HyPER: Bridging Exploration and Exploitation for Scalable LLM Reasoning with Hypothesis Path Expansion and Reduction

Scaling test-time compute with multi-path reasoning improves the accuracy of foundation models, but often incurs substantial redundant computation. We study how to make such reasoning more resource-efficient under a fixed inference budget. Our key observation is that the value of exploration and exploitation is phase-dependent: early decoding benefits from diverse hypothesis paths, whereas later stages require targeted refinement and reliable answer selection. We introduce HyPER, a training-free adaptive test-time compute policy that formulates multi-path reasoning as an online expand--reduce control problem. HyPER reallocates compute using lightweight confidence and diversity statistics, dynamically choosing among path branching, short-horizon expansion, token-level refinement, and standard decoding. To improve exploitation without full-path resampling, HyPER further leverages MoE routing diversity for single-token refinement with shared KV states, and uses a length- and confidence-aware voting rule to reduce answer-selection failures. Across four MoE models and diverse reasoning benchmarks, HyPER consistently improves the accuracy--compute trade-off, achieving the Pareto frontier while outperforming prior methods by 8~10% and reducing token consumption by 25~40%. These results demonstrate that adaptive control is an effective mechanism for resource-efficient foundation-model inference.