# Mining or Synthesis? Rethinking Exploration Efficiency in Iterative Alignment of Mathematical Reasoning

arXiv: https://arxiv.org/abs/2602.05370 · HTML: https://mlsanity.com/paper/2602.05370/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Placed in Mathematical reasoning, one of 17 directions in LLM reasoning.
- Builds on 15 of its 31 references that are in the map.
- First posted on arXiv 5 Feb 2026.

## Placed in

- LLM reasoning / [Mathematical reasoning](https://mlsanity.com/lr/mathematical-reasoning/)
- LLM alignment / RLHF / preference optimisation / [Process reward models for reasoning](https://mlsanity.com/alignment/process-reward-models-for-reasoning/)

## Builds on (most cited first, 15 of 15)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [LLaMA: Open and Efficient Foundation Language Models](https://mlsanity.com/paper/2302.13971/) (2023)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [Qwen2.5 Technical Report](https://mlsanity.com/paper/2412.15115/) (2024)
- [Conservative Q-Learning for Offline Reinforcement Learning](https://mlsanity.com/paper/2006.04779/) (2020)
- [WebGPT: Browser-assisted question-answering with human feedback](https://mlsanity.com/paper/2112.09332/) (2021)
- [Solving Quantitative Reasoning Problems with Language Models](https://mlsanity.com/paper/2206.14858/) (2022)
- [Qwen2.5-Math Technical Report: Toward Mathematical Expert Model via Self-Improvement](https://mlsanity.com/paper/2409.12122/) (2024)
- [STaR: Bootstrapping Reasoning With Reasoning](https://mlsanity.com/paper/2203.14465/) (2022)
- [Self-Rewarding Language Models](https://mlsanity.com/paper/2401.10020/) (2024)
- [The Alignment Ceiling: Objective Mismatch in Reinforcement Learning from Human Feedback](https://mlsanity.com/paper/2311.00168/) (2023)
- [Dynamic Sampling that Adapts: Self-Aware Iterative Data Persistent Optimization for Mathematical Reasoning](https://mlsanity.com/paper/2505.16176/) (2025)

## Built on by (most cited first, 2 of 2)

- [DIAG: Diagnostic Iterative Alignment and Generation for Data-Efficient Mathematical Preference Distillation](https://mlsanity.com/paper/2608.22806/) (2026)
- [JPO: Juris Policy Optimization for Structured Legal Reasoning in Criminal Judgment Prediction](https://mlsanity.com/paper/2608.29616/) (2026)

## Abstract (arXiv)

Iterative Direct Preference Optimization (DPO) has emerged as a widely used paradigm for aligning Large Language Models on reasoning tasks. Existing approaches typically rely on Best-of-N sampling (N≥8) to mine positive trajectories from the distribution tail. In this work, we show that in mathematical reasoning, increasing N yields diminishing returns while increasing verifier-induced false-positive risk and the distribution shift required for policy updates. To address this, we introduce PACE (Proximal Alignment via Corrective Exploration), a generation-based corrective framework that replaces exhaustive mining with low-budget exploration (2≤ N≤3). Rather than searching for increasingly rare positive samples, PACE synthesizes high-fidelity preference pairs from failed explorations through corrective hindsight refinement and verification-guided filtering. Empirically, PACE matches or exceeds the performance of DPO-R1 (N=16) while using about 1/5 of the compute, and remains robust under 20% label corruption, where high-N baselines exhibit substantially higher noise exploitation.