We introduce Graph Kolmogorov-Arnold Networks (GKAN), an innovative neural network architecture that extends the principles of the recently proposed Kolmogorov-Arnold Networks (KAN) to graph-structured data. By adopting the unique characteristics of KANs, notably the use of learnable univariate functions instead of fixed linear weights, we develop a powerful model for graph-based learning tasks. Unlike traditional Graph Convolutional Networks (GCNs) that rely on a fixed convolutional architecture, GKANs implement learnable spline-based functions between layers, transforming the way information is processed across the graph structure. We present two different ways to incorporate KAN layers into GKAN: architecture 1 -- where the learnable functions are applied to input features after aggregation and architecture 2 -- where the learnable functions are applied to input features before aggregation. We evaluate GKAN empirically using a semi-supervised graph learning task on a real-world dataset (Cora). We find that architecture generally performs better. We find that GKANs achieve higher accuracy in semi-supervised learning tasks on graphs compared to the traditional GCN model. For example, when considering 100 features, GCN provides an accuracy of 53.5 while a GKAN with a comparable number of parameters gives an accuracy of 61.76; with 200 features, GCN provides an accuracy of 61.24 while a GKAN with a comparable number of parameters gives an accuracy of 67.66. We also present results on the impact of various parameters such as the number of hidden nodes, grid-size, and the polynomial-degree of the spline on the performance of GKAN.

我们引入了图科尔莫哥洛夫-阿诺德网络（GKAN），一种创新的神经网络架构，它扩展了最近提出的科尔莫哥洛夫-阿诺德网络（KAN）的原理，用于图结构化数据。通过采用KAN的独特特性，尤其是使用可学习的单变量函数而不是固定线性权重，我们为基于图的学习任务开发了一个强大的模型。

图科尔莫戈洛夫-阿诺德网络