From Trial-and-Error to Improvement: A Systematic Analysis of LLM Exploration Mechanisms in RLVR

Reinforcement learning with verifiable rewards (RLVR) has emerged as a powerful paradigm for enhancing the reasoning capabilities of large language models (LLMs). Unlike traditional RL approaches, RLVR leverages rule-based feedback to guide LLMs in generating and refining complex reasoning chains -- a process critically dependent on effective exploration strategies. While prior work has demonstrated RLVR's empirical success, the fundamental mechanisms governing LLMs' exploration behaviors remain underexplored. This technical report presents a systematic investigation of exploration capacities in RLVR, covering four main aspects: (1) exploration space shaping, where we develop quantitative metrics to characterize LLMs' capability boundaries; (2) entropy-performance exchange, analyzed across training stages, individual instances, and token-level patterns; and (3) RL performance optimization, examining methods to effectively translate exploration gains into measurable improvements. By unifying previously identified insights with new empirical evidence, this work aims to provide a foundational framework for advancing RLVR systems.

BEE-RAG: Balanced Entropy Engineering for Retrieval-Augmented Generation

With the rapid advancement of large language models (LLMs), retrieval-augmented generation (RAG) has emerged as a critical approach to supplement the inherent knowledge limitations of LLMs. However, due to the typically large volume of retrieved information, RAG tends to operate with long context lengths. From the perspective of entropy engineering, we identify unconstrained entropy growth and attention dilution due to long retrieval context as significant factors affecting RAG performance. In this paper, we propose the balanced entropy-engineered RAG (BEE-RAG) framework, which improves the adaptability of RAG systems to varying context lengths through the principle of entropy invariance. By leveraging balanced context entropy to reformulate attention dynamics, BEE-RAG separates attention sensitivity from context length, ensuring a stable entropy level. Building upon this, we introduce a zero-shot inference strategy for multi-importance estimation and a parameter-efficient adaptive fine-tuning mechanism to obtain the optimal balancing factor for different settings. Extensive experiments across multiple RAG tasks demonstrate the effectiveness of BEE-RAG.

WSM: Decay-Free Learning Rate Schedule via Checkpoint Merging for LLM Pre-training

Recent advances in learning rate (LR) scheduling have demonstrated the effectiveness of decay-free approaches that eliminate the traditional decay phase while maintaining competitive performance. Model merging techniques have emerged as particularly promising solutions in this domain. We present Warmup-Stable and Merge (WSM), a general framework that establishes a formal connection between learning rate decay and model merging. WSM provides a unified theoretical foundation for emulating various decay strategies-including cosine decay, linear decay and inverse square root decay-as principled model averaging schemes, while remaining fully compatible with diverse optimization methods. Through extensive experiments, we identify merge duration-the training window for checkpoint aggregation-as the most critical factor influencing model performance, surpassing the importance of both checkpoint interval and merge quantity. Our framework consistently outperforms the widely-adopted Warmup-Stable-Decay (WSD) approach across multiple benchmarks, achieving significant improvements of +3.5% on MATH, +2.9% on HumanEval, and +5.5% on MMLU-Pro. The performance advantages extend to supervised fine-tuning scenarios, highlighting WSM's potential for long-term model refinement.

Enhancing Cross-task Transfer of Large Language Models via Activation Steering

Large language models (LLMs) have shown impressive abilities in leveraging pretrained knowledge through prompting, but they often struggle with unseen tasks, particularly in data-scarce scenarios. While cross-task in-context learning offers a direct solution for transferring knowledge across tasks, it still faces critical challenges in terms of robustness, scalability, and efficiency. In this paper, we investigate whether cross-task transfer can be achieved via latent space steering without parameter updates or input expansion. Through an analysis of activation patterns in the latent space of LLMs, we observe that the enhanced activations induced by in-context examples have consistent patterns across different tasks. Inspired by these findings, we propose CAST, a novel Cross-task Activation Steering Transfer framework that enables effective transfer by manipulating the model's internal activation states. Our approach first selects influential and diverse samples from high-resource tasks, then utilizes their contrastive representation-enhanced activations to adapt LLMs to low-resource tasks. Extensive experiments across both cross-domain and cross-lingual transfer settings show that our method outperforms competitive baselines and demonstrates superior scalability and lower computational costs.

AVC-DPO: Aligned Video Captioning via Direct Preference Optimization

Although video multimodal large language models (video MLLMs) have achieved substantial progress in video captioning tasks, it remains challenging to adjust the focal emphasis of video captions according to human preferences. To address this limitation, we propose Aligned Video Captioning via Direct Preference Optimization (AVC-DPO), a post-training framework designed to enhance captioning capabilities in video MLLMs through preference alignment. Our approach designs enhanced prompts that specifically target temporal dynamics and spatial information-two key factors that humans care about when watching a video-thereby incorporating human-centric preferences. AVC-DPO leverages the same foundation model's caption generation responses under varied prompt conditions to conduct preference-aware training and caption alignment. Using this framework, we have achieved exceptional performance in the LOVE@CVPR'25 Workshop Track 1A: Video Detailed Captioning Challenge, achieving first place on the Video Detailed Captioning (VDC) benchmark according to the VDCSCORE evaluation metric.

