GTR-Mamba: Geometry-to-Tangent Routing for Hyperbolic POI Recommendation

TL;DR

GTR-Mamba addresses the dual challenge of capturing static hierarchical structure in POI data and adapting to dynamic, irregular spatio-temporal contexts. It combines hyperbolic embeddings for static hierarchies with a cross-manifold fusion channel that feeds into a geometry-to-tangent routing Mamba layered over a context-driven SSM, enabling stable, efficient updates. The approach achieves state-of-the-art performance on three real-world POI datasets, with robust handling of context switches and favorable efficiency, while ablations confirm the criticality of the SSM, hyperbolic space, and cross-manifold components. This framework offers a principled route to scalable, context-aware next-POI recommendation by leveraging the strengths of hyperbolic geometry for hierarchy and Euclidean tangent-space dynamics for flexible updates.

Abstract

Next Point-of-Interest (POI) recommendation is a critical task in modern Location-Based Social Networks (LBSNs), aiming to model the complex decision-making process of human mobility to provide personalized recommendations for a user's next check-in location. Existing POI recommendation models, predominantly based on Graph Neural Networks and sequential models, have been extensively studied. However, these models face a fundamental limitation: they struggle to simultaneously capture the inherent hierarchical structure of spatial choices and the dynamics and irregular shifts of user-specific temporal contexts. To overcome this limitation, we propose GTR-Mamba, a novel framework for cross-manifold conditioning and routing. GTR-Mamba leverages the distinct advantages of different mathematical spaces for different tasks: it models the static, tree-like preference hierarchies in hyperbolic geometry, while routing the dynamic sequence updates to a novel Mamba layer in the computationally stable and efficient Euclidean tangent space. This process is coordinated by a cross-manifold channel that fuses spatio-temporal information to explicitly steer the State Space Model (SSM), enabling flexible adaptation to contextual changes. Extensive experiments on three real-world datasets demonstrate that GTR-Mamba consistently outperforms state-of-the-art baseline models in next POI recommendation.

Figures (8)

• Figure 1: The hierarchical structure of check-in data
• Figure 2: The overall framework of our proposed GTR-Mamba
• Figure 3: Detailed architecture of the GTR-SSM
• Figure 4: Performance w.r.t. different embedding dimensions and SSM layers
• Figure 5: Performance metrics for different models in scene switching exploration