# HMamba: Hyperbolic Mamba for Sequential Recommendation

arXiv: https://arxiv.org/abs/2505.09205 · HTML: https://mlsanity.com/paper/2505.09205/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 14 May 2025.

## Built on by (most cited first, 11 of 11)

- [AutoHFormer: Efficient Hierarchical Autoregressive Transformer for Time Series Prediction](https://mlsanity.com/paper/2506.16001/) (2025)
- [Hyperbolic Large Language Models](https://mlsanity.com/paper/2509.05757/) (2025)
- [ProWorld: Progress-Aware Hyperbolic World Models for Long-Horizon Visual Goal Reaching](https://mlsanity.com/paper/2608.01926/) (2026)
- [MODE: Efficient Time Series Prediction with Mamba Enhanced by Low-Rank Neural ODEs](https://mlsanity.com/paper/2601.00920/) (2026)
- [GTR-Mamba: Geometry-to-Tangent Routing Mamba for Hyperbolic POI Recommendation](https://mlsanity.com/paper/2510.22942/) (2025)
- [HypEHR: Hyperbolic Modeling of Electronic Health Records for Efficient Question Answering](https://mlsanity.com/paper/2604.21027/) (2026)
- [FEDIN: Frequency-Enhanced Deep Interest Network for Click-Through Rate Prediction](https://mlsanity.com/paper/2605.01726/) (2026)
- [Efficient Content-based Recommendation Model Training via Noise-aware Coreset Selection](https://mlsanity.com/paper/2601.10067/) (2026)
- [Efficient Prompt Learning for Traffic Forecasting](https://mlsanity.com/paper/2605.08273/) (2026)
- [Group-Equivariant Poincar'e Convolutional Networks](https://mlsanity.com/paper/2607.00556/) (2026)
- [Hyperbolic Time Series Forecasting with Learnable Decomposition and Manifold Dynamics](https://mlsanity.com/paper/2610.15760/) (2026)

## Abstract (arXiv)

Sequential recommendation systems have become a cornerstone of personalized services, adept at modeling the temporal evolution of user preferences by capturing dynamic interaction sequences. Existing approaches predominantly rely on traditional models, including RNNs and Transformers. Despite their success in local pattern recognition, Transformer-based methods suffer from quadratic computational complexity and a tendency toward superficial attention patterns, limiting their ability to infer enduring preference hierarchies in sequential recommendation data. Recent advances in Mamba-based sequential models introduce linear-time efficiency but remain constrained by Euclidean geometry, failing to leverage the intrinsic hyperbolic structure of recommendation data. To bridge this gap, we propose Hyperbolic Mamba, a novel architecture that unifies the efficiency of Mamba's selective state space mechanism with hyperbolic geometry's hierarchical representational power. Our framework introduces (1) a hyperbolic selective state space that maintains curvature-aware sequence modeling and (2) stabilized Riemannian operations to enable scalable training. Experiments across four benchmarks demonstrate that Hyperbolic Mamba achieves 3-11% improvement while retaining Mamba's linear-time efficiency, enabling real-world deployment. This work establishes a new paradigm for efficient, hierarchy-aware sequential modeling.