Hyperbolic Deep Learning for Foundation Models: A Survey

• URL: http://arxiv.org/abs/2507.17787v1
• Date: Wed, 23 Jul 2025 09:50:17 GMT
• Title: Hyperbolic Deep Learning for Foundation Models: A Survey
• Authors: Neil He, Hiren Madhu, Ngoc Bui, Menglin Yang, Rex Ying,
• Abstract summary: Foundation models pre-trained on massive datasets have demonstrated remarkable success in diverse downstream tasks.<n>Recent advances have leveraged hyperbolic neural networks to enhance foundation models.<n>This paper provides a comprehensive review of hyperbolic neural networks and their recent development for foundation models.
• Score: 16.14776172953206
• License: http://creativecommons.org/licenses/by-nc-sa/4.0/
• Abstract: Foundation models pre-trained on massive datasets, including large language models (LLMs), vision-language models (VLMs), and large multimodal models, have demonstrated remarkable success in diverse downstream tasks. However, recent studies have shown fundamental limitations of these models: (1) limited representational capacity, (2) lower adaptability, and (3) diminishing scalability. These shortcomings raise a critical question: is Euclidean geometry truly the optimal inductive bias for all foundation models, or could incorporating alternative geometric spaces enable models to better align with the intrinsic structure of real-world data and improve reasoning processes? Hyperbolic spaces, a class of non-Euclidean manifolds characterized by exponential volume growth with respect to distance, offer a mathematically grounded solution. These spaces enable low-distortion embeddings of hierarchical structures (e.g., trees, taxonomies) and power-law distributions with substantially fewer dimensions compared to Euclidean counterparts. Recent advances have leveraged these properties to enhance foundation models, including improving LLMs' complex reasoning ability, VLMs' zero-shot generalization, and cross-modal semantic alignment, while maintaining parameter efficiency. This paper provides a comprehensive review of hyperbolic neural networks and their recent development for foundation models. We further outline key challenges and research directions to advance the field.

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