ChebMixer: Efficient Graph Representation Learning With MLP Mixer

Graph neural networks (GNNs) have achieved remarkable success in learning graph representations, especially graph Transformers, which have recently shown superior performance on various graph mining tasks. However, the graph Transformer generally treats nodes as tokens, which results in quadratic complexity regarding the number of nodes during self-attention computation. The graph multilayer perceptron (MLP) mixer addresses this challenge using the efficient MLP Mixer technique from computer vision. However, the time-consuming process of extracting graph tokens limits its performance. In this article, we present a novel architecture named ChebMixer, a newly proposed graph MLP Mixer that uses fast Chebyshev polynomials-based spectral filtering to extract a sequence of tokens. First, we produce multiscale representations of graph nodes via fast Chebyshev polynomial-based spectral filtering. Next, we consider each node's multiscale representations as a sequence of tokens and refine the node representation with an effective MLP Mixer. Finally, we aggregate the multiscale representations of nodes through Chebyshev interpolation. Owing to the powerful representation capabilities and fast computational properties of the MLP Mixer, we can quickly extract more informative node representations to improve the performance of downstream tasks. The experimental results prove our significant improvements in various scenarios, ranging from homogeneous and heterophilic graph node classification to medical image segmentation. Compared with NAGphormer, the average performance improved by 1.45% on homogeneous graphs and 4.15% on heterophilic graphs. And the average performance improved by 1.39% on medical image segmentation tasks compared with VM-UNet. We will release the source code after this article is accepted.