Songyang Gao

Zijian Wu, Lingkai Kong, Wenwei Zhang et al.

Large language models (LLMs) have achieved significant progress in solving complex reasoning tasks by Reinforcement Learning with Verifiable Rewards (RLVR). This advancement is also inseparable from the oversight automated by reliable verifiers. However, current outcome-based verifiers (OVs) are unable to inspect the unreliable intermediate steps in the long reasoning chains of thought (CoTs). Meanwhile, current process-based verifiers (PVs) have difficulties in reliably detecting errors in the complex long CoTs, limited by the scarcity of high-quality annotations due to the prohibitive costs of human annotations. Therefore, we propose the Outcome-based Process Verifier (OPV), which verifies the rationale process of summarized outcomes from long CoTs to achieve both accurate and efficient verification and enable large-scale annotation. To empower the proposed verifier, we adopt an iterative active learning framework with expert annotations to progressively improve the verification capability of OPV with fewer annotation costs. Specifically, in each iteration, the most uncertain cases of the current best OPV are annotated and then subsequently used to train a new OPV through Rejection Fine-Tuning (RFT) and RLVR for the next round. Extensive experiments demonstrate OPV's superior performance and broad applicability. It achieves new state-of-the-art results on our held-out OPV-Bench, outperforming much larger open-source models such as Qwen3-Max-Preview with an F1 score of 83.1 compared to 76.3. Furthermore, OPV effectively detects false positives within synthetic dataset, closely align with expert assessment. When collaborating with policy models, OPV consistently yields performance gains, e.g., raising the accuracy of DeepSeek-R1-Distill-Qwen-32B from 55.2% to 73.3% on AIME2025 as the compute budget scales.

Chengqi Lyu, Songyang Gao, Yuzhe Gu et al.

Reasoning abilities, especially those for solving complex math problems, are crucial components of general intelligence. Recent advances by proprietary companies, such as o-series models of OpenAI, have made remarkable progress on reasoning tasks. However, the complete technical details remain unrevealed, and the techniques that are believed certainly to be adopted are only reinforcement learning (RL) and the long chain of thoughts. This paper proposes a new RL framework, termed OREAL, to pursue the performance limit that can be achieved through \textbf{O}utcome \textbf{RE}w\textbf{A}rd-based reinforcement \textbf{L}earning for mathematical reasoning tasks, where only binary outcome rewards are easily accessible. We theoretically prove that behavior cloning on positive trajectories from best-of-N (BoN) sampling is sufficient to learn the KL-regularized optimal policy in binary feedback environments. This formulation further implies that the rewards of negative samples should be reshaped to ensure the gradient consistency between positive and negative samples. To alleviate the long-existing difficulties brought by sparse rewards in RL, which are even exacerbated by the partial correctness of the long chain of thought for reasoning tasks, we further apply a token-level reward model to sample important tokens in reasoning trajectories for learning. With OREAL, for the first time, a 7B model can obtain 94.0 pass@1 accuracy on MATH-500 through RL, being on par with 32B models. OREAL-32B also surpasses previous 32B models trained by distillation with 95.0 pass@1 accuracy on MATH-500. Our investigation also indicates the importance of initial policy models and training queries for RL. Code, models, and data will be released to benefit future research\footnote{https://github.com/InternLM/OREAL}.

Chen Yang, Junzhuo Li, Xinyao Niu et al.

Uncovering early-stage metrics that reflect final model performance is one core principle for large-scale pretraining. The existing scaling law demonstrates the power-law correlation between pretraining loss and training flops, which serves as an important indicator of the current training state for large language models. However, this principle only focuses on the model's compression properties on the training data, resulting in an inconsistency with the ability improvements on the downstream tasks. Some follow-up works attempted to extend the scaling-law to more complex metrics (such as hyperparameters), but still lacked a comprehensive analysis of the dynamic differences among various capabilities during pretraining. To address the aforementioned limitations, this paper undertakes a comprehensive comparison of model capabilities at various pretraining intermediate checkpoints. Through this analysis, we confirm that specific downstream metrics exhibit similar training dynamics across models of different sizes, up to 67 billion parameters. In addition to our core findings, we've reproduced Amber and OpenLLaMA, releasing their intermediate checkpoints. This initiative offers valuable resources to the research community and facilitates the verification and exploration of LLM pretraining by open-source researchers. Besides, we provide empirical summaries, including performance comparisons of different models and capabilities, and tuition of key metrics for different training phases. Based on these findings, we provide a more user-friendly strategy for evaluating the optimization state, offering guidance for establishing a stable pretraining process.

