Modeling multi-layer tissue networks in hyperbolic space

Abstract Understanding protein functions in a tissue-specific context is essential for gaining insights into human biology, disease mechanisms, and potential therapeutics. Since protein interactions and functions vary across tissues, treating tissue-specific protein-protein interactions (PPI) as a multi-layer network has become a leading approach. This shift has led to growing interest in computational methods, particularly unsupervised representation learning, to model multi-layer networks and predict protein functions across diverse tissue types. Building on insights from network science, recent research on non-Euclidean embeddings has gained attention for their ability to model scale-free networks with underlying hyperbolic geometry effectively. However, to the best of our knowledge, hyperbolic embeddings have not yet been explored in the context of multi-layer PPI networks. Therefore, we investigate the geometric properties of these networks and propose a contextualized, tissue-aware representation learning approach in hyperbolic space. Our results demonstrate that representations leveraging a geometric inductive bias better align with the scale-free structure of the networks, yielding lower graph distortion and improved performance in tissue-specific protein function prediction. These findings highlight the intrinsic non-Euclidean geometry of the tissue-specific PPI space, providing direction for further research. To support reproducibility and further exploration, we made our PyTorch-based embedding implementation and pre-trained representations publicly available.