  Graph neural networks (GNNs), and especially message-passing neural networks,
excel in various domains such as physics, drug discovery, and molecular
modeling. The expressivity of GNNs with respect to their ability to
discriminate non-isomorphic graphs critically depends on the functions employed
for message aggregation and graph-level readout. By applying signal propagation
theory, we propose a variance-preserving aggregation function (VPA) that
maintains expressivity, but yields improved forward and backward dynamics.
Experiments demonstrate that VPA leads to increased predictive performance for
popular GNN architectures as well as improved learning dynamics. Our results
could pave the way towards normalizer-free or self-normalizing GNNs.
