🤖 AI Summary
Kolmogorov–Arnold Networks (KANs) remain unexplored for 3D point cloud processing, despite their promise as differentiable, structured alternatives to conventional activation functions. Method: We propose PointNet-KAN, the first KAN-based architecture for point clouds, which replaces standard MLP layers in PointNet with learnable KAN layers while preserving permutation invariance. Specifically, we parameterize KAN’s activation functions using Jacobi polynomial families—including Lagrange, Chebyshev, and Gegenbauer polynomials—and introduce a shared-weight design coupled with symmetric aggregation to ensure equivariance and efficiency. Contribution/Results: On ModelNet40 classification and ShapeNet part segmentation, PointNet-KAN achieves performance on par with the original PointNet+MLP baseline using significantly shallower architectures. These results empirically validate KANs as effective, generalizable substitutes for handcrafted or learned activations in geometric deep learning, opening new avenues for structured, differentiable function approximation in point cloud analysis.
📝 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 segmentation, despite employing a shallower and simpler network architecture. 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.