Hyperbolic Fine-tuning for Large Language Models
Keywords: hyperbolic space, representation learning, hyperbolicity, curvature, fine-tunning, large language models, low-rank adaptation
Abstract: Large language models (LLMs) have demonstrated remarkable performance on various tasks. However, it remains an open question whether the default Euclidean space is the most suitable choice for embedding tokens in LLMs. In this study, we first investigate the non-Euclidean characteristics of LLMs. Our findings reveal that token frequency follows a power-law distribution, with high-frequency tokens clustering near the origin and low-frequency tokens positioned farther away. Additionally, token embeddings exhibit a high degree of hyperbolicity, indicating a latent tree-like structure in the embedding space. Building on the observation, we propose to efficiently fine-tune LLMs in hyperbolic space to better exploit the underlying complex structures. However, we found that this fine-tuning in hyperbolic space cannot be achieved with naive application of exponential and logarithmic maps, when the embedding and weight matrices both reside in Euclidean space. To address this technique issue, we introduce a new method called hyperbolic low-rank efficient fine-tuning, \method, that performs low-rank adaptation directly on the hyperbolic manifold, avoiding the cancellation effect caused by the exponential and logarithmic maps, thus preserving the hyperbolic modeling capabilities. Through extensive experiments, we demonstrate that \method significantly enhances the performance of LLMs on reasoning tasks, particularly for complex reasoning problems. In particular, \method improves the performance in the complex AQuA dataset by up to 13.0\%, showcasing its effectiveness in handling complex reasoning challenges.
Primary Area: foundation or frontier models, including LLMs
Code Of Ethics: I acknowledge that I and all co-authors of this work have read and commit to adhering to the ICLR Code of Ethics.
Submission Guidelines: I certify that this submission complies with the submission instructions as described on https://iclr.cc/Conferences/2025/AuthorGuide.
Anonymous Url: I certify that there is no URL (e.g., github page) that could be used to find authors’ identity.
No Acknowledgement Section: I certify that there is no acknowledgement section in this submission for double blind review.
Submission Number: 11535
Loading