Hyperbolic Guidance Boosts LLM Multi-Step Reasoning Efficiency

A new method called HyperGuide uses hyperbolic geometry to improve multi-step reasoning in large language models. The approach addresses the trade-off between single-pass generation, which is fast but inaccurate, and tree-search methods, which are accurate but computationally expensive. By distilling reasoning progress into a hyperbolic geometric signal, HyperGuide guides step-by-step generation. The key insight is that in combinatorial reasoning trees, solution-bearing states are rare while dead ends are abundant. Hyperbolic space naturally captures this asymmetry: distance from the origin encodes solution proximity, and angular separation distinguishes different reasoning branches. The method trains a lightweight head to project LLM hidden states into hyperbolic space, then fine-tunes a low-rank adapter interactively on the model's own reasoning attempts. The paper is published on arXiv with ID 2605.24140.