# PAG: Multi-Turn Reinforced LLM Self-Correction with Policy as Generative Verifier

arXiv: https://arxiv.org/abs/2506.10406 · HTML: https://mlsanity.com/paper/2506.10406/

## Key facts

- Cited by 28 papers in the map (data through 14 Oct 2026).
- Builds on 45 of its 59 references that are in the map.
- First posted on arXiv 12 Jun 2025.

## Builds on (most cited first, 30 of 45)

- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [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)
- [Efficient Memory Management for Large Language Model Serving with PagedAttention](https://mlsanity.com/paper/2309.06180/) (2023)
- [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (2022)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Qwen2.5 Technical Report](https://mlsanity.com/paper/2412.15115/) (2024)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [Self-Refine: Iterative Refinement with Self-Feedback](https://mlsanity.com/paper/2303.17651/) (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)
- [LiveCodeBench: Holistic and Contamination Free Evaluation of Large Language Models for Code](https://mlsanity.com/paper/2403.07974/) (2024)
- [Competition-Level Code Generation with AlphaCode](https://mlsanity.com/paper/2203.07814/) (2022)
- [Solving Quantitative Reasoning Problems with Language Models](https://mlsanity.com/paper/2206.14858/) (2022)
- [AgentBench: Evaluating LLMs as Agents](https://mlsanity.com/paper/2308.03688/) (2023)
- [Large Language Models Cannot Self-Correct Reasoning Yet](https://mlsanity.com/paper/2310.01798/) (2023)
- [Teaching Large Language Models to Self-Debug](https://mlsanity.com/paper/2304.05128/) (2023)
- [STaR: Bootstrapping Reasoning With Reasoning](https://mlsanity.com/paper/2203.14465/) (2022)
- [Self-Rewarding Language Models](https://mlsanity.com/paper/2401.10020/) (2024)
- [UI-TARS: Pioneering Automated GUI Interaction with Native Agents](https://mlsanity.com/paper/2501.12326/) (2025)
- [Humanity's Last Exam](https://mlsanity.com/paper/2501.14249/) (2025)
- [Generative Verifiers: Reward Modeling as Next-Token Prediction](https://mlsanity.com/paper/2408.15240/) (2024)
- [Training Language Models to Self-Correct via Reinforcement Learning](https://mlsanity.com/paper/2409.12917/) (2024)
- [The Lessons of Developing Process Reward Models in Mathematical Reasoning](https://mlsanity.com/paper/2501.07301/) (2025)
- [RAGEN: Understanding Self-Evolution in LLM Agents via Multi-Turn Reinforcement Learning](https://mlsanity.com/paper/2504.20073/) (2025)
- [Self-critiquing models for assisting human evaluators](https://mlsanity.com/paper/2206.05802/) (2022)
- [Is DPO Superior to PPO for LLM Alignment? A Comprehensive Study](https://mlsanity.com/paper/2404.10719/) (2024)

