  The flexibility and effectiveness of message passing based graph neural
networks (GNNs) induced considerable advances in deep learning on
graph-structured data. In such approaches, GNNs recursively update node
representations based on their neighbors and they gain expressivity through the
use of node and edge attribute vectors. E.g., in computational tasks such as
physics and chemistry usage of edge attributes such as relative position or
distance proved to be essential. In this work, we address not what kind of
attributes to use, but how to condition on this information to improve model
performance. We consider three types of conditioning; weak, strong, and pure,
which respectively relate to concatenation-based conditioning, gating, and
transformations that are causally dependent on the attributes. This
categorization provides a unifying viewpoint on different classes of GNNs, from
separable convolutions to various forms of message passing networks. We provide
an empirical study on the effect of conditioning methods in several tasks in
computational chemistry.
