Decoupling feature propagation from the design of graph auto-encoders

We present two instances, L-GAE and L-VGAE, of the variational graph auto-encoding family (VGAE) based on separating feature propagation operations from graph convolution layers typically found in graph learning methods to a single linear matrix computation made prior to input in standard auto-encoder architectures. This decoupling enables the independent and fixed design of the auto-encoder without requiring additional GCN layers for every desired increase in the size of a node's local receptive field. Fixing the auto-encoder enables a fairer assessment on the size of a nodes receptive field in building representations. Furthermore a by-product of fixing the auto-encoder design often results in substantially smaller networks than their VGAE counterparts especially as we increase the number of feature propagations. A comparative downstream evaluation on link prediction tasks show comparable state of the art performance to similar VGAE arrangements despite considerable simplification. We also show the simple application of our methodology to more challenging representation learning scenarios such as spatio-temporal graph representation learning.