GTR-Mamba: Geometry-to-Tangent Routing for Hyperbolic POI Recommendation
This addresses the challenge of simultaneously capturing hierarchical spatial structures and dynamic temporal contexts in location-based social networks, representing an incremental improvement over existing graph neural network and sequential models.
The paper tackles the problem of next point-of-interest recommendation by proposing GTR-Mamba, a framework that models static preference hierarchies in hyperbolic geometry and routes dynamic sequence updates to a Mamba layer in Euclidean tangent space, achieving consistent outperformance over state-of-the-art baselines on three real-world datasets.
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.