# Crossing the Reward Bridge: Expanding RL with Verifiable Rewards Across Diverse Domains

arXiv: https://arxiv.org/abs/2503.23829 · HTML: https://mlsanity.com/paper/2503.23829/

## Key facts

- Cited by 156 papers in the map (data through 14 Oct 2026).
- Placed in Reinforcement learning for reasoning, one of 17 directions in LLM reasoning.
- Builds on 30 of its 40 references that are in the map.
- First posted on arXiv 31 Mar 2025.

## Placed in

- LLM reasoning / [Reinforcement learning for reasoning](https://mlsanity.com/lr/reinforcement-learning-for-reasoning/)
- LLM alignment / RLHF / preference optimisation / [Process reward models for reasoning](https://mlsanity.com/alignment/process-reward-models-for-reasoning/)

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

- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [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)
- [Judging LLM-as-a-Judge with MT-Bench and Chatbot Arena](https://mlsanity.com/paper/2306.05685/) (2023)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [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)
- [Program Synthesis with Large Language Models](https://mlsanity.com/paper/2108.07732/) (2021)
- [DAPO: An Open-Source LLM Reinforcement Learning System at Scale](https://mlsanity.com/paper/2503.14476/) (2025)
- [Learning to summarize from human feedback](https://mlsanity.com/paper/2009.01325/) (2020)
- [Kimi k1.5: Scaling Reinforcement Learning with LLMs](https://mlsanity.com/paper/2501.12599/) (2025)
- [STaR: Bootstrapping Reasoning With Reasoning](https://mlsanity.com/paper/2203.14465/) (2022)
- [Measuring Coding Challenge Competence With APPS](https://mlsanity.com/paper/2105.09938/) (2021)
- [Show Your Work: Scratchpads for Intermediate Computation with Language Models](https://mlsanity.com/paper/2112.00114/) (2021)
- [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)
- [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)
- [ReFT: Reasoning with Reinforced Fine-Tuning](https://mlsanity.com/paper/2401.08967/) (2024)
- [RLEF: Grounding Code LLMs in Execution Feedback with Reinforcement Learning](https://mlsanity.com/paper/2410.02089/) (2024)
- [Stream of Search (SoS): Learning to Search in Language](https://mlsanity.com/paper/2404.03683/) (2024)
- [MAmmoTH2: Scaling Instructions from the Web](https://mlsanity.com/paper/2405.03548/) (2024)
- [Toward Self-Improvement of LLMs via Imagination, Searching, and Criticizing](https://mlsanity.com/paper/2404.12253/) (2024)
- [NaturalReasoning: Reasoning in the Wild with 2.8M Challenging Questions](https://mlsanity.com/paper/2502.13124/) (2025)
- [S2R: Teaching LLMs to Self-verify and Self-correct via Reinforcement Learning](https://mlsanity.com/paper/2502.12853/) (2025)
- [SoRFT: Issue Resolving with Subtask-oriented Reinforced Fine-Tuning](https://mlsanity.com/paper/2502.20127/) (2025)
- [OpenRFT: Adapting Reasoning Foundation Model for Domain-specific Tasks with Reinforcement Fine-Tuning](https://mlsanity.com/paper/2412.16849/) (2024)
- [How Do Humans Write Code? Large Models Do It the Same Way Too](https://mlsanity.com/paper/2402.15729/) (2024)
- [Self-Teaching Machines to Read and Comprehend with Large-Scale Multi-Subject Question-Answering Data](https://mlsanity.com/paper/2102.01226/) (2021)

