  Graph Neural Networks have recently become a prevailing paradigm for various
high-impact graph learning tasks. Existing efforts can be mainly categorized as
spectral-based and spatial-based methods. The major challenge for the former is
to find an appropriate graph filter to distill discriminative information from
input signals for learning. Recently, attempts such as Graph Convolutional
Network (GCN) leverage Chebyshev polynomial truncation to seek an approximation
of graph filters and bridge these two families of methods. It has been shown in
recent studies that GCN and its variants are essentially employing fixed
low-pass filters to perform information denoising. Thus their learning
capability is rather limited and may over-smooth node representations at deeper
layers. To tackle these problems, we develop a novel graph neural network
framework AdaGNN with a well-designed adaptive frequency response filter. At
its core, AdaGNN leverages a simple but elegant trainable filter that spans
across multiple layers to capture the varying importance of different frequency
components for node representation learning. The inherent differences among
different feature channels are also well captured by the filter. As such, it
empowers AdaGNN with stronger expressiveness and naturally alleviates the
over-smoothing problem. We empirically validate the effectiveness of the
proposed framework on various benchmark datasets. Theoretical analysis is also
provided to show the superiority of the proposed AdaGNN. The implementation of
AdaGNN is available at \url{https://github.com/yushundong/AdaGNN}.
