Dynamic graphs evolve continuously, presenting challenges for traditional graph learning due to their changing structures and temporal dependencies. Recent advancements have shown potential in addressing these challenges by developing suitable meta-learning-based dynamic graph neural network models. However, most meta-learning approaches for dynamic graphs rely on fixed weight update parameters, neglecting the essential intrinsic complex high-order topological information of dynamically evolving graphs. We have designed Dowker Zigzag Persistence (DZP), an efficient and stable dynamic graph persistent homology representation method based on Dowker complex and zigzag persistence, to capture the high-order features of dynamic graphs. Armed with the DZP ideas, we propose TMetaNet, a new meta-learning parameter update model based on dynamic topological features. By utilizing the distances between high-order topological features, TMetaNet enables more effective adaptation across snapshots. Experiments on real-world datasets demonstrate TMetaNet's state-of-the-art performance and resilience to graph noise, illustrating its high potential for meta-learning and dynamic graph analysis. Our code is available at https://github.com/Lihaogx/TMetaNet.

Modern networks like social media or cryptocurrency platforms are constantly changing, making it hard for AI models to keep up and make accurate predictions. Our research introduces a new approach that helps these models adapt by focusing on the “shape” of the network over time, capturing its evolving structure using a technique called persistent homology. We designed a system called TMetaNet that uses this topological insight to guide how the model updates itself as the network changes. This allows it to better predict future connections, even when the data is noisy or unpredictable. Our tests across six real-world datasets showed that TMetaNet consistently outperformed other leading methods, offering both stronger accuracy and better stability. This work could help improve AI systems used in fields like fraud detection, recommendation systems, or online behavior analysis, anywhere networks evolve and smart decisions must keep pace.