  In recent years, hypergraph learning has attracted great attention due to its
capacity in representing complex and high-order relationships. However, current
neural network approaches designed for hypergraphs are mostly shallow, thus
limiting their ability to extract information from high-order neighbors. In
this paper, we show both theoretically and empirically, that the performance of
hypergraph neural networks does not improve as the number of layers increases,
which is known as the over-smoothing problem. To avoid this issue, we develop a
new deep hypergraph convolutional network called Deep-HGCN, which can maintain
the heterogeneity of node representation in deep layers. Specifically, we prove
that a $k$-layer Deep-HGCN simulates a polynomial filter of order $k$ with
arbitrary coefficients, which can relieve the problem of over-smoothing.
Experimental results on various datasets demonstrate the superior performance
of the proposed model compared to the state-of-the-art hypergraph learning
approaches.
