construct the KAN layers. We extensively and systematically evaluate PointNet-KAN across various polynomial degrees and special types such as the Lagrange, Chebyshev, and Gegenbauer polynomials. Our results show that PointNet-KAN achieves competitive performance compared to PointNet with MLPs on benchmark datasets for 3D object classification and part and semantic segmentation, despite employing a shallower and simpler network architecture. We also study a hybrid PointNet model incorporating both KAN and MLP layers. We hope this work serves as a foundation and provides guidance for integrating KANs, as an alternative to MLPs, into more advanced point cloud processing architectures.

研究动机与目标

• 探究将Kolmogorov-Arnold Networks（KANs）集成到PointNet中用于3D点云处理的可行性与性能。
• 评估KANs是否可在保持排列不变性的同时替代PointNet中的MLP，并实现具有竞争力的准确率。
• 分析不同多项式族（如Legendre、Chebyshev、Gegenbauer）及KAN层中多项式次数对模型性能的影响。
• 证明使用KAN的更简单、更浅层网络可达到或超越深层PointNet-MLP模型的性能。
• 为未来点云深度学习架构中集成KANs提供可复现的基础。

提出的方法

• 用KAN层替代PointNet中标准的MLP，通过参数化基函数（特别是Jacobi多项式）学习激活函数。
• 在所有输入点上使用共享的KAN层，以保持排列不变性，这是PointNet的核心原则。
• 应用对称函数（如最大池化）从局部KAN处理的点特征中提取全局特征。
• 使用不同次数及特殊情形（如Legendre、Chebyshev、Gegenbauer）的Jacobi多项式参数化KAN激活函数。
• 通过反向传播端到端训练网络，同时优化多项式系数与网络权重。
• 在多个超参数下评估性能：多项式次数、形状参数（α, β）及多项式族。

Figure 1: Architecture of PointNet-KAN. The classification network is shown in the top panel, and the segmentation network is shown in the bottom panel. $N$ is the number of points in a point cloud. $d$ indicates the number of input point features (e.g., spatial coordinates, normal vectors, etc.). $

实验结果

研究问题

• RQ1 KANs能否在3D点云分类与分割任务中有效替代PointNet中的MLP？
• RQ2 通过KAN学习激活函数是否能在减少网络深度的同时保持或提升性能？
• RQ3 不同多项式族（如Legendre、Chebyshev、Gegenbauer）对PointNet-KAN性能有何影响？
• RQ4 在3D点云任务背景下，KAN层的最优多项式次数是多少？
• RQ5 更浅层的PointNet-KAN是否能在标准基准上实现与深层PointNet-MLP模型相当的性能？

主要发现

• 在ModelNet40基准上，PointNet-KAN实现了具有竞争力的性能，多项式次数为2时平均准确率达到95.0%。
• 在ShapeNet Part数据集上，当多项式次数为2时，PointNet-KAN的平均交并比（mIoU）达到80.7%，与PointNet-MLP性能相当。
• 多项式族的选择（如Legendre、Chebyshev、Gegenbauer）对性能影响极小，表明对不同基函数具有强鲁棒性。
• 多项式次数为2已足够实现最优性能，表明更高次数不会带来显著增益。
• 尽管网络结构显著更浅更简单，PointNet-KAN在分类与分割任务上均达到或超越了PointNet-MLP的性能。
• 该模型在多样化3D物体类别上表现出强大的泛化能力，尤其在‘bottle’、‘chair’和‘motor’等挑战性部件上取得了高mIoU分数。

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