Offline Exploration-Aware Fine-Tuning for Long-Chain Mathematical Reasoning

ACL ARR 2026 January Submission6248 Authors

Keywords: mathematical reasoning, SFT, RLVR, exploration, policy entropy

Abstract: Through encouraging self-exploration, reinforcement learning from verifiable rewards (RLVR) has significantly advanced the mathematical reasoning capabilities of large language models. As the starting point for RLVR, the capacity of supervised fine-tuning (SFT) to memorize new chain-of-thought trajectories provides a crucial initialization that shapes the subsequent exploration landscape. However, existing research primarily focuses on facilitating exploration during RLVR training, leaving exploration-aware SFT under-explored. To bridge this gap, we propose Offline eXploration-Aware (OXA) fine-tuning. Specifically, OXA optimizes two objectives: promoting low-confidence verified teacher-distillation data to internalize previously uncaptured reasoning patterns, and suppressing high-confidence incorrect self-distillation data to redistribute probability mass of incorrect patterns toward potentially correct candidates. Experimental results across 6 benchmarks show that OXA consistently improves mathematical reasoning performance, especially achieving an average gain of $+6$ Pass@1 and $+5$ Pass@$k$ points compared to conventional SFT on the Qwen2.5-1.5B-Math. Crucially, OXA elevates initial policy entropy, and performance gains persist throughout extensive RLVR training, demonstrating the long-term value of OXA.

Paper Type: Long

Research Area: Mathematical, Symbolic, Neurosymbolic, and Logical Reasoning

Research Area Keywords: chain-of-thought, fine-tuning

Contribution Types: NLP engineering experiment

Languages Studied: English

Submission Number: 6248