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

arXiv: https://arxiv.org/abs/2510.22942 · HTML: https://mlsanity.com/paper/2510.22942/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Video, motion and generative Mamba models, one of 10 directions in State-space sequence models (S4, Mamba).
- Builds on 14 of its 47 references that are in the map.
- First posted on arXiv 27 Oct 2025.

## Placed in

- State-space sequence models (S4, Mamba) / [Video, motion and generative Mamba models](https://mlsanity.com/ssm/video-motion-and-generative-mamba-models/)

## Builds on (most cited first, 14 of 14)

- [Mamba: Linear-Time Sequence Modeling with Selective State Spaces](https://mlsanity.com/paper/2312.00752/) (2023)
- [Hyperbolic Graph Convolutional Neural Networks](https://mlsanity.com/paper/1910.12933/) (2019)
- [Hyperbolic Deep Neural Networks: A Survey](https://mlsanity.com/paper/2101.04562/) (2021)
- [Sequential Recommender Systems: Challenges, Progress and Prospects](https://mlsanity.com/paper/2001.04830/) (2019)
- [Latent Variable Modelling with Hyperbolic Normalizing Flows](https://mlsanity.com/paper/2002.06336/) (2020)
- [MobTCast: Leveraging Auxiliary Trajectory Forecasting for Human Mobility Prediction](https://mlsanity.com/paper/2110.01401/) (2021)
- [Modeling Scale-free Graphs with Hyperbolic Geometry for Knowledge-aware Recommendation](https://mlsanity.com/paper/2108.06468/) (2021)
- [Reinforced Imitative Graph Representation Learning for Mobile User Profiling: An Adversarial Training Perspective](https://mlsanity.com/paper/2101.02634/) (2021)
- [HAKG: Hierarchy-Aware Knowledge Gated Network for Recommendation](https://mlsanity.com/paper/2204.04959/) (2022)
- [Point-of-Interest Recommender Systems based on Location-Based Social Networks: A Survey from an Experimental Perspective](https://mlsanity.com/paper/2106.10069/) (2021)
- [HMamba: Hyperbolic Mamba for Sequential Recommendation](https://mlsanity.com/paper/2505.09205/) (2025)
- [A Fashion Item Recommendation Model in Hyperbolic Space](https://mlsanity.com/paper/2409.02599/) (2024)
- [Hierarchical Mamba Meets Hyperbolic Geometry: A New Paradigm for Structured Language Embeddings](https://mlsanity.com/paper/2505.18973/) (2025)
- [CAPS: Context Aware Personalized POI Sequence Recommender System](https://mlsanity.com/paper/1803.01245/) (2018)

## Built on by (most cited first, 1 of 1)

- [Mag-Mamba: Modeling Coupled spatiotemporal Asymmetry for POI Recommendation](https://mlsanity.com/paper/2603.00053/) (2026)

## Abstract (arXiv)

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 hyperbolic POI recommendation models, predominantly based on rotations and graph representations, have been extensively investigated. Although hyperbolic geometry has proven superior in representing hierarchical data with low distortion, current hyperbolic sequence models typically rely on performing recurrence via expensive M"obius operations directly on the manifold. This incurs prohibitive computational costs and numerical instability, rendering them ill-suited for trajectory modeling. To resolve this conflict between geometric representational power and sequential efficiency, we propose GTR-Mamba, a novel framework featuring Geometry-to-Tangent Routing. GTR-Mamba strategically routes complex state transitions to the computationally efficient Euclidean tangent space. Crucially, instead of a static approximation, we introduce a Parallel Transport (PT) mechanism that dynamically aligns tangent spaces along the trajectory. This ensures geometric consistency across recursive updates, effectively bridging the gap between the curved manifold and linear tangent operations. This process is orchestrated by an exogenous spatio-temporal channel, which explicitly modulates the SSM discretization parameters. Extensive experiments on three real-world datasets demonstrate that GTR-Mamba consistently outperforms state-of-the-art baselines in next POI recommendation.