Strategically Diverse Sampling for Self-Training

arXiv:2609.31571v1 Announce Type: new Abstract: 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 programming and Next-Chapter Prediction domains, models trained on strategically sampled data outperform IID-trained counterparts on difficult tasks and provide strong initializations for RL and test-time scaling. Most strikingly, self-training on strategically diverse but incorrect traces from Qwen3-4B outperforms IID distillation from a 235B teacher. These results challenge prevailing assumptions about what makes useful self-training data and show that diversity of approaches can matter more than correctness or teacher scale.

Abstract: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 programming and Next-Chapter Prediction domains, models trained on strategically sampled data outperform IID-trained counterparts on difficult tasks and provide strong initializations for RL and test-time scaling. Most strikingly, self-training on strategically diverse but incorrect traces from Qwen3-4B outperforms IID distillation from a 235B teacher. These results challenge prevailing assumptions about what makes useful self-training data and show that diversity of approaches can matter more than correctness or teacher scale.

Computation and Language (cs.CL)

arXiv:2609.31571 [cs.CL]

(or arXiv:2609.31571v1 [cs.CL] for this version)

https://doi.org/10.48550/arXiv.2609.31571 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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Strategically Diverse Sampling for Self-Training

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