  Invariant graph representation learning aims to learn the invariance among
data from different environments for out-of-distribution generalization on
graphs. As the graph environment partitions are usually expensive to obtain,
augmenting the environment information has become the de facto approach.
However, the usefulness of the augmented environment information has never been
verified. In this work, we find that it is fundamentally impossible to learn
invariant graph representations via environment augmentation without additional
assumptions. Therefore, we develop a set of minimal assumptions, including
variation sufficiency and variation consistency, for feasible invariant graph
learning. We then propose a new framework Graph invAriant Learning Assistant
(GALA). GALA incorporates an assistant model that needs to be sensitive to
graph environment changes or distribution shifts. The correctness of the proxy
predictions by the assistant model hence can differentiate the variations in
spurious subgraphs. We show that extracting the maximally invariant subgraph to
the proxy predictions provably identifies the underlying invariant subgraph for
successful OOD generalization under the established minimal assumptions.
Extensive experiments on datasets including DrugOOD with various graph
distribution shifts confirm the effectiveness of GALA.
