Tianhao Hu

Meituan LongCat Team, Anchun Gui, Bei Li et al.

We introduce LongCat-Flash-Thinking-2601, a 560-billion-parameter open-source Mixture-of-Experts (MoE) reasoning model with superior agentic reasoning capability. LongCat-Flash-Thinking-2601 achieves state-of-the-art performance among open-source models on a wide range of agentic benchmarks, including agentic search, agentic tool use, and tool-integrated reasoning. Beyond benchmark performance, the model demonstrates strong generalization to complex tool interactions and robust behavior under noisy real-world environments. Its advanced capability stems from a unified training framework that combines domain-parallel expert training with subsequent fusion, together with an end-to-end co-design of data construction, environments, algorithms, and infrastructure spanning from pre-training to post-training. In particular, the model's strong generalization capability in complex tool-use are driven by our in-depth exploration of environment scaling and principled task construction. To optimize long-tailed, skewed generation and multi-turn agentic interactions, and to enable stable training across over 10,000 environments spanning more than 20 domains, we systematically extend our asynchronous reinforcement learning framework, DORA, for stable and efficient large-scale multi-environment training. Furthermore, recognizing that real-world tasks are inherently noisy, we conduct a systematic analysis and decomposition of real-world noise patterns, and design targeted training procedures to explicitly incorporate such imperfections into the training process, resulting in improved robustness for real-world applications. To further enhance performance on complex reasoning tasks, we introduce a Heavy Thinking mode that enables effective test-time scaling by jointly expanding reasoning depth and width through intensive parallel thinking.

Pengyu Cheng, Yifan Yang, Jian Li et al.

Human preference alignment is essential to improve the interaction quality of large language models (LLMs). Existing alignment methods depend on manually annotated preference data to guide the LLM optimization directions. However, continuously updating LLMs for alignment raises a distribution gap between model-generated samples and human-annotated responses, hindering training effectiveness. To mitigate this issue, previous methods require additional preference annotation on newly generated samples to adapt to the shifted distribution, which consumes a large amount of annotation resources. Targeting more efficient human preference optimization, we propose an Adversarial Preference Optimization (APO) framework, in which the LLM and the reward model update alternatively via a min-max game. Through adversarial training, the reward model can adapt to the shifted generation distribution of the LLM without any additional annotation. With comprehensive experiments, we find the proposed adversarial training framework further enhances existing alignment baselines in terms of LLM helpfulness and harmlessness. The code is at https://github.com/Linear95/APO.

Tianhao Hu, Bangti Jin, Zhi Zhou

In this work, we develop an efficient solver based on neural networks for second-order elliptic equations with variable coefficients and singular sources. This class of problems covers general point sources, line sources and the combination of point-line sources, and has a broad range of practical applications. The proposed approach is based on decomposing the true solution into a singular part that is known analytically using the fundamental solution of the Laplace equation and a regular part that satisfies a suitable modified elliptic PDE with a smoother source, and then solving for the regular part using the deep Ritz method. A path-following strategy is suggested to select the penalty parameter for enforcing the Dirichlet boundary condition. Extensive numerical experiments in two- and multi-dimensional spaces with point sources, line sources or their combinations are presented to illustrate the efficiency of the proposed approach, and a comparative study with several existing approaches based on neural networks is also given, which shows clearly its competitiveness for the specific class of problems. In addition, we briefly discuss the error analysis of the approach.

Tianhao Hu, Bangti Jin, Zhi Zhou

The inverse problem of recovering point sources represents an important class of applied inverse problems. However, there is still a lack of neural network-based methods for point source identification, mainly due to the inherent solution singularity. In this work, we develop a novel algorithm to identify point sources, utilizing a neural network combined with a singularity enrichment technique. We employ the fundamental solution and neural networks to represent the singular and regular parts, respectively, and then minimize an empirical loss involving the intensities and locations of the unknown point sources, as well as the parameters of the neural network. Moreover, by combining the conditional stability argument of the inverse problem with the generalization error of the empirical loss, we conduct a rigorous error analysis of the algorithm. We demonstrate the effectiveness of the method with several challenging experiments.

