arXiv AI By Yuyu Liu, Haotian Xu, Yanan He, Sarang Rajendra Patil, Mengjia Xu, Tengfei Ma

HyperGuide: Hyperbolic Guidance for Efficient Multi-Step Reasoning in Large Language Models

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HyperGuide introduces a hyperbolic geometric signal to guide multi-step reasoning in large language models, addressing the trade-off between efficient single-pass generation and computationally heavy tree-search methods. By projecting LLM hidden states into hyperbolic space, the approach leverages the space’s asymmetry—compact near the origin and exponentially expanding toward the boundary—to encode solution proximity and branch differentiation. A lightweight head and a fine-tuned low-rank adapter use this signal to improve reasoning accuracy, especially on deeper reasoning chains, with consistent gains across multiple benchmarks.

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