Longhui Yu

Longhui Yu, Weisen Jiang, Han Shi et al. · cambridge

Large language models (LLMs) have pushed the limits of natural language understanding and exhibited excellent problem-solving ability. Despite the great success, most existing open-source LLMs (e.g., LLaMA-2) are still far away from satisfactory for solving mathematical problem due to the complex reasoning procedures. To bridge this gap, we propose MetaMath, a fine-tuned language model that specializes in mathematical reasoning. Specifically, we start by bootstrapping mathematical questions by rewriting the question from multiple perspectives without extra knowledge, which results in a new dataset called MetaMathQA. Then we fine-tune the LLaMA-2 models on MetaMathQA. Experimental results on two popular benchmarks (i.e., GSM8K and MATH) for mathematical reasoning demonstrate that MetaMath outperforms a suite of open-source LLMs by a significant margin. Our MetaMath-7B model achieves 66.4% on GSM8K and 19.4% on MATH, exceeding the state-of-the-art models of the same size by 11.5% and 8.7%. Particularly, MetaMath-70B achieves an accuracy of 82.3% on GSM8K, slightly better than GPT-3.5-Turbo. We release all the MetaMathQA dataset, the MetaMath models with different model sizes and the training code for public use.

Weiyang Liu, Longhui Yu, Adrian Weller et al. · cambridge

The neural collapse (NC) phenomenon describes an underlying geometric symmetry for deep neural networks, where both deeply learned features and classifiers converge to a simplex equiangular tight frame. It has been shown that both cross-entropy loss and mean square error can provably lead to NC. We remove NC's key assumption on the feature dimension and the number of classes, and then present a generalized neural collapse (GNC) hypothesis that effectively subsumes the original NC. Inspired by how NC characterizes the training target of neural networks, we decouple GNC into two objectives: minimal intra-class variability and maximal inter-class separability. We then use hyperspherical uniformity (which characterizes the degree of uniformity on the unit hypersphere) as a unified framework to quantify these two objectives. Finally, we propose a general objective -- hyperspherical uniformity gap (HUG), which is defined by the difference between inter-class and intra-class hyperspherical uniformity. HUG not only provably converges to GNC, but also decouples GNC into two separate objectives. Unlike cross-entropy loss that couples intra-class compactness and inter-class separability, HUG enjoys more flexibility and serves as a good alternative loss function. Empirical results show that HUG works well in terms of generalization and robustness.

Kimi Team, Tongtong Bai, Yifan Bai et al.

We introduce Kimi K2.5, an open-source multimodal agentic model designed to advance general agentic intelligence. K2.5 emphasizes the joint optimization of text and vision so that two modalities enhance each other. This includes a series of techniques such as joint text-vision pre-training, zero-vision SFT, and joint text-vision reinforcement learning. Building on this multimodal foundation, K2.5 introduces Agent Swarm, a self-directed parallel agent orchestration framework that dynamically decomposes complex tasks into heterogeneous sub-problems and executes them concurrently. Extensive evaluations show that Kimi K2.5 achieves state-of-the-art results across various domains including coding, vision, reasoning, and agentic tasks. Agent Swarm also reduces latency by up to $4.5\times$ over single-agent baselines. We release the post-trained Kimi K2.5 model checkpoint to facilitate future research and real-world applications of agentic intelligence.

Longhui Yu, Tianyang Hu, Lanqing Hong et al. · cambridge

It has been observed that neural networks perform poorly when the data or tasks are presented sequentially. Unlike humans, neural networks suffer greatly from catastrophic forgetting, making it impossible to perform life-long learning. To address this issue, memory-based continual learning has been actively studied and stands out as one of the best-performing methods. We examine memory-based continual learning and identify that large variation in the representation space is crucial for avoiding catastrophic forgetting. Motivated by this, we propose to diversify representations by using two types of perturbations: model-agnostic variation (i.e., the variation is generated without the knowledge of the learned neural network) and model-based variation (i.e., the variation is conditioned on the learned neural network). We demonstrate that enlarging representational variation serves as a general principle to improve continual learning. Finally, we perform empirical studies which demonstrate that our method, as a simple plug-and-play component, can consistently improve a number of memory-based continual learning methods by a large margin.

Weiyang Liu, Zeju Qiu, Yao Feng et al.

