  Graph Neural Networks have recently become a prevailing paradigm for various
high-impact graph analytical problems. 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, myriads of explorations
are made to achieve better graph filters, e.g., Graph Convolutional Network
(GCN), which leverages Chebyshev polynomial truncation to seek an approximation
of graph filters and bridge these two families of methods. Nevertheless, 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 open-source implementation of AdaGNN can be found here:
https://github.com/yushundong/AdaGNN.
