  Dynamic graph neural networks (DyGNNs) currently struggle with handling
distribution shifts that are inherent in dynamic graphs. Existing work on
DyGNNs with out-of-distribution settings only focuses on the time domain,
failing to handle cases involving distribution shifts in the spectral domain.
In this paper, we discover that there exist cases with distribution shifts
unobservable in the time domain while observable in the spectral domain, and
propose to study distribution shifts on dynamic graphs in the spectral domain
for the first time. However, this investigation poses two key challenges: i) it
is non-trivial to capture different graph patterns that are driven by various
frequency components entangled in the spectral domain; and ii) it remains
unclear how to handle distribution shifts with the discovered spectral
patterns. To address these challenges, we propose Spectral Invariant Learning
for Dynamic Graphs under Distribution Shifts (SILD), which can handle
distribution shifts on dynamic graphs by capturing and utilizing invariant and
variant spectral patterns. Specifically, we first design a DyGNN with Fourier
transform to obtain the ego-graph trajectory spectrums, allowing the mixed
dynamic graph patterns to be transformed into separate frequency components. We
then develop a disentangled spectrum mask to filter graph dynamics from various
frequency components and discover the invariant and variant spectral patterns.
Finally, we propose invariant spectral filtering, which encourages the model to
rely on invariant patterns for generalization under distribution shifts.
Experimental results on synthetic and real-world dynamic graph datasets
demonstrate the superiority of our method for both node classification and link
prediction tasks under distribution shifts.
