Recently, the Muon optimizer based on matrix orthogonalization has demonstrated strong results in training small-scale language models, but the scalability to larger models has not been proven. We identify two crucial techniques for scaling up Muon: (1) adding weight decay and (2) carefully adjusting the per-parameter update scale. These techniques allow Muon to work out-of-the-box on large-scale training without the need of hyper-parameter tuning. Scaling law experiments indicate that Muon achieves $\sim\!2\times$ computational efficiency compared to AdamW with compute optimal training. Based on these improvements, we introduce Moonlight, a 3B/16B-parameter Mixture-of-Expert (MoE) model trained with 5.7T tokens using Muon. Our model improves the current Pareto frontier, achieving better performance with much fewer training FLOPs compared to prior models. We open-source our distributed Muon implementation that is memory optimal and communication efficient. We also release the pretrained, instruction-tuned, and intermediate checkpoints to support future research.

Scaling the effective context length is essential for advancing large language models (LLMs) toward artificial general intelligence (AGI). However, the quadratic increase in computational complexity inherent in traditional attention mechanisms presents a prohibitive overhead. Existing approaches either impose strongly biased structures, such as sink or window attention which are task-specific, or radically modify the attention mechanism into linear approximations, whose performance in complex reasoning tasks remains inadequately explored. In this work, we propose a solution that adheres to the ``less structure'' principle, allowing the model to determine where to attend autonomously, rather than introducing predefined biases. We introduce Mixture of Block Attention (MoBA), an innovative approach that applies the principles of Mixture of Experts (MoE) to the attention mechanism. This novel architecture demonstrates superior performance on long-context tasks while offering a key advantage: the ability to seamlessly transition between full and sparse attention, enhancing efficiency without the risk of compromising performance. MoBA has already been deployed to support Kimi's long-context requests and demonstrates significant advancements in efficient attention computation for LLMs. Our code is available at https://github.com/MoonshotAI/MoBA.

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%).

This paper explores image modeling from the frequency space and introduces DCTdiff, an end-to-end diffusion generative paradigm that efficiently models images in the discrete cosine transform (DCT) space. We investigate the design space of DCTdiff and reveal the key design factors. Experiments on different frameworks (UViT, DiT), generation tasks, and various diffusion samplers demonstrate that DCTdiff outperforms pixel-based diffusion models regarding generative quality and training efficiency. Remarkably, DCTdiff can seamlessly scale up to high-resolution generation without using the latent diffusion paradigm. Finally, we illustrate several intriguing properties of DCT image modeling. For example, we provide a theoretical proof of why `image diffusion can be seen as spectral autoregression', bridging the gap between diffusion and autoregressive models. The effectiveness of DCTdiff and the introduced properties suggest a promising direction for image modeling in the frequency space. The code is at \url{https://github.com/forever208/DCTdiff}.

Large Language Models (LLMs) have shown promising in-context learning abilities. However, conventional In-Context Learning (ICL) approaches are often impeded by length limitations of transformer architecture, which pose challenges when attempting to effectively integrate supervision from a substantial number of demonstration examples. In this paper, we introduce a novel framework, called Naive Bayes-based Context Extension (NBCE), to enable existing LLMs to perform ICL with an increased number of demonstrations by significantly expanding their context size. Importantly, this expansion does not require fine-tuning or dependence on particular model architectures, all the while preserving linear efficiency. NBCE initially splits the context into equal-sized windows fitting the target LLM's maximum length. Then, it introduces a voting mechanism to select the most relevant window, regarded as the posterior context. Finally, it employs Bayes' theorem to generate the test task. Our experimental results demonstrate that NBCE substantially enhances performance, particularly as the number of demonstration examples increases, consistently outperforming alternative methods. The NBCE code will be made publicly accessible. The code NBCE is available at: https://github.com/amurtadha/NBCE-master

