Lorentz Tangent Diffusion Adapter for Multi-label Prediction of Protein-Protein Interaction Types

Protein-protein interactions shape cellular organization and disease processes, but their prediction remains difficult because known interaction networks are incomplete, noisy and highly uneven across proteins. Hyperbolic graph learning is well suited to the hierarchical structure of such networks, yet most methods emphasize learning hyperbolic embeddings and pay less attention to how these embeddings are propagated and decoded for type prediction. Here we introduce the Lorentz Tangent Diffusion Adapter (LTDA), a post-embedding module for PPI type prediction, that is, for predicting which of several interaction types a candidate protein pair undergoes. LTDA learns relation-specific protein representations on the Lorentz manifold, projects them to tangent space, applies lightweight graph diffusion, and decodes the diffused representations directly in tangent space. This design uses the tangent space as a prediction-oriented interface between hierarchical representation learning and interaction classification. On SHS27K and SHS148K under BFS and DFS splits, LTDA consistently improves over representative PPI methods and a reproduced HI-PPI baseline, with average gains of 1.41 percentage points in Micro-F1, 3.21 in AUPR, 1.31 in AUC and 1.25 in accuracy. Ablation, degree-bin and biological-evidence analyses indicate that the gains are not explained by simple smoothing or hub correction. LTDA therefore shows that post-embedding adaptation can make Lorentz representations more effective for PPI type prediction.