## Built on by (most cited first, 28 of 28)

- [A Survey of Reinforcement Learning for Large Reasoning Models](https://mlsanity.com/paper/2509.08827/) (2025)
- [A Survey of Self-Evolving Agents: What, When, How, and Where to Evolve on the Path to Artificial Super Intelligence](https://mlsanity.com/paper/2507.21046/) (2025)
- [Mathematical Proof as a Litmus Test: Revealing Failure Modes of Advanced Large Reasoning Models](https://mlsanity.com/paper/2506.17114/) (2025)
- [Self-Play Only Evolves When Self-Synthetic Pipeline Ensures Learnable Information Gain](https://mlsanity.com/paper/2603.02218/) (2026)
- [Risk-Sensitive RL for Alleviating Exploration Dilemmas in Large Language Models](https://mlsanity.com/paper/2509.24261/) (2025)
- [Failure Makes the Agent Stronger: Enhancing Accuracy through Structured Reflection for Reliable Tool Interactions](https://mlsanity.com/paper/2509.18847/) (2025)
- [CoVerRL: Breaking the Consensus Trap in Label-Free Reasoning via Generator-Verifier Co-Evolution](https://mlsanity.com/paper/2603.17775/) (2026)
- [Autonomous Agents for Scientific Discovery: Orchestrating Scientists, Language, Code, and Physics](https://mlsanity.com/paper/2510.09901/) (2025)
- [Revisiting Entropy Regularization: Adaptive Coefficient Unlocks Its Potential for LLM Reinforcement Learning](https://mlsanity.com/paper/2510.10959/) (2025)
- [LaSeR: Reinforcement Learning with Last-Token Self-Rewarding](https://mlsanity.com/paper/2510.14943/) (2025)
- [Enhancing Large Language Model Reasoning with Reward Models: An Analytical Survey](https://mlsanity.com/paper/2510.01925/) (2025)
- [From Solving to Verifying: A Unified Objective for Robust Reasoning in LLMs](https://mlsanity.com/paper/2511.15137/) (2025)
- [On the Limits of Test-Time Compute: Sequential Reward Filtering for Better Inference](https://mlsanity.com/paper/2512.04558/) (2025)
- [Foundational Automatic Evaluators: Scaling Multi-Task Generative Evaluator Training for Reasoning-Centric Domains](https://mlsanity.com/paper/2510.17793/) (2025)
- [Self-Improvement of Large Language Models: A Technical Overview and Future Outlook](https://mlsanity.com/paper/2603.25681/) (2026)
- [ThinkTwice: Jointly Optimizing Large Language Models for Reasoning and Self-Refinement](https://mlsanity.com/paper/2604.01591/) (2026)
- [Predicting and improving test-time scaling laws via reward tail-guided search](https://mlsanity.com/paper/2602.01485/) (2026)
- [Pause or Fabricate? Training Language Models for Grounded Reasoning](https://mlsanity.com/paper/2604.19656/) (2026)
- [Self-Trained Verification for Training- and Test-Time Self-Improvement](https://mlsanity.com/paper/2605.30290/) (2026)
- [CritiqueDriveVLM: From Verifier-Guided Reinforcement Learning to Latent Thought Distillation for Autonomous Driving](https://mlsanity.com/paper/2607.04179/) (2026)
- [M3-AD: Reflection-aware Multi-modal, Multi-category, and Multi-dimensional Benchmark and Framework for Industrial Anomaly Detection](https://mlsanity.com/paper/2603.00055/) (2026)
- [Skip-Connected Policy Optimization for Implicit Advantage](https://mlsanity.com/paper/2604.08690/) (2026)
- [STRIDE: Learnable Stepwise Language Feedback for LLM Reasoning](https://mlsanity.com/paper/2605.18851/) (2026)
- [A First-Principles Derivation of LLM Policy Optimization: From Expected Reward to GRPO and Its Structural Extensions](https://mlsanity.com/paper/2606.16733/) (2026)
- [The Two-Stage Decision-Sampling Hypothesis: Understanding the Emergence of Self-Reflection in RL-Trained LLMs](https://mlsanity.com/paper/2601.01580/) (2026)
- [CPMobius: Iterative Coach-Player Reasoning for Data-Free Reinforcement Learning](https://mlsanity.com/paper/2602.02979/) (2026)
- [Position: Introspective Experience from Conversational Environments as a Path to Better Learning](https://mlsanity.com/paper/2602.14910/) (2026)
- [REVES: REvision and VErification--Augmented Training for Test-Time Scaling](https://mlsanity.com/paper/2606.18910/) (2026)

## Abstract (arXiv)

Large Language Models (LLMs) have demonstrated impressive capabilities in complex reasoning tasks, yet they still struggle to reliably verify the correctness of their own outputs. Existing solutions to this verification challenge often depend on separate verifier models or require multi-stage self-correction training pipelines, which limit scalability. In this paper, we propose Policy as Generative Verifier (PAG), a simple and effective framework that empowers LLMs to self-correct by alternating between policy and verifier roles within a unified multi-turn reinforcement learning (RL) paradigm. Distinct from prior approaches that always generate a second attempt regardless of model confidence, PAG introduces a selective revision mechanism: the model revises its answer only when its own generative verification step detects an error. This verify-then-revise workflow not only alleviates model collapse but also jointly enhances both reasoning and verification abilities. Extensive experiments across diverse reasoning benchmarks highlight PAG's dual advancements: as a policy, it enhances direct generation and self-correction accuracy; as a verifier, its self-verification outperforms self-consistency.