Kimi K2.5: Visual Agentic Intelligence

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.

Kimi Linear: An Expressive, Efficient Attention Architecture

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.

Native Hybrid Attention for Efficient Sequence Modeling

Transformers excel at sequence modeling but face quadratic complexity, while linear attention offers improved efficiency but often compromises recall accuracy over long contexts. In this work, we introduce Native Hybrid Attention (NHA), a novel hybrid architecture of linear and full attention that integrates both intra \& inter-layer hybridization into a unified layer design. NHA maintains long-term context in key-value slots updated by a linear RNN, and augments them with short-term tokens from a sliding window. A single \texttt{softmax attention} operation is then applied over all keys and values, enabling per-token and per-head context-dependent weighting without requiring additional fusion parameters. The inter-layer behavior is controlled through a single hyperparameter, the sliding window size, which allows smooth adjustment between purely linear and full attention while keeping all layers structurally uniform. Experimental results show that NHA surpasses Transformers and other hybrid baselines on recall-intensive and commonsense reasoning tasks. Furthermore, pretrained LLMs can be structurally hybridized with NHA, achieving competitive accuracy while delivering significant efficiency gains. Code is available at https://github.com/JusenD/NHA.

Multi-Order Wavelet Derivative Transform for Deep Time Series Forecasting

In deep time series forecasting, the Fourier Transform (FT) is extensively employed for frequency representation learning. However, it often struggles in capturing multi-scale, time-sensitive patterns. Although the Wavelet Transform (WT) can capture these patterns through frequency decomposition, its coefficients are insensitive to change points in time series, leading to suboptimal modeling. To mitigate these limitations, we introduce the multi-order Wavelet Derivative Transform (WDT) grounded in the WT, enabling the extraction of time-aware patterns spanning both the overall trend and subtle fluctuations. Compared with the standard FT and WT, which model the raw series, the WDT operates on the derivative of the series, selectively magnifying rate-of-change cues and exposing abrupt regime shifts that are particularly informative for time series modeling. Practically, we embed the WDT into a multi-branch framework named WaveTS, which decomposes the input series into multi-scale time-frequency coefficients, refines them via linear layers, and reconstructs them into the time domain via the inverse WDT. Extensive experiments on ten benchmark datasets demonstrate that WaveTS achieves state-of-the-art forecasting accuracy while retaining high computational efficiency.

Liger: Linearizing Large Language Models to Gated Recurrent Structures

Transformers with linear recurrent modeling offer linear-time training and constant-memory inference. Despite their demonstrated efficiency and performance, pretraining such non-standard architectures from scratch remains costly and risky. The linearization of large language models (LLMs) transforms pretrained standard models into linear recurrent structures, enabling more efficient deployment. However, current linearization methods typically introduce additional feature map modules that require extensive fine-tuning and overlook the gating mechanisms used in state-of-the-art linear recurrent models. To address these issues, this paper presents Liger, short for Linearizing LLMs to gated recurrent structures. Liger is a novel approach for converting pretrained LLMs into gated linear recurrent models without adding extra parameters. It repurposes the pretrained key matrix weights to construct diverse gating mechanisms, facilitating the formation of various gated recurrent structures while avoiding the need to train additional components from scratch. Using lightweight fine-tuning with Low-Rank Adaptation (LoRA), Liger restores the performance of the linearized gated recurrent models to match that of the original LLMs. Additionally, we introduce Liger Attention, an intra-layer hybrid attention mechanism, which significantly recovers 93\% of the Transformer-based LLM at 0.02\% pre-training tokens during the linearization process, achieving competitive results across multiple benchmarks, as validated on models ranging from 1B to 8B parameters. Code is available at https://github.com/OpenSparseLLMs/Linearization.

MoM: Linear Sequence Modeling with Mixture-of-Memories

Linear sequence modeling methods, such as linear attention, state space modeling, and linear RNNs, offer significant efficiency improvements by reducing the complexity of training and inference. However, these methods typically compress the entire input sequence into a single fixed-size memory state, which leads to suboptimal performance on recall-intensive downstream tasks. Drawing inspiration from neuroscience, particularly the brain's ability to maintain robust long-term memory while mitigating "memory interference", we introduce a novel architecture called Mixture-of-Memories (MoM). MoM utilizes multiple independent memory states, with a router network directing input tokens to specific memory states. This approach greatly enhances the overall memory capacity while minimizing memory interference. As a result, MoM performs exceptionally well on recall-intensive tasks, surpassing existing linear sequence modeling techniques. Despite incorporating multiple memory states, the computation of each memory state remains linear in complexity, allowing MoM to retain the linear-complexity advantage during training, while constant-complexity during inference. Our experimental results show that MoM significantly outperforms current linear sequence models on downstream language tasks, particularly recall-intensive tasks, and even achieves performance comparable to Transformer models. The code is released at https://github.com/OpenSparseLLMs/MoM and is also released as a part of https://github.com/OpenSparseLLMs/Linear-MoE.

Toward Physics-guided Time Series Embedding

In various scientific and engineering fields, the primary research areas have revolved around physics-based dynamical systems modeling and data-driven time series analysis. According to the embedding theory, dynamical systems and time series can be mutually transformed using observation functions and physical reconstruction techniques. