# Trust, But Verify: A Self-Verification Approach to Reinforcement Learning with Verifiable Rewards

arXiv: https://arxiv.org/abs/2505.13445 · HTML: https://mlsanity.com/paper/2505.13445/

## Key facts

- Cited by 38 papers in the map (data through 14 Oct 2026).
- Builds on 37 of its 50 references that are in the map.
- First posted on arXiv 19 May 2025.

## Builds on (most cited first, 30 of 37)

- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [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)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [Direct Preference Optimization: Your Language Model is Secretly a Reward Model](https://mlsanity.com/paper/2305.18290/) (2023)
- [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)
- [Deep reinforcement learning from human preferences](https://mlsanity.com/paper/1706.03741/) (2017)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [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)
- [Solving Quantitative Reasoning Problems with Language Models](https://mlsanity.com/paper/2206.14858/) (2022)
- [Kimi k1.5: Scaling Reinforcement Learning with LLMs](https://mlsanity.com/paper/2501.12599/) (2025)
- [OlympiadBench: A Challenging Benchmark for Promoting AGI with Olympiad-Level Bilingual Multimodal Scientific Problems](https://mlsanity.com/paper/2402.14008/) (2024)
- [Tulu 3: Pushing Frontiers in Open Language Model Post-Training](https://mlsanity.com/paper/2411.15124/) (2024)
- [Does Reinforcement Learning Really Incentivize Reasoning Capacity in LLMs Beyond the Base Model?](https://mlsanity.com/paper/2504.13837/) (2025)
- [STaR: Bootstrapping Reasoning With Reasoning](https://mlsanity.com/paper/2203.14465/) (2022)
- [Math-Shepherd: Verify and Reinforce LLMs Step-by-step without Human Annotations](https://mlsanity.com/paper/2312.08935/) (2023)
- [Self-Rewarding Language Models](https://mlsanity.com/paper/2401.10020/) (2024)
- [SimpleRL-Zoo: Investigating and Taming Zero Reinforcement Learning for Open Base Models in the Wild](https://mlsanity.com/paper/2503.18892/) (2025)
- [Generative Verifiers: Reward Modeling as Next-Token Prediction](https://mlsanity.com/paper/2408.15240/) (2024)
- [Open-Reasoner-Zero: An Open Source Approach to Scaling Up Reinforcement Learning on the Base Model](https://mlsanity.com/paper/2503.24290/) (2025)
- [Demystifying Long Chain-of-Thought Reasoning in LLMs](https://mlsanity.com/paper/2502.03373/) (2025)
- [DeepMath-103K: A Large-Scale, Challenging, Decontaminated, and Verifiable Mathematical Dataset for Advancing Reasoning](https://mlsanity.com/paper/2504.11456/) (2025)
- [OpenMathInstruct-2: Accelerating AI for Math with Massive Open-Source Instruction Data](https://mlsanity.com/paper/2410.01560/) (2024)
- [Crossing the Reward Bridge: Expanding RL with Verifiable Rewards Across Diverse Domains](https://mlsanity.com/paper/2503.23829/) (2025)
- [Self-Improvement in Language Models: The Sharpening Mechanism](https://mlsanity.com/paper/2412.01951/) (2024)

