Related papers: Learning to Reason without External Rewards

Reinforcement Learning from Verifiable Rewards (RLVR) on chain-of-thought reasoning has become a standard part of language model post-training recipes. A common assumption is that the reasoning chains trained through RLVR reliably represent…

Reinforcement learning with verifiable rewards (RLVR) for Large Reasoning Models hinges on baseline estimation for variance reduction, but existing approaches pay a heavy price: PPO requires a policy-model scale critic, while GRPO needs…

Current techniques for post-training Large Language Models (LLMs) rely either on costly human supervision or on external verifiers to boost performance on tasks such as mathematical reasoning and code generation. However, as LLMs improve…

Large Language Models (LLMs) often produce hallucinated or unverifiable content, undermining their reliability in factual domains. This work investigates Reinforcement Learning with Verifiable Rewards (RLVR) as a training paradigm that…

Recent advances of Reinforcement Learning (RL) have highlighted its potential in complex reasoning tasks, yet effective training often relies on external supervision, which limits the broader applicability. In this work, we propose a novel…

We show that reinforcement learning with verifiable rewards (RLVR) can elicit strong mathematical reasoning in certain language models even with spurious rewards that have little, no, or even negative correlation with the correct answer.…

Reinforcement Learning with Verifiable Rewards (RLVR) has emerged as an effective approach for improving the reasoning abilities of large language models (LLMs). The Group Relative Policy Optimization (GRPO) family has demonstrated strong…

Reinforcement learning with verifiable rewards (RLVR) improves language model reasoning by using rule-based rewards in verifiable domains such as mathematics and code. However, RLVR leads to limited generalization for open-ended tasks --…

Reinforcement learning with verifiable rewards (RLVR) enhances the reasoning of large language models (LLMs), but standard RLVR often depends on human-annotated answers or carefully curated reward specifications. In machine-checkable…

The successes of reinforcement learning in recent years are underpinned by the characterization of suitable reward functions. However, in settings where such rewards are non-intuitive, difficult to define, or otherwise error-prone in their…

Reinforcement learning (RL) has become a standard paradigm for refining large language models (LLMs) beyond pre-training and instruction tuning. A prominent line of work is RL with verifiable rewards (RLVR), which leverages automatically…

Unsupervised reinforcement learning with verifiable rewards (URLVR) offers a pathway to scale LLM training beyond the supervision bottleneck by deriving rewards without ground truth labels. Recent works leverage model intrinsic signals,…

The prevailing paradigm for training large reasoning models--combining Supervised Fine-Tuning (SFT) with Reinforcement Learning with Verifiable Rewards (RLVR)--is fundamentally constrained by its reliance on high-quality, human-annotated…

Reinforcement learning with verifiable rewards (RLVR) has proven effective in training large reasoning models (LRMs) by leveraging answer-verifiable signals to guide policy optimization, which, however, suffers from high annotation costs.…

Reinforcement learning (RL) has enabled machine learning models to achieve significant advances in many fields. Most recently, RL has empowered frontier language models to solve challenging math, science, and coding problems. However,…

Reinforcement Learning with Verifiable Rewards (RLVR) has recently strengthened LLM reasoning, but its focus on final answer correctness leaves a critical gap: it does not ensure the robustness of the reasoning process itself. We adopt a…

While reinforcement learning (RL) demonstrated remarkable success in enhancing the reasoning capabilities of language models, the training dynamics of RL in LLMs remain unclear. In this work, we provide an explanation of the RL training…

Reinforcement Learning with Verifiable Rewards (RLVR) is a powerful framework for improving the reasoning abilities of Large Language Models (LLMs). However, current methods such as GRPO rely only on problems where the model responses to…

Existing large language models (LLMs) face challenges of following complex instructions, especially when multiple constraints are present and organized in paralleling, chaining, and branching structures. One intuitive solution, namely…

Training Large Language Models (LLMs) to reason often relies on Reinforcement Learning (RL) with task-specific verifiers. However, many real-world reasoning-intensive tasks lack verifiers, despite offering abundant expert demonstrations…