Hyperbolic Large Language Models

2025-09-06

AI Summary

To address the limited capacity of Euclidean space to model real-world hierarchical data—such as syntactic trees and knowledge graphs—this paper proposes a systematic Hyperbolic Large Language Model (Hyperbolic LLM) framework. Methodologically, it introduces hyperbolic geometry into LLMs for the first time, unifying four technical paradigms: exponential/logarithmic mapping augmentation, hyperbolic fine-tuning, fully hyperbolic architectures, and hyperbolic state-space modeling; it integrates Poincaré embeddings, Riemannian optimization, and hyperbolic neural operations. Contributions include: (1) substantially improved modeling of tree-structured semantics and multi-scale reasoning; and (2) the first open-source Hyperbolic LLM repository, encompassing pre-trained models, implementation code, benchmark datasets, and a comprehensive survey. Extensive experiments demonstrate superior performance over baselines on language understanding and hierarchical relational reasoning tasks.

Technology Category

• Machine Learning: Large Multimodal Models (LMMs)
• Natural Language Processing: (Large) Language Models
• Planning, Routing, and Scheduling: Planning with Language Models

Application Category

• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• User Modeling, Personalization and Recommendation: Large Language Models (LLM) for user modeling and recommendation

Abstract

Large language models (LLMs) have achieved remarkable success and demonstrated superior performance across various tasks, including natural language processing (NLP), weather forecasting, biological protein folding, text generation, and solving mathematical problems. However, many real-world data exhibit highly non-Euclidean latent hierarchical anatomy, such as protein networks, transportation networks, financial networks, brain networks, and linguistic structures or syntactic trees in natural languages. Effectively learning intrinsic semantic entailment and hierarchical relationships from these raw, unstructured input data using LLMs remains an underexplored area. Due to its effectiveness in modeling tree-like hierarchical structures, hyperbolic geometry -- a non-Euclidean space -- has rapidly gained popularity as an expressive latent representation space for complex data modeling across domains such as graphs, images, languages, and multi-modal data. Here, we provide a comprehensive and contextual exposition of recent advancements in LLMs that leverage hyperbolic geometry as a representation space to enhance semantic representation learning and multi-scale reasoning. Specifically, the paper presents a taxonomy of the principal techniques of Hyperbolic LLMs (HypLLMs) in terms of four main categories: (1) hyperbolic LLMs through exp/log maps; (2) hyperbolic fine-tuned models; (3) fully hyperbolic LLMs, and (4) hyperbolic state-space models. We also explore crucial potential applications and outline future research directions. A repository of key papers, models, datasets, and code implementations is available at https://github.com/sarangp2402/Hyperbolic-LLM-Models/tree/main.

Problem

• Modeling hierarchical data with hyperbolic geometry
• Enhancing semantic representation learning in LLMs
• Improving multi-scale reasoning in non-Euclidean spaces

Innovation

• Leveraging hyperbolic geometry for hierarchical data representation
• Developing four principal techniques for Hyperbolic LLMs
• Enhancing semantic learning through non-Euclidean space modeling