HyperGuide guides LLM reasoning along a single trajectory via virtual tokens in hyperbolic space, matching or exceeding search and verifier baselines on competition math and code generation with far fewer tokens
HyperGuide treats reasoning as movement through a tree of states embedded in hyperbolic space (the Poincaré ball), first training a state encoder and then a guidance head that predicts the direction of a minimum-cost transition from the current state, and inserts that direction into the decoder as a virtual token after each reasoning step so inference follows a single autoregressive trajectory without expanding or reranking candidates; on competition mathematics and code generation experiments it matches or exceeds the accuracy of search- and verifier-based baselines while generating substantially fewer tokens than those baselines and about as many as few-shot prompting.