Diffusion models have demonstrated impressive generative capabilities, but their \textit{exposure bias} problem, described as the input mismatch between training and sampling, lacks in-depth exploration. In this paper, we systematically investigate the exposure bias problem in diffusion models by first analytically modelling the sampling distribution, based on which we then attribute the prediction error at each sampling step as the root cause of the exposure bias issue. Furthermore, we discuss potential solutions to this issue and propose an intuitive metric for it. Along with the elucidation of exposure bias, we propose a simple, yet effective, training-free method called Epsilon Scaling to alleviate the exposure bias. We show that Epsilon Scaling explicitly moves the sampling trajectory closer to the vector field learned in the training phase by scaling down the network output (Epsilon), mitigating the input mismatch between training and sampling. Experiments on various diffusion frameworks (ADM, DDPM/DDIM, EDM, LDM), unconditional and conditional settings, and deterministic vs. stochastic sampling verify the effectiveness of our method. Remarkably, our ADM-ES, as a SOTA stochastic sampler, obtains 2.17 FID on CIFAR-10 under 100-step unconditional generation. The code is available at \url{https://github.com/forever208/ADM-ES} and \url{https://github.com/forever208/EDM-ES}.

Semi-supervised text classification-based paradigms (SSTC) typically employ the spirit of self-training. The key idea is to train a deep classifier on limited labeled texts and then iteratively predict the unlabeled texts as their pseudo-labels for further training. However, the performance is largely affected by the accuracy of pseudo-labels, which may not be significant in real-world scenarios. This paper presents a Rank-aware Negative Training (RNT) framework to address SSTC in learning with noisy label manner. To alleviate the noisy information, we adapt a reasoning with uncertainty-based approach to rank the unlabeled texts based on the evidential support received from the labeled texts. Moreover, we propose the use of negative training to train RNT based on the concept that ``the input instance does not belong to the complementary label''. A complementary label is randomly selected from all labels except the label on-target. Intuitively, the probability of a true label serving as a complementary label is low and thus provides less noisy information during the training, resulting in better performance on the test data. Finally, we evaluate the proposed solution on various text classification benchmark datasets. Our extensive experiments show that it consistently overcomes the state-of-the-art alternatives in most scenarios and achieves competitive performance in the others. The code of RNT is publicly available at:https://github.com/amurtadha/RNT.

Copy mechanisms explicitly obtain unchanged tokens from the source (input) sequence to generate the target (output) sequence under the neural seq2seq framework. However, most of the existing copy mechanisms only consider single word copying from the source sentences, which results in losing essential tokens while copying long spans. In this work, we propose a plug-and-play architecture, namely BioCopy, to alleviate the problem aforementioned. Specifically, in the training stage, we construct a BIO tag for each token and train the original model with BIO tags jointly. In the inference stage, the model will firstly predict the BIO tag at each time step, then conduct different mask strategies based on the predicted BIO label to diminish the scope of the probability distributions over the vocabulary list. Experimental results on two separate generative tasks show that they all outperform the baseline models by adding our BioCopy to the original model structure.

Position encoding in transformer architecture provides supervision for dependency modeling between elements at different positions in the sequence. We investigate various methods to encode positional information in transformer-based language models and propose a novel implementation named Rotary Position Embedding(RoPE). The proposed RoPE encodes absolute positional information with rotation matrix and naturally incorporates explicit relative position dependency in self-attention formulation. Notably, RoPE comes with valuable properties such as flexibility of being expand to any sequence lengths, decaying inter-token dependency with increasing relative distances, and capability of equipping the linear self-attention with relative position encoding. As a result, the enhanced transformer with rotary position embedding, or RoFormer, achieves superior performance in tasks with long texts. We release the theoretical analysis along with some preliminary experiment results on Chinese data. The undergoing experiment for English benchmark will soon be updated.

Pre-training models such as BERT have achieved great success in many natural language processing tasks. However, how to obtain better sentence representation through these pre-training models is still worthy to exploit. Previous work has shown that the anisotropy problem is an critical bottleneck for BERT-based sentence representation which hinders the model to fully utilize the underlying semantic features. Therefore, some attempts of boosting the isotropy of sentence distribution, such as flow-based model, have been applied to sentence representations and achieved some improvement. In this paper, we find that the whitening operation in traditional machine learning can similarly enhance the isotropy of sentence representations and achieve competitive results. Furthermore, the whitening technique is also capable of reducing the dimensionality of the sentence representation. Our experimental results show that it can not only achieve promising performance but also significantly reduce the storage cost and accelerate the model retrieval speed.