Thinking Seeds: Leveraging Historical Diversity for Position-Aware RL in LLMs

On-policy reinforcement learning (RL) for language model post-training suffers from a fundamental tension: as training progresses, policy entropy collapses and sampling diversity diminishes, causing the model to ``forget'' its own earlier exploratory capacity. While off-policy data can restore diversity, existing methods mix entire trajectories at the sequence level, introducing severe policy mismatch and training instability. We argue that the core question is not \emph{whether} to use off-policy data, but \emph{where} in the sequence it should appear. Based on this insight, we propose \textbf{Thinking Seeds}, a token-level mix-policy framework that uses the model's own historical checkpoints as off-policy prefixes, providing diverse starting points for reasoning, while the critical continuation is generated on-policy to preserve gradient quality. Through token-level importance ratios, Thinking Seeds effectively leverages historical diversity without compromising training stability. Extensive experiments across models and mathematical reasoning benchmarks demonstrate that Thinking Seeds consistently outperforms standard on-policy training and existing off-policy extensions. Our analysis reveals that the method maintains higher effective entropy, reduces gradient loss from clipping, and expands the explorable solution space, clarifying how position-aware mix-policy modeling improves both exploration and final performance in LLM RL.