# S2R: Teaching LLMs to Self-verify and Self-correct via Reinforcement Learning

arXiv: https://arxiv.org/abs/2502.12853 · HTML: https://mlsanity.com/paper/2502.12853/

## Key facts

- Cited by 39 papers in the map (data through 14 Oct 2026).
- Placed in Reinforcement learning for reasoning, one of 17 directions in LLM reasoning.
- Builds on 64 of its 75 references that are in the map.
- First posted on arXiv 18 Feb 2025.

## Placed in

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

## Builds on (most cited first, 30 of 64)

- [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)
- [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)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [Training a Helpful and Harmless Assistant with Reinforcement Learning from Human Feedback](https://mlsanity.com/paper/2204.05862/) (2022)
- [Self-Refine: Iterative Refinement with Self-Feedback](https://mlsanity.com/paper/2303.17651/) (2023)
- [Learning to summarize from human feedback](https://mlsanity.com/paper/2009.01325/) (2020)
- [Fine-Tuning Language Models from Human Preferences](https://mlsanity.com/paper/1909.08593/) (2019)
- [Scaling LLM Test-Time Compute Optimally can be More Effective than Scaling Model Parameters](https://mlsanity.com/paper/2408.03314/) (2024)
- [MMLU-Pro: A More Robust and Challenging Multi-Task Language Understanding Benchmark](https://mlsanity.com/paper/2406.01574/) (2024)
- [OlympiadBench: A Challenging Benchmark for Promoting AGI with Olympiad-Level Bilingual Multimodal Scientific Problems](https://mlsanity.com/paper/2402.14008/) (2024)
- [Scaling Laws for Reward Model Overoptimization](https://mlsanity.com/paper/2210.10760/) (2022)
- [Qwen2.5-Math Technical Report: Toward Mathematical Expert Model via Self-Improvement](https://mlsanity.com/paper/2409.12122/) (2024)
- [Large Language Models Cannot Self-Correct Reasoning Yet](https://mlsanity.com/paper/2310.01798/) (2023)
- [Large Language Monkeys: Scaling Inference Compute with Repeated Sampling](https://mlsanity.com/paper/2407.21787/) (2024)
- [Math-Shepherd: Verify and Reinforce LLMs Step-by-step without Human Annotations](https://mlsanity.com/paper/2312.08935/) (2023)
- [Did Aristotle Use a Laptop? A Question Answering Benchmark with Implicit Reasoning Strategies](https://mlsanity.com/paper/2101.02235/) (2021)
- [Do NOT Think That Much for 2+3=? On the Overthinking of o1-Like LLMs](https://mlsanity.com/paper/2412.21187/) (2024)
- [Process Reinforcement through Implicit Rewards](https://mlsanity.com/paper/2502.01456/) (2025)
- [Generative Verifiers: Reward Modeling as Next-Token Prediction](https://mlsanity.com/paper/2408.15240/) (2024)
- [Improve Mathematical Reasoning in Language Models by Automated Process Supervision](https://mlsanity.com/paper/2406.06592/) (2024)
- [Training Language Models to Self-Correct via Reinforcement Learning](https://mlsanity.com/paper/2409.12917/) (2024)
- [The Reversal Curse: LLMs trained on "A is B" fail to learn "B is A"](https://mlsanity.com/paper/2309.12288/) (2023)
- [Self-critiquing models for assisting human evaluators](https://mlsanity.com/paper/2206.05802/) (2022)
- [ReST-MCTS*: LLM Self-Training via Process Reward Guided Tree Search](https://mlsanity.com/paper/2406.03816/) (2024)
- [rStar-Math: Small LLMs Can Master Math Reasoning with Self-Evolved Deep Thinking](https://mlsanity.com/paper/2501.04519/) (2025)
- [CRUXEval: A Benchmark for Code Reasoning, Understanding and Execution](https://mlsanity.com/paper/2401.03065/) (2024)

