Graph structure learning is a well-established problem that aims at optimizing graph structures adaptive to specific graph datasets to help message passing neural networks (i.e., GNNs) to yield effective and robust node embeddings. However, the common limitation of existing models lies in the underlying \textit{closed-world assumption}: the testing graph is the same as the training graph. This premise requires independently training the structure learning model from scratch for each graph dataset, which leads to prohibitive computation costs and potential risks for serious over-fitting. To mitigate these issues, this paper explores a new direction that moves forward to learn a universal structure learning model that can generalize across graph datasets in an open world. We first introduce the mathematical definition of this novel problem setting, and describe the model formulation from a probabilistic data-generative aspect. Then we devise a general framework that coordinates a single graph-shared structure learner and multiple graph-specific GNNs to capture the generalizable patterns of optimal message-passing topology across datasets. The well-trained structure learner can directly produce adaptive structures for unseen target graphs without any fine-tuning. Across diverse datasets and various challenging cross-graph generalization protocols, our experiments show that even without training on target graphs, the proposed model i) significantly outperforms expressive GNNs trained on input (non-optimized) topology, and ii) surprisingly performs on par with state-of-the-art models that independently optimize adaptive structures for specific target graphs, with notably orders-of-magnitude acceleration for training on the target graph.
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