# From P(y|x) to P(y): Investigating Reinforcement Learning in Pre-train Space

arXiv: https://arxiv.org/abs/2604.14142 · HTML: https://mlsanity.com/paper/2604.14142/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Placed in Reinforcement learning for reasoning, one of 17 directions in LLM reasoning.
- Builds on 67 of its 71 references that are in the map.
- First posted on arXiv 15 Apr 2026.

## Placed in

- LLM reasoning / [Reinforcement learning for reasoning](https://mlsanity.com/lr/reinforcement-learning-for-reasoning/)
- Deep reinforcement learning methods / [RL training of language and agent models](https://mlsanity.com/deeprl/rl-training-of-language-and-agent-models/)

## Builds on (most cited first, 30 of 67)

- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [Exploring the Limits of Transfer Learning with a Unified Text-to-Text Transformer](https://mlsanity.com/paper/1910.10683/) (2019)
- [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)
- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [Efficient Memory Management for Large Language Model Serving with PagedAttention](https://mlsanity.com/paper/2309.06180/) (2023)
- [GPT-4o System Card](https://mlsanity.com/paper/2410.21276/) (2024)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [GPQA: A Graduate-Level Google-Proof Q&A Benchmark](https://mlsanity.com/paper/2311.12022/) (2023)
- [DAPO: An Open-Source LLM Reinforcement Learning System at Scale](https://mlsanity.com/paper/2503.14476/) (2025)
- [HybridFlow: A Flexible and Efficient RLHF Framework](https://mlsanity.com/paper/2409.19256/) (2024)
- [High-Dimensional Continuous Control Using Generalized Advantage Estimation](https://mlsanity.com/paper/1506.02438/) (2015)
- [MMLU-Pro: A More Robust and Challenging Multi-Task Language Understanding Benchmark](https://mlsanity.com/paper/2406.01574/) (2024)
- [Challenging BIG-Bench Tasks and Whether Chain-of-Thought Can Solve Them](https://mlsanity.com/paper/2210.09261/) (2022)
- [Solving Quantitative Reasoning Problems with Language Models](https://mlsanity.com/paper/2206.14858/) (2022)
- [Understanding R1-Zero-Like Training: A Critical Perspective](https://mlsanity.com/paper/2503.20783/) (2025)
- [OlympiadBench: A Challenging Benchmark for Promoting AGI with Olympiad-Level Bilingual Multimodal Scientific Problems](https://mlsanity.com/paper/2402.14008/) (2024)
- [Does Reinforcement Learning Really Incentivize Reasoning Capacity in LLMs Beyond the Base Model?](https://mlsanity.com/paper/2504.13837/) (2025)
- [Do NOT Think That Much for 2+3=? On the Overthinking of o1-Like LLMs](https://mlsanity.com/paper/2412.21187/) (2024)
- [SimpleRL-Zoo: Investigating and Taming Zero Reinforcement Learning for Open Base Models in the Wild](https://mlsanity.com/paper/2503.18892/) (2025)
- [Kimi K2.5: Visual Agentic Intelligence](https://mlsanity.com/paper/2602.02276/) (2026)
- [Open-Reasoner-Zero: An Open Source Approach to Scaling Up Reinforcement Learning on the Base Model](https://mlsanity.com/paper/2503.24290/) (2025)
- [Learning to Reason under Off-Policy Guidance](https://mlsanity.com/paper/2504.14945/) (2025)
- [ERNIE 2.0: A Continual Pre-training Framework for Language Understanding](https://mlsanity.com/paper/1907.12412/) (2019)
- [Reasoning Models Can Be Effective Without Thinking](https://mlsanity.com/paper/2504.09858/) (2025)
- [What Matters In On-Policy Reinforcement Learning? A Large-Scale Empirical Study](https://mlsanity.com/paper/2006.05990/) (2020)
- [The Surprising Effectiveness of Negative Reinforcement in LLM Reasoning](https://mlsanity.com/paper/2506.01347/) (2025)

## Built on by (most cited first, 3 of 3)

- [SFT Conflicts, RL Coexists: A Theoretical and Empirical Analysis of Multi-Task Learning for LLMs](https://mlsanity.com/paper/2608.03573/) (2026)
- [Breaking the Impasse: Dual-Scale Evolutionary Policy Training for Social Language Agents](https://mlsanity.com/paper/2605.08721/) (2026)
- [Not All Synthetic Data Is Yours to Learn From](https://mlsanity.com/paper/2605.31126/) (2026)

## Abstract (arXiv)

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 14.89x and 6.54x, 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. Extensive experiments demonstrate that DSRL consistently outperforms strong baselines, proving that pre-train space pruning effectively steers the policy toward a refined correct reasoning subspace.