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In this paper, we propose R$^3$: Learning Reasoning through Reverse Curriculum Reinforcement Learning (RL), a novel method that employs only outcome supervision to achieve the benefits of process supervision for large language models. The…

Reinforcement learning with verifiable rewards (RLVR) has been a main driver of recent breakthroughs in large reasoning models. Yet it remains a mystery how rewards based solely on final outcomes can help overcome the long-horizon barrier…

Transformers trained via Reinforcement Learning (RL) with outcome-based supervision can spontaneously develop the ability to generate intermediate reasoning steps (Chain-of-Thought). Yet the mechanism by which sparse rewards drive policy…

Reasoning in large language models has long been a central research focus, and recent studies employing reinforcement learning (RL) have introduced diverse methods that yield substantial performance gains with minimal or even no external…

Inspired by the success of DeepSeek-R1, we explore the potential of rule-based reinforcement learning (RL) in large reasoning models. To analyze reasoning dynamics, we use synthetic logic puzzles as training data due to their controllable…

Test-time scaling has been shown to substantially improve large language models' (LLMs) mathematical reasoning. However, for a large portion of mathematical corpora, especially theorem proving, RLVR's scalability is limited: intermediate…

The application of reinforcement learning (RL) to enhance the reasoning capabilities of Multimodal Large Language Models (MLLMs) constitutes a rapidly advancing research area. While MLLMs extend Large Language Models (LLMs) to handle…

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…

Reinforcement learning (RL) commonly relies on scalar rewards with limited ability to express temporal, conditional, or safety-critical goals, and can lead to reward hacking. Temporal logic expressible via the more general class of…

Through reinforcement learning (RL) with outcome correctness rewards, large reasoning models (LRMs) with scaled inference computation have demonstrated substantial success on complex reasoning tasks. However, the one-sided reward, focused…

As a paradigm for sequential decision making in unknown environments, reinforcement learning (RL) has received a flurry of attention in recent years. However, the explosion of model complexity in emerging applications and the presence of…

Reinforcement Learning with Verifiable Reward (RLVR) has proven effective in improving Large Language Model's (LLM) reasoning ability. However, the learning dynamics of RLVR remain underexplored. In this paper, we reveal a counterintuitive…

Large Vision-Language Models (LVLMs) have recently advanced robotic manipulation by leveraging vision for scene perception and language for instruction following. However, existing methods rely heavily on costly human-annotated training…

Large language models excel at short-horizon reasoning tasks, but performance drops as reasoning horizon lengths increase. Existing approaches to combat this rely on inference-time scaffolding or costly step-level supervision, neither of…

Large language models (LLMs) have demonstrated impressive performance on reasoning-intensive tasks, but enhancing their reasoning abilities typically relies on either reinforcement learning (RL) with verifiable signals or supervised…

Exploration in reinforcement learning is a challenging problem: in the worst case, the agent must search for high-reward states that could be hidden anywhere in the state space. Can we define a more tractable class of RL problems, where the…

While reinforcement learning with verifiable rewards (RLVR) is effective to improve the reasoning ability of large language models (LLMs), its reliance on human-annotated labels leads to the scaling up dilemma, especially for complex tasks.…

Reinforcement learning (RL) has emerged as a promising approach for eliciting reasoning chains before generating final answers. However, multimodal large language models (MLLMs) generate reasoning that lacks integration of visual…

Long chain-of-thought (CoT) significantly enhances the reasoning capabilities of large language models (LLMs). However, extensive reasoning traces lead to inefficiencies and increased time-to-first-token (TTFT). We propose a training…

Current image-based reinforcement learning (RL) algorithms typically operate on the whole image without performing object-level reasoning. This leads to inefficient goal sampling and ineffective reward functions. In this paper, we improve…