  Graphical models capture relations between entities in a wide range of
applications including social networks, biology, and natural language
processing, among others. Graph neural networks (GNN) are neural models that
operate over graphs, enabling the model to leverage the complex relationships
and dependencies in graph-structured data. A graph explanation is a subgraph
which is an `almost sufficient' statistic of the input graph with respect to
its classification label. Consequently, the classification label is invariant,
with high probability, to perturbations of graph edges not belonging to its
explanation subgraph. This work considers two methods for leveraging such
perturbation invariances in the design and training of GNNs. First,
explanation-assisted learning rules are considered. It is shown that the sample
complexity of explanation-assisted learning can be arbitrarily smaller than
explanation-agnostic learning. Next, explanation-assisted data augmentation is
considered, where the training set is enlarged by artificially producing new
training samples via perturbation of the non-explanation edges in the original
training set. It is shown that such data augmentation methods may improve
performance if the augmented data is in-distribution, however, it may also lead
to worse sample complexity compared to explanation-agnostic learning rules if
the augmented data is out-of-distribution. Extensive empirical evaluations are
provided to verify the theoretical analysis.
