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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.<\/jats:p>","DOI":"10.1007\/s41109-025-00764-1","type":"journal-article","created":{"date-parts":[[2025,12,12]],"date-time":"2025-12-12T10:36:57Z","timestamp":1765535817000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Modeling multi-layer tissue networks in hyperbolic space"],"prefix":"10.1007","volume":"11","author":[{"given":"Domonkos","family":"Pog\u00e1ny","sequence":"first","affiliation":[]},{"given":"P\u00e9ter","family":"Antal","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2025,12,12]]},"reference":[{"issue":"16","key":"764_CR1","doi-asserted-by":"publisher","first-page":"2826","DOI":"10.1093\/bioinformatics\/bty206","volume":"34","author":"G Alanis-Lobato","year":"2018","unstructured":"Alanis-Lobato G, Mier P, Andrade-Navarro M (2018) The latent geometry of the human protein interaction network. 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