# P2S: Probabilistic Process Supervision for General-Domain Reasoning Question Answering

arXiv: https://arxiv.org/abs/2601.20649 · HTML: https://mlsanity.com/paper/2601.20649/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Placed in Reinforcement learning for reasoning, one of 17 directions in LLM reasoning.
- Builds on 27 of its 34 references that are in the map.
- First posted on arXiv 28 Jan 2026.

## Placed in

- LLM reasoning / [Reinforcement learning for reasoning](https://mlsanity.com/lr/reinforcement-learning-for-reasoning/)

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

- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [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)
- [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (2022)
- [Qwen2.5 Technical Report](https://mlsanity.com/paper/2412.15115/) (2024)
- [DAPO: An Open-Source LLM Reinforcement Learning System at Scale](https://mlsanity.com/paper/2503.14476/) (2025)
- [A Survey on LLM-as-a-Judge](https://mlsanity.com/paper/2411.15594/) (2024)
- [Math-Shepherd: Verify and Reinforce LLMs Step-by-step without Human Annotations](https://mlsanity.com/paper/2312.08935/) (2023)
- [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)
- [Open-Reasoner-Zero: An Open Source Approach to Scaling Up Reinforcement Learning on the Base Model](https://mlsanity.com/paper/2503.24290/) (2025)
- [Training Language Models to Self-Correct via Reinforcement Learning](https://mlsanity.com/paper/2409.12917/) (2024)
- [Rewarding Progress: Scaling Automated Process Verifiers for LLM Reasoning](https://mlsanity.com/paper/2410.08146/) (2024)
- [HuatuoGPT-o1, Towards Medical Complex Reasoning with LLMs](https://mlsanity.com/paper/2412.18925/) (2024)
- [Logic-RL: Unleashing LLM Reasoning with Rule-Based Reinforcement Learning](https://mlsanity.com/paper/2502.14768/) (2025)
- [Light-R1: Curriculum SFT, DPO and RL for Long COT from Scratch and Beyond](https://mlsanity.com/paper/2503.10460/) (2025)
- [Skywork Open Reasoner 1 Technical Report](https://mlsanity.com/paper/2505.22312/) (2025)
- [Teaching Large Language Models to Reason with Reinforcement Learning](https://mlsanity.com/paper/2403.04642/) (2024)
- [Generative Reward Models](https://mlsanity.com/paper/2410.12832/) (2024)
- [General-Reasoner: Advancing LLM Reasoning Across All Domains](https://mlsanity.com/paper/2505.14652/) (2025)
- [RLPR: Extrapolating RLVR to General Domains without Verifiers](https://mlsanity.com/paper/2506.18254/) (2025)
- [Reinforcing General Reasoning without Verifiers](https://mlsanity.com/paper/2505.21493/) (2025)
- [Segment Policy Optimization: Effective Segment-Level Credit Assignment in RL for Large Language Models](https://mlsanity.com/paper/2505.23564/) (2025)
- [GHPO: Adaptive Guidance for Stable and Efficient LLM Reinforcement Learning](https://mlsanity.com/paper/2507.10628/) (2025)
- [Copyright Protection for Large Language Models: A Survey of Methods, Challenges, and Trends](https://mlsanity.com/paper/2508.11548/) (2025)
- [Direct Reasoning Optimization: Token-Level Reasoning Reflectivity Meets Rubric Gates for Unverifiable Tasks](https://mlsanity.com/paper/2506.13351/) (2025)
- [PSPO*: An Effective Process-supervised Policy Optimization for Reasoning Alignment](https://mlsanity.com/paper/2411.11681/) (2024)

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

- [Rewarding Better Thinking for LLM Preference Alignment](https://mlsanity.com/paper/2607.19824/) (2026)
- [DeltaTTG: Training Multi-Turn Agents with a Token-to-Go Progress Meter](https://mlsanity.com/paper/2610.17666/) (2026)

## Abstract (arXiv)

While reinforcement learning with verifiable rewards (RLVR) has advanced LLM reasoning in structured domains like mathematics and programming, its application to general-domain reasoning tasks remains challenging due to the absence of verifiable reward signals. To this end, methods like Reinforcement Learning with Reference Probability Reward (RLPR) have emerged, leveraging the probability of generating the final answer as a reward signal. However, these outcome-focused approaches neglect crucial step-by-step supervision of the reasoning process itself. To address this gap, we introduce Probabilistic Process Supervision (P2S), a novel self-supervision framework that provides fine-grained process rewards without requiring a separate reward model or human-annotated reasoning steps. During reinforcement learning, P2S synthesizes and filters a high-quality reference reasoning chain (gold-CoT). The core of our method is to calculate a Path Faithfulness Reward (PFR) for each reasoning step, which is derived from the conditional probability of generating the gold-CoT's suffix, given the model's current reasoning prefix. Crucially, this PFR can be flexibly integrated with any outcome-based reward, directly tackling the reward sparsity problem by providing dense guidance. Extensive experiments on reading comprehension and medical Question Answering benchmarks show that P2S significantly outperforms strong baselines.