Torsion Graph Neural Networks
Cong Shen Xiang Liu Jiawei Luo Kelin Xia
Geometric deep learning (GDL) models have demonstrated a great potential for
the analysis of non-Euclidian data. They are developed to incorporate the
geometric and topological information of non-Euclidian data into the end-to-end
deep learning architectures. Motivated by the recent success of discrete Ricci
curvature in graph neural network (GNNs), we propose TorGNN, an analytic
Torsion enhanced Graph Neural Network model. The essential idea is to
characterize graph local structures with an analytic torsion based weight
formula. Mathematically, analytic torsion is a topological invariant that can
distinguish spaces which are homotopy equivalent but not homeomorphic. In our
TorGNN, for each edge, a corresponding local simplicial complex is identified,
then the analytic torsion (for this local simplicial complex) is calculated,
and further used as a weight (for this edge) in message-passing process. Our
TorGNN model is validated on link prediction tasks from sixteen different types
of networks and node classification tasks from three types of networks. It has
been found that our TorGNN can achieve superior performance on both tasks, and
outperform various state-of-the-art models. This demonstrates that analytic
torsion is a highly efficient topological invariant in the characterization of
graph structures and can significantly boost the performance of GNNs.