Junhao Shen, Haiteng Zhao, Yuzhe Gu et al.

Enhancing large vision-language models (LVLMs) with visual slow-thinking reasoning is crucial for solving complex multimodal tasks. However, since LVLMs are mainly trained with vision-language alignment, it is difficult to adopt on-policy reinforcement learning (RL) to develop the slow thinking ability because the rollout space is restricted by its initial abilities. Off-policy RL offers a way to go beyond the current policy, but directly distilling trajectories from external models may cause visual hallucinations due to mismatched visual perception abilities across models. To address these issues, this paper proposes SOPHIA, a simple and scalable Semi-Off-Policy RL for vision-language slow-tHInking reAsoning. SOPHIA builds a semi-off-policy behavior model by combining on-policy visual understanding from a trainable LVLM with off-policy slow-thinking reasoning from a language model, assigns outcome-based rewards to reasoning, and propagates visual rewards backward. Then LVLM learns slow-thinking reasoning ability from the obtained reasoning trajectories using propagated rewards via off-policy RL algorithms. Extensive experiments with InternVL2.5 and InternVL3.0 with 8B and 38B sizes show the effectiveness of SOPHIA. Notably, SOPHIA improves InternVL3.0-38B by 8.50% in average, reaching state-of-the-art performance among open-source LVLMs on multiple multimodal reasoning benchmarks, and even outperforms some closed-source models (e.g., GPT-4.1) on the challenging MathVision and OlympiadBench, achieving 49.08% and 49.95% pass@1 accuracy, respectively. Analysis shows SOPHIA outperforms supervised fine-tuning and direct on-policy RL methods, offering a better policy initialization for further on-policy training.

Xiaomin Yu, Pengxiang Ding, Wenjie Zhang et al.

Training vision-language models (VLMs) typically requires large-scale, high-quality image-text pairs, but collecting or synthesizing such data is costly. In contrast, text data is abundant and inexpensive, prompting the question: can high-quality multimodal training data be synthesized purely from text? To tackle this, we propose a cross-integrated three-stage multimodal data synthesis framework, which generates two datasets: Unicorn-1.2M and Unicorn-471K-Instruction. In Stage 1: Diverse Caption Data Synthesis, we construct 1.2M semantically diverse high-quality captions by expanding sparse caption seeds using large language models (LLMs). In Stage 2: Instruction-Tuning Data Generation, we further process 471K captions into multi-turn instruction-tuning tasks to support complex reasoning. Finally, in Stage 3: Modality Representation Transfer, these textual captions representations are transformed into visual representations, resulting in diverse synthetic image representations. This three-stage process enables us to construct Unicorn-1.2M for pretraining and Unicorn-471K-Instruction for instruction-tuning, without relying on real images. By eliminating the dependency on real images while maintaining data quality and diversity, our framework offers a cost-effective and scalable solution for VLMs training. Code is available at https://github.com/Yu-xm/Unicorn.git.

Junnan Liu, Hongwei Liu, Linchen Xiao et al.

The rapid advancement of large language models (LLMs) has shown remarkable progress in complex reasoning tasks. However, a significant disparity exists between benchmark performances and real-world applications. We attribute this gap primarily to current evaluation protocols and metrics, which inadequately capture the full spectrum of LLM capabilities, especially in complex reasoning tasks where both accuracy and consistency are essential. In this paper, we introduce G-Pass@$k$, a novel evaluation metric that continuously assesses model performance across multiple sampling attempts, quantifying both the model's performance potential and its stability. Through extensive experiments on various public and newly constructed benchmarks, we employ G-Pass@$k$ in conjunction with state-of-the-art large language models to provide comprehensive insights into their potential capabilities and operational consistency. Our findings reveal a significant opportunity to enhance the realistic reasoning abilities of LLMs, underscoring the necessity for more robust evaluation metrics.

Haiteng Zhao, Junhao Shen, Yiming Zhang et al.

