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

arXiv: https://arxiv.org/abs/2505.16176 · HTML: https://mlsanity.com/paper/2505.16176/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Placed in Test-time compute and efficient thinking, one of 17 directions in LLM reasoning.
- Builds on 27 of its 50 references that are in the map.
- First posted on arXiv 22 May 2025.

## Placed in

- LLM reasoning / [Test-time compute and efficient thinking](https://mlsanity.com/lr/test-time-compute-and-efficient-thinking/)
- LLM alignment / RLHF / preference optimisation / [Process reward models for reasoning](https://mlsanity.com/alignment/process-reward-models-for-reasoning/)

## Builds on (most cited first, 27 of 27)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [Qwen Technical Report](https://mlsanity.com/paper/2309.16609/) (2023)
- [Solving Quantitative Reasoning Problems with Language Models](https://mlsanity.com/paper/2206.14858/) (2022)
- [s1: Simple test-time scaling](https://mlsanity.com/paper/2501.19393/) (2025)
- [OpenAI o1 System Card](https://mlsanity.com/paper/2412.16720/) (2024)
- [Kimi k1.5: Scaling Reinforcement Learning with LLMs](https://mlsanity.com/paper/2501.12599/) (2025)
- [Qwen2.5-Math Technical Report: Toward Mathematical Expert Model via Self-Improvement](https://mlsanity.com/paper/2409.12122/) (2024)
- [DeepSeek-V3 Technical Report](https://mlsanity.com/paper/2412.19437/) (2024)
- [SimpleRL-Zoo: Investigating and Taming Zero Reinforcement Learning for Open Base Models in the Wild](https://mlsanity.com/paper/2503.18892/) (2025)
- [LIMO: Less is More for Reasoning](https://mlsanity.com/paper/2502.03387/) (2025)
- [Scaling Relationship on Learning Mathematical Reasoning with Large Language Models](https://mlsanity.com/paper/2308.01825/) (2023)
- [Direct Language Model Alignment from Online AI Feedback](https://mlsanity.com/paper/2402.04792/) (2024)
- [Iterative Reasoning Preference Optimization](https://mlsanity.com/paper/2404.19733/) (2024)
- [REINFORCE++: Stabilizing Critic-Free Policy Optimization with Global Advantage Normalization](https://mlsanity.com/paper/2501.03262/) (2025)
- [MathScale: Scaling Instruction Tuning for Mathematical Reasoning](https://mlsanity.com/paper/2403.02884/) (2024)
- [Self-Evolving Curriculum for LLM Reasoning](https://mlsanity.com/paper/2505.14970/) (2025)
- [Enhancing LLM Reasoning with Iterative DPO: A Comprehensive Empirical Investigation](https://mlsanity.com/paper/2503.12854/) (2025)
- [B-STaR: Monitoring and Balancing Exploration and Exploitation in Self-Taught Reasoners](https://mlsanity.com/paper/2412.17256/) (2024)
- [Pangu Ultra: Pushing the Limits of Dense Large Language Models on Ascend NPUs](https://mlsanity.com/paper/2504.07866/) (2025)
- [Self-Evolved Preference Optimization for Enhancing Mathematical Reasoning in Small Language Models](https://mlsanity.com/paper/2503.04813/) (2025)

## Built on by (most cited first, 8 of 8)

- [REA-RL: Reflection-Aware Online Reinforcement Learning for Efficient Reasoning](https://mlsanity.com/paper/2505.19862/) (2025)
- [Curvature-Adaptive Consistency Flow Matching: Autonomous Trajectory Optimization via Reinforcement Learning](https://mlsanity.com/paper/2606.22394/) (2026)
- [FAST: A Synergistic Framework of Attention and State-space Models for Spatiotemporal Traffic Prediction](https://mlsanity.com/paper/2604.13453/) (2026)
- [From Past To Path: Masked History Learning for Next-Item Prediction in Generative Recommendation](https://mlsanity.com/paper/2509.23649/) (2025)
- [Mining or Synthesis? Rethinking Exploration Efficiency in Iterative Alignment of Mathematical Reasoning](https://mlsanity.com/paper/2602.05370/) (2026)
- [Universally Empowering Zeroth-Order Optimization via Adaptive Layer-wise Sampling](https://mlsanity.com/paper/2604.18264/) (2026)
- [CoCoReviewBench: A Completeness- and Correctness-Oriented Benchmark for AI Reviewers](https://mlsanity.com/paper/2605.07905/) (2026)
- [DIAG: Diagnostic Iterative Alignment and Generation for Data-Efficient Mathematical Preference Distillation](https://mlsanity.com/paper/2608.22806/) (2026)

## Abstract (arXiv)

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.