Reasoning with Exploration: An Entropy Perspective

Balancing exploration and exploitation is a central goal in reinforcement learning (RL). Despite recent advances in enhancing language model (LM) reasoning, most methods lean toward exploitation, and increasingly encounter performance plateaus. In this work, we revisit entropy -- a signal of exploration in RL -- and examine its relationship to exploratory reasoning in LMs. Through empirical analysis, we uncover strong positive correlations between high-entropy regions and three types of exploratory reasoning actions: (1) pivotal tokens that determine or connect logical steps, (2) reflective actions such as self-verification and correction, and (3) rare behaviors under-explored by the base LMs. Motivated by this, we introduce a minimal modification to standard RL with only one line of code: augmenting the advantage function with an entropy-based term. Unlike traditional maximum-entropy methods which encourage exploration by promoting uncertainty, we encourage exploration by promoting longer and deeper reasoning chains. Notably, our method achieves significant gains on the Pass@K metric -- an upper-bound estimator of LM reasoning capabilities -- even when evaluated with extremely large K values, pushing the boundaries of LM reasoning.

ICPC-Eval: Probing the Frontiers of LLM Reasoning with Competitive Programming Contests

With the significant progress of large reasoning models in complex coding and reasoning tasks, existing benchmarks, like LiveCodeBench and CodeElo, are insufficient to evaluate the coding capabilities of large language models (LLMs) in real competition environments. Moreover, current evaluation metrics such as Pass@K fail to capture the reflective abilities of reasoning models. To address these challenges, we propose \textbf{ICPC-Eval}, a top-level competitive coding benchmark designed to probing the frontiers of LLM reasoning. ICPC-Eval includes 118 carefully curated problems from 11 recent ICPC contests held in various regions of the world, offering three key contributions: 1) A challenging realistic ICPC competition scenario, featuring a problem type and difficulty distribution consistent with actual contests. 2) A robust test case generation method and a corresponding local evaluation toolkit, enabling efficient and accurate local evaluation. 3) An effective test-time scaling evaluation metric, Refine@K, which allows iterative repair of solutions based on execution feedback. The results underscore the significant challenge in evaluating complex reasoning abilities: top-tier reasoning models like DeepSeek-R1 often rely on multi-turn code feedback to fully unlock their in-context reasoning potential when compared to non-reasoning counterparts. Furthermore, despite recent advancements in code generation, these models still lag behind top-performing human teams. We release the benchmark at: https://github.com/RUCAIBox/Slow_Thinking_with_LLMs

Towards Effective Code-Integrated Reasoning

In this paper, we investigate code-integrated reasoning, where models generate code when necessary and integrate feedback by executing it through a code interpreter. To acquire this capability, models must learn when and how to use external code tools effectively, which is supported by tool-augmented reinforcement learning (RL) through interactive learning. Despite its benefits, tool-augmented RL can still suffer from potential instability in the learning dynamics. In light of this challenge, we present a systematic approach to improving the training effectiveness and stability of tool-augmented RL for code-integrated reasoning. Specifically, we develop enhanced training strategies that balance exploration and stability, progressively building tool-use capabilities while improving reasoning performance. Through extensive experiments on five mainstream mathematical reasoning benchmarks, our model demonstrates significant performance improvements over multiple competitive baselines. Furthermore, we conduct an in-depth analysis of the mechanism and effect of code-integrated reasoning, revealing several key insights, such as the extension of model's capability boundaries and the simultaneous improvement of reasoning efficiency through code integration. All data and code for reproducing this work are available at: https://github.com/RUCAIBox/CIR.

Reinforced Informativeness Optimization for Long-Form Retrieval-Augmented Generation

Long-form question answering (LFQA) presents unique challenges for large language models, requiring the synthesis of coherent, paragraph-length answers. While retrieval-augmented generation (RAG) systems have emerged as a promising solution, existing research struggles with key limitations: the scarcity of high-quality training data for long-form generation, the compounding risk of hallucination in extended outputs, and the absence of reliable evaluation metrics for factual completeness. In this paper, we propose RioRAG, a novel reinforcement learning (RL) framework that advances long-form RAG through reinforced informativeness optimization. Our approach introduces two fundamental innovations to address the core challenges. First, we develop an RL training paradigm of reinforced informativeness optimization that directly optimizes informativeness and effectively addresses the slow-thinking deficit in conventional RAG systems, bypassing the need for expensive supervised data. Second, we propose a nugget-centric hierarchical reward modeling approach that enables precise assessment of long-form answers through a three-stage process: extracting the nugget from every source webpage, constructing a nugget claim checklist, and computing rewards based on factual alignment. Extensive experiments on two LFQA benchmarks LongFact and RAGChecker demonstrate the effectiveness of the proposed method. Our codes are available at https://github.com/RUCAIBox/RioRAG.

MMATH: A Multilingual Benchmark for Mathematical Reasoning

The advent of large reasoning models, such as OpenAI o1 and DeepSeek R1, has significantly advanced complex reasoning tasks. However, their capabilities in multilingual complex reasoning remain underexplored, with existing efforts largely focused on simpler tasks like MGSM. To address this gap, we introduce MMATH, a benchmark for multilingual complex reasoning spanning 374 high-quality math problems across 10 typologically diverse languages. Using MMATH, we observe that even advanced models like DeepSeek R1 exhibit substantial performance disparities across languages and suffer from a critical off-target issue-generating responses in unintended languages. To address this, we explore strategies including prompting and training, demonstrating that reasoning in English and answering in target languages can simultaneously enhance performance and preserve target-language consistency. Our findings offer new insights and practical strategies for advancing the multilingual reasoning capabilities of large language models. Our code and data could be found at https://github.com/RUCAIBox/MMATH.