Large language model (LLM) agents exhibit strong mathematical problem-solving abilities and can even solve International Mathematical Olympiad (IMO) level problems with the assistance of formal proof systems. However, due to weak heuristics for auxiliary constructions, AI for geometry problem solving remains dominated by expert models such as AlphaGeometry 2, which rely heavily on large-scale data synthesis and search for both training and evaluation. In this work, we make the first attempt to build a medalist-level LLM agent for geometry and present InternGeometry. InternGeometry overcomes the heuristic limitations in geometry by iteratively proposing propositions and auxiliary constructions, verifying them with a symbolic engine, and reflecting on the engine's feedback to guide subsequent proposals. A dynamic memory mechanism enables InternGeometry to conduct more than two hundred interactions with the symbolic engine per problem. To further accelerate learning, we introduce Complexity-Boosting Reinforcement Learning (CBRL), which gradually increases the complexity of synthesized problems across training stages. Built on InternThinker-32B, InternGeometry solves 44 of 50 IMO geometry problems (2000-2024), exceeding the average gold medalist score (40.9), using only 13K training examples, just 0.004% of the data used by AlphaGeometry 2, demonstrating the potential of LLM agents on expert-level geometry tasks. InternGeometry can also propose novel auxiliary constructions for IMO problems that do not appear in human solutions.

Songyang Gao, Yuzhe Gu, Zijian Wu et al.

Large Reasoning Models (LRMs) have expanded the mathematical reasoning frontier through Chain-of-Thought (CoT) techniques and Reinforcement Learning with Verifiable Rewards (RLVR), capable of solving AIME-level problems. However, the performance of LRMs is heavily dependent on the extended reasoning context length. For solving ultra-hard problems like those in the International Mathematical Olympiad (IMO), the required reasoning complexity surpasses the space that an LRM can explore in a single round. Previous works attempt to extend the reasoning context of LRMs but remain prompt-based and built upon proprietary models, lacking systematic structures and training pipelines. Therefore, this paper introduces Intern-S1-MO, a long-horizon math agent that conducts multi-round hierarchical reasoning, composed of an LRM-based multi-agent system including reasoning, summary, and verification. By maintaining a compact memory in the form of lemmas, Intern-S1-MO can more freely explore the lemma-rich reasoning spaces in multiple reasoning stages, thereby breaking through the context constraints for IMO-level math problems. Furthermore, we propose OREAL-H, an RL framework for training the LRM using the online explored trajectories to simultaneously bootstrap the reasoning ability of LRM and elevate the overall performance of Intern-S1-MO. Experiments show that Intern-S1-MO can obtain 26 out of 35 points on the non-geometry problems of IMO2025, matching the performance of silver medalists. It also surpasses the current advanced LRMs on inference benchmarks such as HMMT2025, AIME2025, and CNMO2025. In addition, our agent officially participates in CMO2025 and achieves a score of 102/126 under the judgment of human experts, reaching the gold medal level.

Zhouqi Hua, Wenwei Zhang, Chengqi Lyu et al.

Length generalization, the ability to solve problems of longer sequences than those observed during training, poses a core challenge of Transformer-based large language models (LLM). Although existing studies have predominantly focused on data-driven approaches for arithmetic operations and symbolic manipulation tasks, these approaches tend to be task-specific with limited overall performance. To pursue a more general solution, this paper focuses on a broader case of reasoning problems that are computable, i.e., problems that algorithms can solve, thus can be solved by the Turing Machine. From this perspective, this paper proposes Turing MAchine Imitation Learning (TAIL) to improve the length generalization ability of LLMs. TAIL synthesizes chain-of-thoughts (CoT) data that imitate the execution process of a Turing Machine by computer programs, which linearly expands the reasoning steps into atomic states to alleviate shortcut learning and explicit memory fetch mechanism to reduce the difficulties of dynamic and long-range data access in elementary operations. To validate the reliability and universality of TAIL, we construct a challenging synthetic dataset covering 8 classes of algorithms and 18 tasks. Without bells and whistles, TAIL significantly improves the length generalization ability as well as the performance of Qwen2.5-7B on various tasks using only synthetic data, surpassing previous methods and DeepSeek-R1. The experimental results reveal that the key concepts in the Turing Machine, instead of the thinking styles, are indispensable for TAIL for length generalization, through which the model exhibits read-and-write behaviors consistent with the properties of the Turing Machine in their attention layers. This work provides a promising direction for future research in the learning of LLM reasoning from synthetic data.