Large foundation models are becoming ubiquitous, but training them from scratch is prohibitively expensive. Thus, efficiently adapting these powerful models to downstream tasks is increasingly important. In this paper, we study a principled finetuning paradigm -- Orthogonal Finetuning (OFT) -- for downstream task adaptation. Despite demonstrating good generalizability, OFT still uses a fairly large number of trainable parameters due to the high dimensionality of orthogonal matrices. To address this, we start by examining OFT from an information transmission perspective, and then identify a few key desiderata that enable better parameter-efficiency. Inspired by how the Cooley-Tukey fast Fourier transform algorithm enables efficient information transmission, we propose an efficient orthogonal parameterization using butterfly structures. We apply this parameterization to OFT, creating a novel parameter-efficient finetuning method, called Orthogonal Butterfly (BOFT). By subsuming OFT as a special case, BOFT introduces a generalized orthogonal finetuning framework. Finally, we conduct an extensive empirical study of adapting large vision transformers, large language models, and text-to-image diffusion models to various downstream tasks in vision and language.

Yuqing Wang, Yizhi Wang, Longhui Yu et al.

Vector font synthesis is a challenging and ongoing problem in the fields of Computer Vision and Computer Graphics. The recently-proposed DeepVecFont achieved state-of-the-art performance by exploiting information of both the image and sequence modalities of vector fonts. However, it has limited capability for handling long sequence data and heavily relies on an image-guided outline refinement post-processing. Thus, vector glyphs synthesized by DeepVecFont still often contain some distortions and artifacts and cannot rival human-designed results. To address the above problems, this paper proposes an enhanced version of DeepVecFont mainly by making the following three novel technical contributions. First, we adopt Transformers instead of RNNs to process sequential data and design a relaxation representation for vector outlines, markedly improving the model's capability and stability of synthesizing long and complex outlines. Second, we propose to sample auxiliary points in addition to control points to precisely align the generated and target Bézier curves or lines. Finally, to alleviate error accumulation in the sequential generation process, we develop a context-based self-refinement module based on another Transformer-based decoder to remove artifacts in the initially synthesized glyphs. Both qualitative and quantitative results demonstrate that the proposed method effectively resolves those intrinsic problems of the original DeepVecFont and outperforms existing approaches in generating English and Chinese vector fonts with complicated structures and diverse styles.

Longhui Yu, Yifan Zhang, Lanqing Hong et al.

Object detection for autonomous vehicles has received increasing attention in recent years, where labeled data are often expensive while unlabeled data can be collected readily, calling for research on semi-supervised learning for this area. Existing semi-supervised object detection (SSOD) methods usually assume that the labeled and unlabeled data come from the same data distribution. In autonomous driving, however, data are usually collected from different scenarios, such as different weather conditions or different times in a day. Motivated by this, we study a novel but challenging domain inconsistent SSOD problem. It involves two kinds of distribution shifts among different domains, including (1) data distribution discrepancy, and (2) class distribution shifts, making existing SSOD methods suffer from inaccurate pseudo-labels and hurting model performance. To address this problem, we propose a novel method, namely Dual-Curriculum Teacher (DucTeacher). Specifically, DucTeacher consists of two curriculums, i.e., (1) domain evolving curriculum seeks to learn from the data progressively to handle data distribution discrepancy by estimating the similarity between domains, and (2) distribution matching curriculum seeks to estimate the class distribution for each unlabeled domain to handle class distribution shifts. In this way, DucTeacher can calibrate biased pseudo-labels and handle the domain-inconsistent SSOD problem effectively. DucTeacher shows its advantages on SODA10M, the largest public semi-supervised autonomous driving dataset, and COCO, a widely used SSOD benchmark. Experiments show that DucTeacher achieves new state-of-the-art performance on SODA10M with 2.2 mAP improvement and on COCO with 0.8 mAP improvement.

Kimi Team, Yu Zhang, Zongyu Lin et al.

We introduce Kimi Linear, a hybrid linear attention architecture that, for the first time, outperforms full attention under fair comparisons across various scenarios -- including short-context, long-context, and reinforcement learning (RL) scaling regimes. At its core lies Kimi Delta Attention (KDA), an expressive linear attention module that extends Gated DeltaNet with a finer-grained gating mechanism, enabling more effective use of limited finite-state RNN memory. Our bespoke chunkwise algorithm achieves high hardware efficiency through a specialized variant of the Diagonal-Plus-Low-Rank (DPLR) transition matrices, which substantially reduces computation compared to the general DPLR formulation while remaining more consistent with the classical delta rule. We pretrain a Kimi Linear model with 3B activated parameters and 48B total parameters, based on a layerwise hybrid of KDA and Multi-Head Latent Attention (MLA). Our experiments show that with an identical training recipe, Kimi Linear outperforms full MLA with a sizeable margin across all evaluated tasks, while reducing KV cache usage by up to 75% and achieving up to 6 times decoding throughput for a 1M context. These results demonstrate that Kimi Linear can be a drop-in replacement for full attention architectures with superior performance and efficiency, including tasks with longer input and output lengths. To support further research, we open-source the KDA kernel and vLLM implementations, and release the pre-trained and instruction-tuned model checkpoints.