## Built on by (most cited first, 30 of 38)

- [Pass@k Training for Adaptively Balancing Exploration and Exploitation of Large Reasoning Models](https://mlsanity.com/paper/2508.10751/) (2025)
- [Perception-Aware Policy Optimization for Multimodal Reasoning](https://mlsanity.com/paper/2507.06448/) (2025)
- [The Invisible Leash: Why RLVR May or May Not Escape Its Origin](https://mlsanity.com/paper/2507.14843/) (2025)
- [RLVER: Reinforcement Learning with Verifiable Emotion Rewards for Empathetic Agents](https://mlsanity.com/paper/2507.03112/) (2025)
- [Decomposing the Entropy-Performance Exchange: The Missing Keys to Unlocking Effective Reinforcement Learning](https://mlsanity.com/paper/2508.02260/) (2025)
- [Learning to Self-Verify Makes Language Models Better Reasoners](https://mlsanity.com/paper/2602.07594/) (2026)
- [Mitigating LLM Hallucination via Behaviorally Calibrated Reinforcement Learning](https://mlsanity.com/paper/2512.19920/) (2025)
- [Linking Process to Outcome: Conditional Reward Modeling for LLM Reasoning](https://mlsanity.com/paper/2509.26578/) (2025)
- [V1: Unifying Generation and Self-Verification for Parallel Reasoners](https://mlsanity.com/paper/2603.04304/) (2026)
- [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)
- [LaSeR: Reinforcement Learning with Last-Token Self-Rewarding](https://mlsanity.com/paper/2510.14943/) (2025)
- [Trust but Verify! A Survey on Verification Design for Test-time Scaling](https://mlsanity.com/paper/2508.16665/) (2025)
- [From Solving to Verifying: A Unified Objective for Robust Reasoning in LLMs](https://mlsanity.com/paper/2511.15137/) (2025)
- [The End of Manual Decoding: Towards Truly End-to-End Language Models](https://mlsanity.com/paper/2510.26697/) (2025)
- [MSRL: Scaling Generative Multimodal Reward Modeling via Multi-Stage Reinforcement Learning](https://mlsanity.com/paper/2603.25108/) (2026)
- [Sparse Reward Subsystem in Large Language Models](https://mlsanity.com/paper/2602.00986/) (2026)
- [ICRL: Learning to Internalize Self-Critique with Reinforcement Learning](https://mlsanity.com/paper/2605.15224/) (2026)
- [Pseudo-Formalization for Automatic Proof Verification](https://mlsanity.com/paper/2605.20531/) (2026)
- [GraphPO: Graph-based Policy Optimization for Reasoning Models](https://mlsanity.com/paper/2606.18954/) (2026)
- [Round-trip Reinforcement Learning: Self-Consistent Training for Better Chemical LLMs](https://mlsanity.com/paper/2510.01527/) (2025)
- [OpenReward: Learning to Reward Long-form Agentic Tasks via Reinforcement Learning](https://mlsanity.com/paper/2510.24636/) (2025)
- [Recursive Think-Answer Process for LLMs and VLMs](https://mlsanity.com/paper/2603.02099/) (2026)
- [Recursive Inference Machines for Neural Reasoning](https://mlsanity.com/paper/2603.05234/) (2026)
- [Bridging Visual Representation and Reinforcement Learning from Verifiable Rewards in Large Vision-Language Models](https://mlsanity.com/paper/2603.27375/) (2026)
- [Verification Mirage: Mapping the Reliability Boundary of Self-Verification in Medical VQA](https://mlsanity.com/paper/2605.10850/) (2026)
- [Critique to Verify: Accurate and Honest Test-Time Scaling with RL-Trained Verifiers](https://mlsanity.com/paper/2509.23152/) (2025)
- [Learning from Self-Debate: Preparing Reasoning Models for Multi-Agent Debate](https://mlsanity.com/paper/2601.22297/) (2026)
- [Selective Off-Policy Reference Tuning with Plan Guidance](https://mlsanity.com/paper/2605.11505/) (2026)
- [STRIDE: Learnable Stepwise Language Feedback for LLM Reasoning](https://mlsanity.com/paper/2605.18851/) (2026)

## Abstract (arXiv)

Large Language Models (LLMs) show great promise in complex reasoning, with Reinforcement Learning with Verifiable Rewards (RLVR) being a key enhancement strategy. However, a prevalent issue is ``superficial self-reflection'', where models fail to robustly verify their own outputs. We introduce RISE (Reinforcing Reasoning with Self-Verification), a novel online RL framework designed to tackle this. RISE explicitly and simultaneously trains an LLM to improve both its problem-solving and self-verification abilities within a single, integrated RL process. The core mechanism involves leveraging verifiable rewards from an outcome verifier to provide on-the-fly feedback for both solution generation and self-verification tasks. In each iteration, the model generates solutions, then critiques its own on-policy generated solutions, with both trajectories contributing to the policy update. Extensive experiments on diverse mathematical reasoning benchmarks show that RISE consistently improves model's problem-solving accuracy while concurrently fostering strong self-verification skills. Our analyses highlight the advantages of online verification and the benefits of increased verification compute. Additionally, RISE models exhibit more frequent and accurate self-verification behaviors during reasoning. These advantages reinforce RISE as a flexible and effective path towards developing more robust and self-aware reasoners.