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We present two instances, L-GAE and L-VGAE, of the variational graphauto-encoding family (VGAE) based on separating feature propagation operationsfrom graph convolution layers typically found in graph learning methods to asingle linear matrix computation made prior to input in standard auto-encoderarchitectures. This decoupling enables the independent and fixed design of theauto-encoder without requiring additional GCN layers for every desired increasein the size of a node's local receptive field. Fixing the auto-encoder enablesa fairer assessment on the size of a nodes receptive field in buildingrepresentations. Furthermore a by-product of fixing the auto-encoder designoften results in substantially smaller networks than their VGAE counterpartsespecially as we increase the number of feature propagations. A comparativedownstream evaluation on link prediction tasks show comparable state of the artperformance to similar VGAE arrangements despite considerable simplification.We also show the simple application of our methodology to more challengingrepresentation learning scenarios such as spatio-temporal graph representationlearning.

Decoupling feature propagation from the design of graph auto-encoders