Kimi K2: Open Agentic Intelligence

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.

DIFFUMA: High-Fidelity Spatio-Temporal Video Prediction via Dual-Path Mamba and Diffusion Enhancement

Spatio-temporal video prediction plays a pivotal role in critical domains, ranging from weather forecasting to industrial automation. However, in high-precision industrial scenarios such as semiconductor manufacturing, the absence of specialized benchmark datasets severely hampers research on modeling and predicting complex processes. To address this challenge, we make a twofold contribution.First, we construct and release the Chip Dicing Lane Dataset (CHDL), the first public temporal image dataset dedicated to the semiconductor wafer dicing process. Captured via an industrial-grade vision system, CHDL provides a much-needed and challenging benchmark for high-fidelity process modeling, defect detection, and digital twin development.Second, we propose DIFFUMA, an innovative dual-path prediction architecture specifically designed for such fine-grained dynamics. The model captures global long-range temporal context through a parallel Mamba module, while simultaneously leveraging a diffusion module, guided by temporal features, to restore and enhance fine-grained spatial details, effectively combating feature degradation. Experiments demonstrate that on our CHDL benchmark, DIFFUMA significantly outperforms existing methods, reducing the Mean Squared Error (MSE) by 39% and improving the Structural Similarity (SSIM) from 0.926 to a near-perfect 0.988. This superior performance also generalizes to natural phenomena datasets. Our work not only delivers a new state-of-the-art (SOTA) model but, more importantly, provides the community with an invaluable data resource to drive future research in industrial AI.

Kimina-Prover Preview: Towards Large Formal Reasoning Models with Reinforcement Learning

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-VL Technical Report

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. Developed through long chain-of-thought (CoT) supervised fine-tuning (SFT) and reinforcement learning (RL), this model exhibits strong long-horizon reasoning capabilities. It achieves scores of 61.7 on MMMU, 36.8 on MathVision, and 71.3 on MathVista while maintaining the compact 2.8B activated LLM parameters, setting a new standard for efficient multimodal thinking models. Code and models are publicly accessible at https://github.com/MoonshotAI/Kimi-VL.

Enhancing Neural Mathematical Reasoning by Abductive Combination with Symbolic Library

Mathematical reasoning recently has been shown as a hard challenge for neural systems. Abilities including expression translation, logical reasoning, and mathematics knowledge acquiring appear to be essential to overcome the challenge. This paper demonstrates that some abilities can be achieved through abductive combination with discrete systems that have been programmed with human knowledge. On a mathematical reasoning dataset, we adopt the recently proposed abductive learning framework, and propose the ABL-Sym algorithm that combines the Transformer neural models with a symbolic mathematics library. ABL-Sym shows 9.73% accuracy improvement on the interpolation tasks and 47.22% accuracy improvement on the extrapolation tasks, over the state-of-the-art approaches. Online demonstration: http://math.polixir.ai