arXiv AI
Oct 2

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

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.

By Yuyu Liu, Haotian Xu, Yanan He, Sarang Rajendra Patil, Mengjia Xu, Tengfei Ma
arXiv AI
Oct 2

New Snake-in-the-Box Records via Snakepit Surgery and Learned Construction

The paper reports a new record for the snake-in-the-box problem, presenting a length‑191 snake in the 9‑dimensional hypercube, surpassing the previous 190‑length record that had stood for 14 years. It also establishes new lower bounds for dimensions 10 through 13. The authors introduce a novel search technique called snakepits, which expands the search space by considering collections of disjoint snakes, and propose a new benchmark, Snakepit‑in‑the‑Box, that evaluates maximal edge counts across multiple components. Additionally, they present Beam Anchor, a learned construction algorithm that generates 100 inequivalent length‑190 snakes in dimension 9.

By Paul Orland, Lucas Fagan, Michele Tarquini, Davide Passaro, Maksymilian Manko, Elli Heyes, Angus Gruen, Giorgi Butbaia, Justin Tan, Sergei Gukov