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

Scaling test-time compute with multi-path chainof-thought can improve reasoning accuracy, but its gains hinge on an effective explorationexploitation trade-off. Existing methods handle this trade-off in rigid ways: tree-structured search hard-codes exploration via brittle expansion rules that disrupt post-trained reasoning, while parallel reasoning over-explores redundant hypothesis paths and relies on a weak answer selection strategy. Driven by the insight that the optimal balance is phase-dependent and that correct vs. incorrect paths often diverge only at late stages, we reconceptualize test-time scaling as a dynamic expand-reduce control problem over a pool of hypothesis paths. We introduce Hy-PER, a training-free online control policy for MoE multi-path decoding that reallocates compute under a fixed budget using lightweight path statistics. HyPER features (i) an online controller that shifts from exploration to exploitation as the hypothesis pool evolves, (ii) an MoE-based tokenlevel refinement primitive for efficient generationtime exploitation without full-path resampling, and (iii) a length-and confidence-aware aggregation rule to bridge the existence-selection gap for reliable answer-time exploitation. Extensive experimental results across four MoE models and diverse benchmarks demonstrate HyPER consistently achieves the accuracy-compute Pareto frontier, outperforming prior-art methods by 8 ∼ 10% while reducing token consumption by 25 ∼ 40%. Code is available at https://github.com/ ShengxuanQiu/HyPER .