Strategically Diverse Sampling for Self-Training

Many LLM training and inference methods, including RL and test-time scaling, depend on repeated sampling, but benefit only when the responses meaningfully differ. Self-training faces the same challenge: training data is typically constructed by sampling IID responses and filtering primarily for correctness, thereby overrepresenting strategies a model already favours. We investigate strategic diversity, or substantive variation among approaches to a problem, as an alternative principle for constructing self-training data. We generate strategically diverse data with two sampling methods: GROOT, a new method which constructs a hierarchical tree of approaches and samples distinct paths, and Verbalized Sampling (VS), adapted to produce an unstructured set of approaches. Across competitive progr