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

Large language models show strong reasoning ability, but their internal reasoning process can remain unstable in complex multi-step settings, where early hidden-state errors may propagate to incorrect predictions. We propose ReLAR, a reinforcement-guided latent refinement framework that iteratively updates hidden representations before decoding. ReLAR maintains a compact latent reasoning state and uses learned depth and action controllers to adaptively determine both the number and direction of refinement steps. The controllers are trained with a policy gradient objective based on step-wise likelihood improvement, enabling efficient input-dependent reasoning without explicit chain-of-thought generation. Experiments on medical, mathematical, multi-hop reasoning, and open-ended generation benchmarks show that ReLAR improves accuracy, generation quality, and reasoning stability with substantially lower inference overhead than explicit reasoning baselines.

Large language models solve complex problems by generating lengthy chains of explicit reasoning tokens. While effective, this makes reasoning expensive, length-sensitive, and constrained to (discrete) natural language. While latent reasoning offers a continuous alternative, determining useful structures for intermediate latent states is an open challenge. In this paper, we formulate latent reasoning as a geometric path-approximation problem within the model's pretrained token-embedding space. We introduce Geometric Latent Reasoning (GLR), which uses a lightweight transition head to predict iterative direction updates in embedding space. Using textual chain-of-thought traces as anchors, GLR learns to approximate discrete reasoning trajectories while permitting continuous deviations from exact token embeddings. Evaluations on mathematical reasoning benchmarks using Qwen3 models reveal an emergent phenomenon: geometric latent reasoning induces substantially shorter generations without an explicit length objective. By replacing early explicit reasoning with continuous latent steps, models often reach correct answers using substantially fewer total generation steps. These findings suggest that continuous trajectories act as compact intermediate reasoning states, exposing a new tradeoff between latent computation budget, output length, and accuracy.

Large language models increasingly tackle hard reasoning problems by spending more test-time compute, yet the dominant strategy remains naive repeated sampling: draw many independent solutions and hope one is correct. Because such sampling explores only through local decoding noise, it tends to produce many near duplicate attempts rather than genuinely different ideas. We ask whether exploration can instead be steered at a semantic level, by first sampling problem specific concepts, hints, or strategies and then conditioning answer generation on them. We refine this into a simple, more exploratory procedure that emits many diverse concepts in a single trajectory, and evaluate it on hard problems where repeated sampling struggles. We then go a step further and make concept generation trainable: a small concept generator is optimized with reinforcement learning so that its concepts maximize the downstream success of a larger, frozen answer generator. On hard mathematical reasoning problems, the trained concept generator substantially improves the answer generator's pass@k over naive repeated sampling at the same answer generation allocation, surpasses concepts drawn from much larger untuned models, and transfers to answer generators it was never trained against, including a model from a different family. A small model can thus be trained into an effective, reusable search policy for a much larger one.