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.

Existing alignment methods for preference optimization of large language models (LLMs) aim to enhance model performance by utilizing pairs of positive and negative samples. However, due to the limited capacity of models in scoring or generating responses, the quality of positive and negative samples may become similar during training, which complicates optimization for preference learning. To address this issue, we introduce SeaPO, a Strategic Error Amplification method that leverages three error types commonly occurring in LLMs to introduce specific error patterns into the model Preference Optimization. This strategy ensures that negative samples are more erroneous than positive samples and preference-based training is employed to mitigate the occurrence of these errors, thereby enhancing model performance. Evaluations across five capability dimensions and different model scales (1.5B to 14B) demonstrate that the generated data significantly improved overall model performance, particularly in terms of truthfulness, with improvements of 5–10 percentage points observed. Further analysis reveals that task performance varies depending on the error types introduced. Injecting the most common error types improves performance in related tasks, while a mix of error types leads to a broader performance enhancement: most tasks show stable improvements, while a few tasks exhibit significant gains.

Large Language Models (LLMs) often require domain-specific fine-tuning to address targeted tasks, which risks degrading their general capabilities. Maintaining a balance between domain-specific enhancements and general model utility is a key challenge. This paper proposes a novel approach named APT (Weakness Case Acquisition and Iterative Preference Training) to enhance domain-specific performance with self-generated dis-preferred weakness data (bad cases and similar cases). APT uniquely focuses on training the model using only those samples where errors occur, alongside a small, similar set of samples retrieved for this purpose. This targeted training minimizes interference with the model’s existing knowledge base, effectively retaining generic capabilities. Experimental results on the LLama-2 and Mistral-V0.3 models across various benchmarks demonstrate that APT ensures no reduction in generic capacity and achieves superior performance on downstream tasks compared to various existing methods. This validates our method as an effective strategy for enhancing domain-specific capabilities without sacrificing the model’s broader applicability.