Abstract: Most graph deep learning methods extract feature information from graph data by using learnable weights and specific activation functions. The selection of different activations has a significant impact on performance. Aiming at the above problems, this paper proposes a fully connected neural model G-KAN based on the Kolmogorov-Arnold Network (KAN), which does not require specific activations and explicit node message passing modules. It dynamically learns activations through KAN and introduces a contrastive loss guided by node similarity to implicitly extract the original graph information. Firstly, G-KAN maps the graph data to the feature space through a linear layer. Secondly, the KAN layers extract the latent features from the input data. Thirdly, G-KAN maps the output to a probability distribution of labels using a linear layer and a softmax function. Finally, the contrastive loss was used to optimize the output of the KAN layer, encouraging high-similarity nodes to be close to each other and low-similarity nodes to be far away. In the node classification task, G-KAN outperforms the currently advanced baselines and raises Micro-F1 and Macro-F1 by 50.42% 52.84% respectively compared to Graph Convolutional Networks (GCN) on BlogCatalog. In activation comparison experiments, the method introduced by KAN outperforms the variants that use different activation functions and demonstrates stronger generalization across various datasets. The results show that the learnable activation strategy used by G-KAN can enhance the representation capacity of fully connected neural networks and generate low-dimensional node representations with higher discriminability.

Key words: graph convolutional networks, multi-layer perceptron, Kolmogorov-Arnold networks, contrastive learning, node classification

摘要： 多数图深度学习模型通过可学习权重加固定激活函数的方式提取图数据的特征信息，采用不同激活函数时对模型性能有较为显著的影响。针对上述问题，提出了一种基于Kolmogorov-Arnold网络（KAN）的全连接神经网络模型G-KAN，无需特定的激活函数和显式的节点信息传递策略，通过KAN动态学习激活函数，并引入节点相似度引导的对比损失隐式提取原始图特征信息。首先，G-KAN通过线性层将图数据映射到特征空间，然后通过KAN层提取输入数据中的潜在特征，最后通过线性层和softmax函数将KAN层的输出映射为节点标签的概率分布，并引入对比损失对KAN层的输出进行优化，推动高相似度节点彼此接近、低相似度节点彼此远离。在节点分类任务中，G-KAN优于当前较为先进的基线模型，特别是在BlogCatalog数据集上，G-KAN的Micro-F1和Macro-F1相较图卷积网络（GCN）提高了50.42%和52.84%。此外，在激活函数对比实验中，引入KAN的方法不仅优于采用不同激活函数的变体，对不同数据集的泛化能力也更强。上述实验结果表明，G-KAN采用的可学习激活函数策略能够提高全连接神经网络的表征能力，使生成的低维节点表示具有更高的区分性。

关键词: 图卷积网络, 多层感知机, Kolmogorov-Arnold网络, 对比学习, 节点分类