  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.
