Neural dynamics of complex networks embedded in hyperbolic spaces

A neural dynamics model of complex networks based on hyperbolic space is proposed, which maps node features to hyperbolic space, avoiding the problem of node representation embedding distortion existing in scale-free graphs or graphs with hierarchical structures. Introduce linear transformation, aggregation operation and activation operation on tangent plane space to solve the difficulty that operations in hyperbolic space do not satisfy permutation invariance. The experimental results show that compared with the NDCN, the method is applied to the extrapolation prediction tasks of four network dynamics on four different networks, and the results are significantly improved. The classification tasks of the Airport dataset and the Disease dataset are increased by 15.4 and 6.1 percentage points, respectively.