## Built on by (most cited first, 30 of 156)

- [Rubrics as Rewards: Reinforcement Learning Beyond Verifiable Domains](https://mlsanity.com/paper/2507.17746/) (2025)
- [R-Zero: Self-Evolving Reasoning LLM from Zero Data](https://mlsanity.com/paper/2508.05004/) (2025)
- [A Survey of Reinforcement Learning for Large Reasoning Models](https://mlsanity.com/paper/2509.08827/) (2025)
- [General-Reasoner: Advancing LLM Reasoning Across All Domains](https://mlsanity.com/paper/2505.14652/) (2025)
- [REASONING GYM: Reasoning Environments for Reinforcement Learning with Verifiable Rewards](https://mlsanity.com/paper/2505.24760/) (2025)
- [Does Math Reasoning Improve General LLM Capabilities? Understanding Transferability of LLM Reasoning](https://mlsanity.com/paper/2507.00432/) (2025)
- [Reinforcement Learning Optimization for Large-Scale Learning: An Efficient and User-Friendly Scaling Library](https://mlsanity.com/paper/2506.06122/) (2025)
- [A Sober Look at Progress in Language Model Reasoning: Pitfalls and Paths to Reproducibility](https://mlsanity.com/paper/2504.07086/) (2025)
- [Reinforcing General Reasoning without Verifiers](https://mlsanity.com/paper/2505.21493/) (2025)
- [Rethinking Rubric Generation for Improving LLM Judge and Reward Modeling for Open-ended Tasks](https://mlsanity.com/paper/2602.05125/) (2026)
- [One Token to Fool LLM-as-a-Judge](https://mlsanity.com/paper/2507.08794/) (2025)
- [ExGRPO: Learning to Reason from Experience](https://mlsanity.com/paper/2510.02245/) (2025)
- [Writing-Zero: Bridge the Gap Between Non-verifiable Tasks and Verifiable Rewards](https://mlsanity.com/paper/2506.00103/) (2025)
- [Consistent Paths Lead to Truth: Self-Rewarding Reinforcement Learning for LLM Reasoning](https://mlsanity.com/paper/2506.08745/) (2025)
- [s3: You Don't Need That Much Data to Train a Search Agent via RL](https://mlsanity.com/paper/2505.14146/) (2025)
- [Nemotron 3 Ultra: Open, Efficient Mixture-of-Experts Hybrid Mamba-Transformer Model for Agentic Reasoning](https://mlsanity.com/paper/2606.15007/) (2026)
- [CompassVerifier: A Unified and Robust Verifier for LLMs Evaluation and Outcome Reward](https://mlsanity.com/paper/2508.03686/) (2025)
- [Trust, But Verify: A Self-Verification Approach to Reinforcement Learning with Verifiable Rewards](https://mlsanity.com/paper/2505.13445/) (2025)
- [CapRL: Stimulating Dense Image Caption Capabilities via Reinforcement Learning](https://mlsanity.com/paper/2509.22647/) (2025)
- [Guided Self-Evolving LLMs with Minimal Human Supervision](https://mlsanity.com/paper/2512.02472/) (2025)
- [Unlocking Exploration in RLVR: Uncertainty-aware Advantage Shaping for Deeper Reasoning](https://mlsanity.com/paper/2510.10649/) (2025)
- [Nemotron-CrossThink: Scaling Self-Learning beyond Math Reasoning](https://mlsanity.com/paper/2504.13941/) (2025)
- [Reward Is Enough: LLMs Are In-Context Reinforcement Learners](https://mlsanity.com/paper/2506.06303/) (2025)
- [Energy-Based Transformers are Scalable Learners and Thinkers](https://mlsanity.com/paper/2507.02092/) (2025)
- [Beyond Trajectory-Level Attribution: Graph-Based Credit Assignment for Agentic Reinforcement Learning](https://mlsanity.com/paper/2605.26684/) (2026)
- [100 Days After DeepSeek-R1: A Survey on Replication Studies and More Directions for Reasoning Language Models](https://mlsanity.com/paper/2505.00551/) (2025)
- [Scaling Reasoning, Losing Control: Evaluating Instruction Following in Large Reasoning Models](https://mlsanity.com/paper/2505.14810/) (2025)
- [QA-LIGN: Aligning LLMs through Constitutionally Decomposed QA](https://mlsanity.com/paper/2506.08123/) (2025)
- [CAPO: Towards Enhancing LLM Reasoning through Generative Credit Assignment](https://mlsanity.com/paper/2508.02298/) (2025)
- [RLVER: Reinforcement Learning with Verifiable Emotion Rewards for Empathetic Agents](https://mlsanity.com/paper/2507.03112/) (2025)

## Abstract (arXiv)

Reinforcement learning with verifiable rewards (RLVR) has demonstrated significant success in enhancing mathematical reasoning and coding performance of large language models (LLMs), especially when structured reference answers are accessible for verification. However, its extension to broader, less structured domains remains unexplored. In this work, we investigate the effectiveness and scalability of RLVR across diverse real-world domains including medicine, chemistry, psychology, economics, and education, where structured reference answers are typically unavailable. We reveal that binary verification judgments on broad-domain tasks exhibit high consistency across various LLMs provided expert-written reference answers exist. Motivated by this finding, we utilize a generative scoring technique that yields soft, model-based reward signals to overcome limitations posed by binary verifications, especially in free-form, unstructured answer scenarios. We further demonstrate the feasibility of training cross-domain generative reward models using relatively small (7B) LLMs without the need for extensive domain-specific annotation. Through comprehensive experiments, our RLVR framework establishes clear performance gains, significantly outperforming state-of-the-art open-source aligned models such as Qwen2.5-72B and DeepSeek-R1-Distill-Qwen-32B across domains in free-form settings. Our approach notably enhances the robustness, flexibility, and scalability of RLVR, representing a substantial step towards practical reinforcement learning applications in complex, noisy-label scenarios.