Tianhao Hu, Guanglian Li, Fengru Wang et al.

The reliable and accurate numerical approximation of the $p$-Laplacian is particularly challenging in the extreme regimes $p \to 1^{+}$ and $p \gg 1$, where the operator becomes either highly singular or strongly degenerate, often causing severe instability in standard numerical methods. To address these difficulties, we propose a novel deep learning based framework, termed the dual variational neural network, for $p$-Laplace problems. The approach is based on a mixed formulation and an $L^q$-based Helmholtz decomposition, which decouples the original problem into two convex subproblems: a linear Poisson problem for the irrotational component and an unconstrained minimization problem over divergence-free fields for the solenoidal component. Following the decomposition, we employ two neural networks using a gradient--curl representation to approximate the flux, and further establish an error analysis of the neural approximation. The analysis relies on fundamental vector inequalities together with tools from statistical learning theory. Numerical experiments demonstrate robust convergence of the proposed method in challenging settings, including the extreme cases $p \to 1^{+}$ and $p \gg 1$, as well as the $p(x)$-Laplace equation.

Pengyu Cheng, Tianhao Hu, Han Xu et al.

We explore the potential of self-play training for large language models (LLMs) in a two-player adversarial language game called Adversarial Taboo. In this game, an attacker and a defender communicate around a target word only visible to the attacker. The attacker aims to induce the defender to speak the target word unconsciously, while the defender tries to infer the target word from the attacker's utterances. To win the game, both players must have sufficient knowledge about the target word and high-level reasoning ability to infer and express in this information-reserved conversation. Hence, we are curious about whether LLMs' reasoning ability can be further enhanced by Self-Playing this Adversarial language Game (SPAG). With this goal, we select several open-source LLMs and let each act as the attacker and play with a copy of itself as the defender on an extensive range of target words. Through reinforcement learning on the game outcomes, we observe that the LLMs' performances uniformly improve on a broad range of reasoning benchmarks. Furthermore, iteratively adopting this self-play process can continuously promote LLMs' reasoning abilities. The code is available at https://github.com/Linear95/SPAG.

Tianhao Hu, Xiangcheng Liu, Youshao Xiao et al.

Reinforcement learning (RL) has become a critical paradigm for LLM post-training, yet the rollout phase -- accounting for 50--80% of total step time -- is bottlenecked by skewed generation: long-tailed trajectories indispensable for model performance block the entire training pipeline. Asynchronous training offers a natural remedy by overlapping generation with training, but introduces a fundamental tension between efficiency and algorithmic correctness. We identify three constraints in asynchronous training to preserve convergence: intra-trajectory policy consistency, data integrity, and bounded staleness. Existing approaches fail to intrinsically address the long-tailed trajectory problem, which is further exacerbated by the imbalance characteristic of Mix-of-Experts models, or deviate from the standard RL training formulation, thereby hindering model convergence. Therefore, we propose DORA (Dynamic ORchestration for Asynchronous Rollout), which addresses this challenge through algorithm-system co-design. DORA introduces multi-version streaming rollout, a novel asynchronous paradigm that maintains multiple policy versions concurrently -- simultaneously achieving full bubble elimination without compromising algorithmic constraints. Experimental results demonstrate that our DORA system achieves substantial improvements in throughput -- up to 2--3 times higher than state-of-the-art systems on open-source benchmarks -- without compromising convergence. Furthermore, in large-scale industrial applications with tens of thousands of accelerators, DORA accelerates RL training by 2--4 times compared to synchronous training across various scenarios. The resultant open-source models, LongCat-Flash-Thinking, exhibit competitive performance on complex reasoning benchmarks, matching the capability of most advanced LLMs.

Meituan LongCat Team, Anchun Gui, Bei Li et al.