## Built on by (most cited first, 30 of 39)

- [Towards Reasoning Era: A Survey of Long Chain-of-Thought for Reasoning Large Language Models](https://mlsanity.com/paper/2503.09567/) (2025)
- [Crossing the Reward Bridge: Expanding RL with Verifiable Rewards Across Diverse Domains](https://mlsanity.com/paper/2503.23829/) (2025)
- [Process vs. Outcome Reward: Which is Better for Agentic RAG Reinforcement Learning](https://mlsanity.com/paper/2505.14069/) (2025)
- [The Illusion of Diminishing Returns: Measuring Long Horizon Execution in LLMs](https://mlsanity.com/paper/2509.09677/) (2025)
- [SPC: Evolving Self-Play Critic via Adversarial Games for LLM Reasoning](https://mlsanity.com/paper/2504.19162/) (2025)
- [100 Days After DeepSeek-R1: A Survey on Replication Studies and More Directions for Reasoning Language Models](https://mlsanity.com/paper/2505.00551/) (2025)
- [PAG: Multi-Turn Reinforced LLM Self-Correction with Policy as Generative Verifier](https://mlsanity.com/paper/2506.10406/) (2025)
- [Heimdall: test-time scaling on the generative verification](https://mlsanity.com/paper/2504.10337/) (2025)
- [RLVER: Reinforcement Learning with Verifiable Emotion Rewards for Empathetic Agents](https://mlsanity.com/paper/2507.03112/) (2025)
- [R3-RAG: Learning Step-by-Step Reasoning and Retrieval for LLMs via Reinforcement Learning](https://mlsanity.com/paper/2505.23794/) (2025)
- [Beyond 'Aha!': Toward Systematic Meta-Abilities Alignment in Large Reasoning Models](https://mlsanity.com/paper/2505.10554/) (2025)
- [Boosting LLM Reasoning via Spontaneous Self-Correction](https://mlsanity.com/paper/2506.06923/) (2025)
- [Generative AI Act II: Test Time Scaling Drives Cognition Engineering](https://mlsanity.com/paper/2504.13828/) (2025)
- [CoVerRL: Breaking the Consensus Trap in Label-Free Reasoning via Generator-Verifier Co-Evolution](https://mlsanity.com/paper/2603.17775/) (2026)
- [LeTS: Learning to Think-and-Search via Process-and-Outcome Reward Hybridization](https://mlsanity.com/paper/2505.17447/) (2025)
- [ReSeek: A Self-Correcting Framework for Search Agents with Instructive Rewards](https://mlsanity.com/paper/2510.00568/) (2025)
- [Enhancing Large Language Model Reasoning with Reward Models: An Analytical Survey](https://mlsanity.com/paper/2510.01925/) (2025)
- [Large Language Model Post-Training: A Unified View of Off-Policy and On-Policy Learning](https://mlsanity.com/paper/2604.07941/) (2026)
- [RuCL: Stratified Rubric-Based Curriculum Learning for Multimodal Large Language Model Reasoning](https://mlsanity.com/paper/2602.21628/) (2026)
- [ThinkTwice: Jointly Optimizing Large Language Models for Reasoning and Self-Refinement](https://mlsanity.com/paper/2604.01591/) (2026)
- [Demystifying Scientific Problem-Solving in LLMs by Probing Knowledge and Reasoning](https://mlsanity.com/paper/2508.19202/) (2025)
- [Can RL Improve Generalization of LLM Agents? An Empirical Study](https://mlsanity.com/paper/2603.12011/) (2026)
- [ICRL: Learning to Internalize Self-Critique with Reinforcement Learning](https://mlsanity.com/paper/2605.15224/) (2026)
- [Closing the Reflection Gap: A Free Calibration Bonus for Agentic RL](https://mlsanity.com/paper/2606.14211/) (2026)
- [Mind the Gap: Bridging Thought Leap for Improved Chain-of-Thought Tuning](https://mlsanity.com/paper/2505.14684/) (2025)
- [Planning with Unified Multimodal Models](https://mlsanity.com/paper/2509.23014/) (2025)
- [Boosting Accuracy and Efficiency of Budget Forcing in LLMs via Reinforcement Learning for Mathematical Reasoning](https://mlsanity.com/paper/2510.21398/) (2025)
- [Evaluate-as-Action: Self-Evaluated Process Rewards for Retrieval-Augmented Agents](https://mlsanity.com/paper/2603.09203/) (2026)
- [SVSR: A Self-Verification and Self-Rectification Paradigm for Multimodal Reasoning](https://mlsanity.com/paper/2604.10228/) (2026)
- [Decoupling Understanding from Reasoning via Problem Space Mapping for Small-Scale Model Reasoning](https://mlsanity.com/paper/2508.10019/) (2025)

## Abstract (arXiv)

Recent studies have demonstrated the effectiveness of LLM test-time scaling. However, existing approaches to incentivize LLMs' deep thinking abilities generally require large-scale data or significant training efforts. Meanwhile, it remains unclear how to improve the thinking abilities of less powerful base models. In this work, we introduce S2R, an efficient framework that enhances LLM reasoning by teaching models to self-verify and self-correct during inference. Specifically, we first initialize LLMs with iterative self-verification and self-correction behaviors through supervised fine-tuning on carefully curated data. The self-verification and self-correction skills are then further strengthened by both outcome-level and process-level reinforcement learning, with minimized resource requirements, enabling the model to adaptively refine its reasoning process during inference. Our results demonstrate that, with only 3.1k self-verifying and self-correcting behavior initialization samples, Qwen2.5-math-7B achieves an accuracy improvement from 51.0% to 81.6%, outperforming models trained on an equivalent amount of long-CoT distilled data. Extensive experiments and analysis based on three base models across both in-domain and out-of-domain benchmarks validate the effectiveness of S2R. Our code and data are available at https://github.com/NineAbyss/S2R.