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.

Dynamic graph neural networks (DyGNNs) currently struggle with handling distribution shifts that are inherent in dynamic graphs.

Lastly, we propose an invariance regularization term to minimize the variance of predictions in intervened distributions so that our model can make predictions based on invariant patterns with stable predictive abilities and thereforehandle distribution shifts. Experiments onthree real-worlddatasets andone synthetic dataset demonstrate the superiority ofour method overstate-of-the-art baselines under distribution shifts.

Dynamic graph neural networks (DGNNs) are increasingly pervasive in exploiting spatio-temporal patterns on dynamic graphs. However, existing works fail to generalize under distribution shifts, which are common in real-world scenarios. As the generation of dynamic graphs is heavily influenced by latent environments, investigating their impacts on the out-of-distribution (OOD) generalization is critical.

Dynamic graph neural networks (DyGNNs) have demonstrated powerful predictive abilities by exploiting graph structural and temporal dynamics. However, the existing DyGNNs fail to handle distribution shifts, which naturally exist in dynamic graphs, mainly because the patterns exploited by DyGNNs may be variant with respect to labels under distribution shifts. In this paper, we propose to handle spatio-temporal distribution shifts in dynamic graphs by discovering and utilizing {\it invariant patterns}, i.e., structures and features whose predictive abilities are stable across distribution shifts, which faces two key challenges: 1) How to discover the complex variant and invariant spatio-temporal patterns in dynamic graphs, which involve both time-varying graph structures and node features.