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Graph Transformers (GTs) facilitate the comprehension of graph-structureddata by calculating the self-attention of node pairs without considering nodeposition information. To address this limitation, we introduce an innovativeand efficient framework that introduces Positional Encodings (PEs) into theTransformer, generating a set of learnable positional encodings in thehyperbolic space, a non-Euclidean domain. This approach empowers us to explorediverse options for optimal selection of PEs for specific downstream tasks,leveraging hyperbolic neural networks or hyperbolic graph convolutionalnetworks. Additionally, we repurpose these positional encodings to mitigate theimpact of over-smoothing in deep Graph Neural Networks (GNNs). Comprehensiveexperiments on molecular benchmark datasets, co-author, and co-purchasenetworks substantiate the effectiveness of hyperbolic positional encodings inenhancing the performance of deep GNNs.

HyPE-GT: where Graph Transformers meet Hyperbolic Positional Encodings