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.

翻译：动态图神经网络（DyGNN）目前难以处理动态图中固有的分布偏移。现有针对分布外设置的DyGNN研究仅关注时域，无法处理频域中的分布偏移情形。本文发现，存在时域不可观测但频域可观测的分布偏移案例，并首次提出在频域中研究动态图的分布偏移。然而，这一研究面临两大挑战：i) 难以捕捉由频域中纠缠的不同频率分量驱动的多样图模式；ii) 如何利用发现的频谱模式处理分布偏移尚不明确。为解决这些问题，我们提出**频谱不变学习**（Spectral Invariant Learning for Dynamic Graphs under Distribution Shifts, SILD），通过捕捉并利用不变与可变的频谱模式处理动态图的分布偏移。具体而言，首先设计基于傅里叶变换的动态图神经网络，获取自我图谱轨迹频谱，将混合的动态图模式转化为分离的频率分量。随后开发解耦频谱掩码，从不同频率分量中过滤图动态，发现不变与可变的频谱模式。最后提出不变频谱滤波，鼓励模型依赖不变模式进行分布偏移下的泛化。在合成和真实动态图数据集上的实验结果表明，本方法在节点分类和链接预测任务中均优于现有方法。