HMamba: 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 ( \(\mathcal{O}(L)\) ) but operate in Euclidean space, which distorts hierarchical patterns; hyperbolic models capture taxonomies well but suffer quadratic complexity ( \(\mathcal{O}(L^{2})\) ). 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 \(\kappa\) simultaneously governs: (1) state transition granularity through \(\mathbf{\bar{A}}=\exp(\Delta\mathbf{A}\odot\mathbf{K}(\kappa))\) and (2) hierarchical distance preservation via \(d_{\mathcal{L}}\propto\sqrt{\kappa}\log(\cdot)\) . 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 \(\times\) 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.