myWiki/raw/papers/pre-train-space-reinforcement-learning-2026.md

title, arxiv, authors, venue, date, type, tags

title	arxiv	authors	venue	date	type	tags
Pre-train Space Reinforcement Learning: From P(y|x) to P(y)	2604.14142	Yuqiao Tan Minzheng Wang Bo Liu Zichen Liu Tian Liang Shizhu He Jun Zhao Kang Liu	arXiv preprint	2026-04-15	paper	reinforcement-learning pre-training LLM reasoning GRPO

Pre-train Space Reinforcement Learning

arXiv: 2604.14142 Authors: Yuqiao Tan¹²*, Minzheng Wang¹²*, Bo Liu³, Zichen Liu³, Tian Liang⁴, Shizhu He¹²†, Jun Zhao¹², Kang Liu¹² Affiliations: ¹ CASIA, ² UCAS, ³ NUS, ⁴ Tencent AI Lab

• Equal contribution, † Corresponding author

Abstract

While reinforcement learning with verifiable rewards (RLVR) significantly enhances LLM reasoning by optimizing the conditional distribution P(y|x), its potential is fundamentally bounded by the base model's existing output distribution. Optimizing the marginal distribution P(y) in the Pre-train Space addresses this bottleneck by encoding reasoning ability and preserving broad exploration capacity. Yet, conventional pre-training relies on static corpora for passive learning, leading to a distribution shift that hinders targeted reasoning enhancement. In this paper, we introduce PreRL (Pre-train Space RL), which applies reward-driven online updates directly to P(y). We theoretically and empirically validate the strong gradient alignment between log P(y) and log P(y|x), establishing PreRL as a viable surrogate for standard RL. Furthermore, we uncover a critical mechanism: Negative Sample Reinforcement (NSR) within PreRL serves as an exceptionally effective driver for reasoning. NSR-PreRL rapidly prunes incorrect reasoning spaces while stimulating endogenous reflective behaviors, increasing transition and reflection thoughts by 14.89× and 6.54×, respectively. Leveraging these insights, we propose Dual Space RL (DSRL), a Policy Reincarnation strategy that initializes models with NSR-PreRL to expand the reasoning horizon before transitioning to standard RL for fine-grained optimization.

Key Claims

1. Gradient Alignment: <∇log P(y), ∇log P(y|x)> ≥ 0 for all samples (empirically validated), confirming PreRL as a viable surrogate for standard RL
2. NSR > PSR in Pre-train Space: Negative Sample Reinforcement (suppressing incorrect paths) is far more effective than Positive Sample Reinforcement in the pre-train space
3. DSRL outperforms GRPO: Dual Space RL achieves +2-5 point improvement on benchmarks like AIME24/25, with 1.6×-2.5× sample efficiency
4. NSR-PreRL stimulates endogenous reasoning: 14.89× more transition thoughts, 6.54× more reflection thoughts