  Deep Graph Networks (DGNs) currently dominate the research landscape of
learning from graphs, due to their efficiency and ability to implement an
adaptive message-passing scheme between the nodes. However, DGNs are typically
limited in their ability to propagate and preserve long-term dependencies
between nodes, i.e., they suffer from the over-squashing phenomena. This
reduces their effectiveness, since predictive problems may require to capture
interactions at different, and possibly large, radii in order to be effectively
solved. In this work, we present Anti-Symmetric Deep Graph Networks (A-DGNs), a
framework for stable and non-dissipative DGN design, conceived through the lens
of ordinary differential equations. We give theoretical proof that our method
is stable and non-dissipative, leading to two key results: long-range
information between nodes is preserved, and no gradient vanishing or explosion
occurs in training. We empirically validate the proposed approach on several
graph benchmarks, showing that A-DGN yields to improved performance and enables
to learn effectively even when dozens of layers are used.
