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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…

Recent extensive research has demonstrated that the enhanced reasoning capabilities acquired by models through Reinforcement Learning with Verifiable Rewards (RLVR) are primarily concentrated within the rank-1 components. Predicated on this…

The advancement of Large Reasoning Models (LRMs) has catalyzed a paradigm shift from reactive ``fast thinking'' text generation to systematic, step-by-step ``slow thinking'' reasoning, unlocking state-of-the-art performance in complex…

We show that reinforcement learning with verifiable reward using one training example (1-shot RLVR) is effective in incentivizing the math reasoning capabilities of large language models (LLMs). Applying RLVR to the base model…

Recently, Reinforcement Learning with Verifiable Rewards (RLVR) has emerged as an effective approach to incentivizing reasoning capability in Large Multimodal Models (LMMs), while the underlying mechanisms behind this post-training paradigm…

The functionality of Large Language Model (LLM) agents is primarily determined by two capabilities: action planning and answer summarization. The former, action planning, is the core capability that dictates an agent's performance. However,…

Decoding strategies play a central role in shaping the reasoning ability of large language models (LLMs). Traditional methods such as greedy decoding and beam search often suffer from error propagation, while sampling-based approaches…

Reinforcement Learning with Verifiable Rewards (RLVR) improves the reasoning ability of Large Language Models (LLMs), but sparse outcome rewards make token-level credit assignment difficult. We study token-level credit as a…

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…

Reinforcement learning (RL) has substantially improved the ability of large language model (LLM) agents to interact with environments and solve multi-turn tasks. However, effective agentic RL remains challenging: sparse outcome-only rewards…

Reinforcement learning with verifiable rewards (RLVR) has driven significant performance gains in reasoning-oriented large language models (LLMs), yet its internal training dynamics remain largely a black box. In this work, we perform a…

The ongoing debate on whether reinforcement learning with verifiable rewards (RLVR) expands or shrinks the reasoning capabilities of large language models (LLMs) remains unresolved. Some studies contend that RLVR mainly improves sampling…

Reinforcement learning with verifiable rewards (RLVR) enables large language models to acquire slow, multi-step reasoning from sparse final-answer signals. We provide a statistical-physics picture of this emergence. We show that an…

Human guidance in reinforcement learning (RL) is often impractical for large-scale applications due to high costs and time constraints. Large Language Models (LLMs) offer a promising alternative to mitigate RL sample inefficiency and…

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 with Verifiable Rewards (RLVR) effectively trains reasoning models that rely on abundant perfect labels, but its vulnerability to unavoidable noisy labels due to expert scarcity remains critically underexplored. In…

Extending Reinforcement Learning with Verifiable Rewards (RLVR) to multimodal large language models (MLLMs) faces a fundamental challenge: their responses inherently interleave perception-related tokens, which ground visual content, with…

The development of autonomous agents for complex, long-horizon tasks is a central goal in AI. However, dominant training paradigms face a critical limitation: reinforcement learning (RL) methods that optimize solely for final task success…

Reinforcement Learning with Verifiable Rewards (RLVR) has emerged as a powerful paradigm for enhancing the reasoning capabilities of LLMs. Existing research has predominantly concentrated on isolated reasoning domains such as mathematical…

Large language models have achieved significant reasoning improvements through reinforcement learning with verifiable rewards (RLVR). Yet as model capabilities grow, constructing high-quality reward signals becomes increasingly difficult,…