We present LongCat-Flash-Thinking, an efficient 560-billion-parameter open-source Mixture-of-Experts (MoE) reasoning model. Its advanced capabilities are cultivated through a meticulously crafted training process, beginning with long Chain-of-Thought (CoT) data cold-start and culminating in large-scale Reinforcement Learning (RL). We first employ a well-designed cold-start training strategy, which significantly enhances the reasoning potential and equips the model with specialized skills in both formal and agentic reasoning. Then, a core innovation is our domain-parallel training scheme, which decouples optimization across distinct domains (e.g., STEM, Code, Agentic) and subsequently fuses the resulting expert models into a single, nearly Pareto-optimal model. This entire process is powered by our Dynamic ORchestration for Asynchronous rollout (DORA) system, a large-scale RL framework that delivers a greater than threefold training speedup over synchronous methods on tens of thousands of accelerators. As a result, LongCat-Flash-Thinking achieves state-of-the-art performance among open-source models on a suite of complex reasoning tasks. The model exhibits exceptional efficiency in agentic reasoning, reducing average token consumption by 64.5% (from 19, 653 to 6, 965) on AIME-25, without degrading task accuracy. We release LongCat-Flash-Thinking to promote further advances in reasoning systems and agentic AI research.

Dun Zeng, Yong Dai, Pengyu Cheng et al.

Aligning large language models (LLMs) with human preferences has been recognized as the key to improving LLMs' interaction quality. However, in this pluralistic world, human preferences can be diversified due to annotators' different tastes, which hinders the effectiveness of LLM alignment methods. This paper presents the first quantitative analysis of the experimental scaling law for reward models with varying sizes, from 1.3 billion to 7 billion parameters, trained with human feedback exhibiting diverse preferences. Our analysis reveals that the impact of diversified human preferences depends on both model size and data size. Larger models with sufficient capacity mitigate the negative effects of diverse preferences, while smaller models struggle to accommodate them. To mitigate the impact of diverse preferences, we introduce a new metric, Expected Calibration Error (ECE), to evaluate RMs and show their obvious positive correlation with the alignment performance of LLMs. Furthermore, we propose a Multi-Objective Reward learning method (MORE) to enhance the calibration performance of RMs on shared preferences. Through experiments on four models and five human preference datasets, we find the calibration error can be adopted as a key metric for evaluating RMs and MORE can obtain superior alignment performance.

Zhiyuan Yao, Yi-Kai Zhang, Yuxin Chen et al.

Reinforcement Learning with Verifiable Rewards (RLVR) has emerged as a key approach for enhancing LLM reasoning. However, standard frameworks like Group Relative Policy Optimization (GRPO) typically employ a uniform rollout budget, leading to resource inefficiency. Moreover, existing adaptive methods often rely on instance-level metrics, such as task pass rates, failing to capture the model's dynamic learning state. To address these limitations, we propose CoBA-RL, a reinforcement learning algorithm designed to adaptively allocate rollout budgets based on the model's evolving capability. Specifically, CoBA-RL utilizes a Capability-Oriented Value function to map tasks to their potential training gains and employs a heap-based greedy strategy to efficiently self-calibrate the distribution of computational resources to samples with high training value. Extensive experiments demonstrate that our approach effectively orchestrates the trade-off between exploration and exploitation, delivering consistent generalization improvements across multiple challenging benchmarks. These findings underscore that quantifying sample training value and optimizing budget allocation are pivotal for advancing LLM post-training efficiency.

Tianhao Hu, Bangti Jin, Fengru Wang

In this work, we present a novel iterative deep Ritz method (IDRM) for solving a general class of elliptic problems. It is inspired by the iterative procedure for minimizing the loss during the training of the neural network, but at each step encodes the geometry of the underlying function space and incorporates a convex penalty to enhance the performance of the algorithm. The algorithm is applicable to elliptic problems involving a monotone operator (not necessarily of variational form) and does not impose any stringent regularity assumption on the solution. It improves several existing neural PDE solvers, e.g., physics informed neural network and deep Ritz method, in terms of the accuracy for the concerned class of elliptic problems. Further, we establish a convergence rate for the method using tools from geometry of Banach spaces and theory of monotone operators, and also analyze the learning error. To illustrate the effectiveness of the method, we present several challenging examples, including a comparative study with existing techniques.