Weisen Jiang, Han Shi, Longhui Yu et al.

Self-Consistency samples diverse reasoning chains with answers and chooses the final answer by majority voting. It is based on forward reasoning and cannot further improve performance by sampling more reasoning chains when saturated. To further boost performance, we introduce backward reasoning to verify candidate answers. Specifically, for mathematical tasks, we mask a number in the question and ask the LLM to answer a backward question created by a simple template, i.e., to predict the masked number when a candidate answer is provided. Instead of using forward or backward reasoning alone, we propose FOBAR to combine FOrward and BAckward Reasoning for verification. Extensive experiments on six standard mathematical data sets and three LLMs show that FOBAR achieves state-of-the-art performance. In particular, FOBAR outperforms Self-Consistency, which uses forward reasoning alone, demonstrating that combining forward and forward reasoning is better. In addition, FOBAR performs better than existing verification methods, showing the effectiveness of the simple template used in backward reasoning and the proposed combination. Extensions to non-mathematical problems are also discussed and validated empirically.

Kimi Team, Angang Du, Bohong Yin et al. · pku, tsinghua

We present Kimi-VL, an efficient open-source Mixture-of-Experts (MoE) vision-language model (VLM) that offers advanced multimodal reasoning, long-context understanding, and strong agent capabilities - all while activating only 2.8B parameters in its language decoder (Kimi-VL-A3B). Kimi-VL demonstrates strong performance across challenging domains: as a general-purpose VLM, Kimi-VL excels in multi-turn agent tasks (e.g., OSWorld), matching flagship models. Furthermore, it exhibits remarkable capabilities across diverse challenging vision language tasks, including college-level image and video comprehension, OCR, mathematical reasoning, and multi-image understanding. In comparative evaluations, it effectively competes with cutting-edge efficient VLMs such as GPT-4o-mini, Qwen2.5-VL-7B, and Gemma-3-12B-IT, while surpassing GPT-4o in several key domains. Kimi-VL also advances in processing long contexts and perceiving clearly. With a 128K extended context window, Kimi-VL can process diverse long inputs, achieving impressive scores of 64.5 on LongVideoBench and 35.1 on MMLongBench-Doc. Its native-resolution vision encoder, MoonViT, further allows it to see and understand ultra-high-resolution visual inputs, achieving 83.2 on InfoVQA and 34.5 on ScreenSpot-Pro, while maintaining lower computational cost for common tasks. Building upon Kimi-VL, we introduce an advanced long-thinking variant: Kimi-VL-Thinking-2506. Developed through long chain-of-thought (CoT) supervised fine-tuning (SFT) and reinforcement learning (RL), the latest model exhibits strong long-horizon reasoning capabilities (64.0 on MMMU, 46.3 on MMMU-Pro, 56.9 on MathVision, 80.1 on MathVista, 65.2 on VideoMMMU) while obtaining robust general abilities. Code and models are publicly accessible at https://github.com/MoonshotAI/Kimi-VL.

Haiming Wang, Mert Unsal, Xiaohan Lin et al. · cambridge

We introduce Kimina-Prover Preview, a large language model that pioneers a novel reasoning-driven exploration paradigm for formal theorem proving, as showcased in this preview release. Trained with a large-scale reinforcement learning pipeline from Qwen2.5-72B, Kimina-Prover demonstrates strong performance in Lean 4 proof generation by employing a structured reasoning pattern we term \textit{formal reasoning pattern}. This approach allows the model to emulate human problem-solving strategies in Lean, iteratively generating and refining proof steps. Kimina-Prover sets a new state-of-the-art on the miniF2F benchmark, reaching 80.7% with pass@8192. Beyond improved benchmark performance, our work yields several key insights: (1) Kimina-Prover exhibits high sample efficiency, delivering strong results even with minimal sampling (pass@1) and scaling effectively with computational budget, stemming from its unique reasoning pattern and RL training; (2) we demonstrate clear performance scaling with model size, a trend previously unobserved for neural theorem provers in formal mathematics; (3) the learned reasoning style, distinct from traditional search algorithms, shows potential to bridge the gap between formal verification and informal mathematical intuition. We open source distilled versions with 1.5B and 7B parameters of Kimina-Prover

