Transferring knowledge across graphs plays a pivotal role in many high-stake domains, ranging from transportation networks to e-commerce networks, from neuroscience to finance. To date, the vast majority of existing works assume both source and target domains are sampled from a universal and stationary distribution. However, many real-world systems are intrinsically dynamic, where the underlying domains are evolving over time. To bridge the gap, we propose to shift the problem to the dynamic setting and ask: given the label-rich source graphs and the label-scarce target graphs observed in previous T timestamps, how can we effectively characterize the evolving domain discrepancy and optimize the generalization performance of the target domain at the incoming T+1 timestamp? To answer the question, for the first time, we propose a generalization bound under the setting of dynamic transfer learning across graphs, which implies the generalization performance is dominated by domain evolution and domain discrepancy between source and target domains. Inspired by the theoretical results, we propose a novel generic framework DyTrans to improve knowledge transferability across dynamic graphs. In particular, we start with a transformer-based temporal encoding module to model temporal information of the evolving domains; then, we further design a dynamic domain unification module to efficiently learn domain-invariant representations across the source and target domains. Finally, extensive experiments on various real-world datasets demonstrate the effectiveness of DyTrans in transferring knowledge from dynamic source domains to dynamic target domains.

翻译：在图间进行知识迁移在诸多高风险领域中发挥着关键作用，涵盖交通网络、电子商务网络、神经科学及金融系统等。迄今为止，绝大多数现有研究假设源域和目标域均采样自一个通用且平稳的分布。然而，众多真实世界系统本质上是动态的，其底层领域会随时间演化。为填补这一空白，我们提出将问题转向动态设定，并探究：给定前T个时间戳中已观测的标签丰富源图与标签稀缺目标图，如何有效刻画演化的领域差异，并优化目标域在即将到来的第T+1个时间戳上的泛化性能？为回答该问题，我们首次提出了动态跨图迁移学习设定下的泛化界，该界表明泛化性能主要受领域演化与源-目标域间领域差异主导。受理论结果启发，我们提出了一种新颖的通用框架DyTrans以增强动态图间的知识可迁移性。具体而言，我们首先构建基于Transformer的时间编码模块来建模演化领域的时间信息；随后进一步设计动态领域统一模块，以高效学习跨源域与目标域的领域不变表示。最终，在多种真实世界数据集上的广泛实验证明了DyTrans在将知识从动态源域迁移至动态目标域方面的有效性。