HMamba: Hyperbolic Mamba for Sequential Recommendation

TL;DR

Hyperbolic Mamba is a new efficient sequential recommendation model that leverages hyperbolic geometry to better capture hierarchical user preferences, outperforming traditional and Euclidean-based models in accuracy and scalability.

Contribution

It introduces Hyperbolic Mamba, combining hyperbolic geometry with Mamba's efficiency for improved hierarchy-aware sequential recommendation.

Findings

Achieves 3-11% performance improvement over baselines.

Maintains linear-time efficiency in sequence modeling.

Demonstrates scalability and effectiveness across four benchmark datasets.

Abstract

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.