Kimi Team, Yifan Bai, Yiping Bao et al. · tsinghua

We introduce Kimi K2, a Mixture-of-Experts (MoE) large language model with 32 billion activated parameters and 1 trillion total parameters. We propose the MuonClip optimizer, which improves upon Muon with a novel QK-clip technique to address training instability while enjoying the advanced token efficiency of Muon. Based on MuonClip, K2 was pre-trained on 15.5 trillion tokens with zero loss spike. During post-training, K2 undergoes a multi-stage post-training process, highlighted by a large-scale agentic data synthesis pipeline and a joint reinforcement learning (RL) stage, where the model improves its capabilities through interactions with real and synthetic environments. Kimi K2 achieves state-of-the-art performance among open-source non-thinking models, with strengths in agentic capabilities. Notably, K2 obtains 66.1 on Tau2-Bench, 76.5 on ACEBench (En), 65.8 on SWE-Bench Verified, and 47.3 on SWE-Bench Multilingual -- surpassing most open and closed-sourced baselines in non-thinking settings. It also exhibits strong capabilities in coding, mathematics, and reasoning tasks, with a score of 53.7 on LiveCodeBench v6, 49.5 on AIME 2025, 75.1 on GPQA-Diamond, and 27.1 on OJBench, all without extended thinking. These results position Kimi K2 as one of the most capable open-source large language models to date, particularly in software engineering and agentic tasks. We release our base and post-trained model checkpoints to facilitate future research and applications of agentic intelligence.

Kimi Team, Angang Du, Bofei Gao et al. · pku, tsinghua

Language model pretraining with next token prediction has proved effective for scaling compute but is limited to the amount of available training data. Scaling reinforcement learning (RL) unlocks a new axis for the continued improvement of artificial intelligence, with the promise that large language models (LLMs) can scale their training data by learning to explore with rewards. However, prior published work has not produced competitive results. In light of this, we report on the training practice of Kimi k1.5, our latest multi-modal LLM trained with RL, including its RL training techniques, multi-modal data recipes, and infrastructure optimization. Long context scaling and improved policy optimization methods are key ingredients of our approach, which establishes a simplistic, effective RL framework without relying on more complex techniques such as Monte Carlo tree search, value functions, and process reward models. Notably, our system achieves state-of-the-art reasoning performance across multiple benchmarks and modalities -- e.g., 77.5 on AIME, 96.2 on MATH 500, 94-th percentile on Codeforces, 74.9 on MathVista -- matching OpenAI's o1. Moreover, we present effective long2short methods that use long-CoT techniques to improve short-CoT models, yielding state-of-the-art short-CoT reasoning results -- e.g., 60.8 on AIME, 94.6 on MATH500, 47.3 on LiveCodeBench -- outperforming existing short-CoT models such as GPT-4o and Claude Sonnet 3.5 by a large margin (up to +550%).

Xin Wang, Yifan Zhang, Xiaojing Zhang et al.

Pharmaceutical patents play a vital role in biochemical industries, especially in drug discovery, providing researchers with unique early access to data, experimental results, and research insights. With the advancement of machine learning, patent analysis has evolved from manual labor to tasks assisted by automatic tools. However, there still lacks an unified agent that assists every aspect of patent analysis, from patent reading to core chemical identification. Leveraging the capabilities of Large Language Models (LLMs) to understand requests and follow instructions, we introduce the $\textbf{first}$ intelligent agent in this domain, $\texttt{PatentAgent}$, poised to advance and potentially revolutionize the landscape of pharmaceutical research. $\texttt{PatentAgent}$ comprises three key end-to-end modules -- $\textit{PA-QA}$, $\textit{PA-Img2Mol}$, and $\textit{PA-CoreId}$ -- that respectively perform (1) patent question-answering, (2) image-to-molecular-structure conversion, and (3) core chemical structure identification, addressing the essential needs of scientists and practitioners in pharmaceutical patent analysis. Each module of $\texttt{PatentAgent}$ demonstrates significant effectiveness with the updated algorithm and the synergistic design of $\texttt{PatentAgent}$ framework. $\textit{PA-Img2Mol}$ outperforms existing methods across CLEF, JPO, UOB, and USPTO patent benchmarks with an accuracy gain between 2.46% and 8.37% while $\textit{PA-CoreId}$ realizes accuracy improvement ranging from 7.15% to 7.62% on PatentNetML benchmark. Our code and dataset will be publicly available.

