Title: Hierarchical Mamba Meets Hyperbolic Geometry: A New Paradigm for Structured Language Embeddings
Primary area: foundation or frontier models, including LLMs
Keywords: Hierarchical language modeling, non-Euclidean Neural Networks, hyperbolic geometry, state-space models

Abstract: Selective state-space models excel at long-sequence modeling, but their capacity for language representation -- in complex hierarchical reasoning -- remains underexplored. Most large language models rely on *flat* Euclidean embeddings, limiting their ability to capture latent hierarchies. To address this, we propose *Hierarchical Mamba (HiM)*, integrating efficient Mamba2 with hyperbolic geometry to learn hierarchy-aware language embeddings for deeper linguistic understanding. Mamba2-processed sequences are projected to the Poincar\'e ball or Lorentzian manifold with "learnable" curvature, optimized with a hyperbolic loss. Our HiM model facilitates the capture of relational distances across varying hierarchical levels, enabling effective long-range reasoning for tasks like mixed-hop prediction and multi-hop inference in hierarchical classification. Experimental results show both HiM effectively capture hierarchical relationships across four linguistic and medical datasets, surpassing Euclidean baselines, with HiM-Poincar\'e providing fine-grained distinctions with higher h-norms, while HiM-Lorentz offers more stable, compact, and hierarchy-preserving embeddings.

TL;DR: Hierarchical Mamba for Structure-Aware Language Embedding