Dynamic Sampling that Adapts: Self-Aware Iterative Data Persistent Optimization for Mathematical Reasoning

In mathematical reasoning, data selection strategies predominantly rely on static, externally defined metrics, which fail to adapt to the evolving capabilities of models during training. This misalignment limits the efficiency of Supervised Fine-Tuning and Reinforcement Learning. To bridge this gap, we introduce SAI-DPO (Self-Aware Iterative Data Persistent Optimization), a dynamic sampling framework that aligns training data with the model's intrinsic competence. SAI-DPO operationalizes two novel metrics: Knowledge Semantic Alignment for targeting domain weaknesses, and Self-Aware Difficulty, derived from pass rates and reasoning path characteristics, to gauge instance complexity relative to the model's current state. By iteratively recalibrating the data distribution based on real-time feedback, SAI-DPO dynamically aligns training samples with the model's evolving competence, ensuring the data remains strictly relevant to the model's current capability level. Extensive experiments on eight benchmarks (including AIME24 and AMC23) demonstrate that SAI-DPO outperforms static baselines at most nearly 6 points, achieving state-of-the-art efficiency with significantly less data.