Zhiqing Sun, Longhui Yu, Yikang Shen et al.

Current AI alignment methodologies rely on human-provided demonstrations or judgments, and the learned capabilities of AI systems would be upper-bounded by human capabilities as a result. This raises a challenging research question: How can we keep improving the systems when their capabilities have surpassed the levels of humans? This paper answers this question in the context of tackling hard reasoning tasks (e.g., level 4-5 MATH problems) via learning from human annotations on easier tasks (e.g., level 1-3 MATH problems), which we term as easy-to-hard generalization. Our key insight is that an evaluator (reward model) trained on supervisions for easier tasks can be effectively used for scoring candidate solutions of harder tasks and hence facilitating easy-to-hard generalization over different levels of tasks. Based on this insight, we propose a novel approach to scalable alignment, which firstly trains the (process-supervised) reward models on easy problems (e.g., level 1-3), and then uses them to evaluate the performance of policy models on hard problems. We show that such easy-to-hard generalization from evaluators can enable easy-to-hard generalizations in generators either through re-ranking or reinforcement learning (RL). Notably, our process-supervised 7b RL model and 34b model (reranking@1024) achieves an accuracy of 34.0% and 52.5% on MATH500, respectively, despite only using human supervision on easy problems. Our approach suggests a promising path toward AI systems that advance beyond the frontier of human supervision.

Shoukang Hu, Kaichen Zhou, Kaiyu Li et al.

Neural Radiance Fields (NeRF) has demonstrated remarkable 3D reconstruction capabilities with dense view images. However, its performance significantly deteriorates under sparse view settings. We observe that learning the 3D consistency of pixels among different views is crucial for improving reconstruction quality in such cases. In this paper, we propose ConsistentNeRF, a method that leverages depth information to regularize both multi-view and single-view 3D consistency among pixels. Specifically, ConsistentNeRF employs depth-derived geometry information and a depth-invariant loss to concentrate on pixels that exhibit 3D correspondence and maintain consistent depth relationships. Extensive experiments on recent representative works reveal that our approach can considerably enhance model performance in sparse view conditions, achieving improvements of up to 94% in PSNR, 76% in SSIM, and 31% in LPIPS compared to the vanilla baselines across various benchmarks, including DTU, NeRF Synthetic, and LLFF.

Longhui Yu, Zhenyu Weng, Yuqing Wang et al.

Incremental learning methods can learn new classes continually by distilling knowledge from the last model (as a teacher model) to the current model (as a student model) in the sequentially learning process. However, these methods cannot work for Incremental Implicitly-Refined Classification (IIRC), an incremental learning extension where the incoming classes could have two granularity levels, a superclass label and a subclass label. This is because the previously learned superclass knowledge may be occupied by the subclass knowledge learned sequentially. To solve this problem, we propose a novel Multi-Teacher Knowledge Distillation (MTKD) strategy. To preserve the subclass knowledge, we use the last model as a general teacher to distill the previous knowledge for the student model. To preserve the superclass knowledge, we use the initial model as a superclass teacher to distill the superclass knowledge as the initial model contains abundant superclass knowledge. However, distilling knowledge from two teacher models could result in the student model making some redundant predictions. We further propose a post-processing mechanism, called as Top-k prediction restriction to reduce the redundant predictions. Our experimental results on IIRC-ImageNet120 and IIRC-CIFAR100 show that the proposed method can achieve better classification accuracy compared with existing state-of-the-art methods.

Liyuan Wang, Xingxing Zhang, Kuo Yang et al.

Continual learning needs to overcome catastrophic forgetting of the past. Memory replay of representative old training samples has been shown as an effective solution, and achieves the state-of-the-art (SOTA) performance. However, existing work is mainly built on a small memory buffer containing a few original data, which cannot fully characterize the old data distribution. In this work, we propose memory replay with data compression (MRDC) to reduce the storage cost of old training samples and thus increase their amount that can be stored in the memory buffer. Observing that the trade-off between the quality and quantity of compressed data is highly nontrivial for the efficacy of memory replay, we propose a novel method based on determinantal point processes (DPPs) to efficiently determine an appropriate compression quality for currently-arrived training samples. In this way, using a naive data compression algorithm with a properly selected quality can largely boost recent strong baselines by saving more compressed data in a limited storage space. We extensively validate this across several benchmarks of class-incremental learning and in a realistic scenario of object detection for autonomous driving.