H Mamba : Hyperbolic Mamba for Sequential Recommendation

Sequential recommendation systems require both temporal efficiency to handle long interaction histories and hierarchical representation to model complex user-item relationships. Existing approaches face a fundamental tension: Mamba-based methods offer linear-time efficiency ( \(O(L)\) ) but operate in Euclidean space, which distorts hierarchical patterns; hyperbolic models capture taxonomies well but suffer quadratic complexity ( \(O(L²)\) ). To solve this dual challenge , we propose Hyperbolic Mamba (HMamba), the first architecture that unifies curvature-aware state spaces with hyperbolic geometry. Our key insight is that hyperbolic curvature \(κ\) simultaneously governs: (1) state transition granularity through \({Ā}=exp((κ))\) and (2) hierarchical distance preservation via \(dL∝√κlog(·)\) . This enables joint optimization of efficiency and hierarchy - addressing the previously unsolved problem of deep-long modeling . Experiments show HMamba achieves 3-11% accuracy gains while maintaining 3.2 \(×\) faster training than attention-based models, establishing a new paradigm for hierarchy-aware sequential recommendation. The code and datasets accompanying our paper are publicly available at https://github.com/CoderPowerBeyond/HMamba .