  Although Graph Convolutional Networks (GCNs) have demonstrated their power in
various applications, the graph convolutional layers, as the most important
component of GCN, are still using linear transformations and a simple pooling
step. In this paper, we propose a novel generalization of Factorized Bilinear
(FB) layer to model the feature interactions in GCNs. FB performs two
matrix-vector multiplications, that is, the weight matrix is multiplied with
the outer product of the vector of hidden features from both sides. However,
the FB layer suffers from the quadratic number of coefficients, overfitting and
the spurious correlations due to correlations between channels of hidden
representations that violate the i.i.d. assumption. Thus, we propose a compact
FB layer by defining a family of summarizing operators applied over the
quadratic term. We analyze proposed pooling operators and motivate their use.
Our experimental results on multiple datasets demonstrate that the GFB-GCN is
competitive with other methods for text classification.
