Dynamic Graph CNN with Jacobi Kolmogorov-Arnold Networks for 3D Classification of Point Sets

TL;DR

This paper presents Jacobi-KAN-DGCNN, a novel 3D point cloud classification framework combining dynamic graph CNNs with Jacobi Kolmogorov-Arnold Networks, improving accuracy and convergence speed over traditional methods.

Contribution

It introduces a new integration of polynomial-based KAN layers into DGCNN, replacing MLPs, and demonstrates enhanced performance on ModelNet40 with parameter efficiency.

Findings

KAN layers outperform linear layers in accuracy and speed

Higher polynomial degrees do not necessarily improve performance

The method maintains parameter efficiency while enhancing results

Abstract

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.