标题： GTR-Mamba：双曲POI推荐的几何到切向路由 显示英文标题

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

摘要： 下一个兴趣点（POI）推荐是现代基于位置的社交网络（LBSNs）中的关键任务，旨在建模人类移动的复杂决策过程，为用户提供下一个签到位置的个性化推荐。现有的POI推荐模型主要基于图神经网络和序列模型，已经得到了广泛研究。然而，这些模型面临一个根本性的局限：它们难以同时捕捉空间选择的固有层次结构以及用户特定时间上下文的动态性和不规则变化。为了克服这一限制，我们提出了GTR-Mamba，一种用于跨流形条件和路由的新框架。GTR-Mamba利用不同数学空间在不同任务中的独特优势：它在双曲几何中对静态、树状的偏好层次进行建模，同时将动态序列更新路由到计算稳定且高效的欧几里得切空间中的新型Mamba层。这一过程由一个跨流形通道协调，该通道融合时空信息以显式引导状态空间模型（SSM），从而灵活适应上下文变化。在三个真实数据集上的大量实验表明，GTR-Mamba在下一个POI推荐中始终优于最先进的基线模型。 显示英文摘要

摘要： 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.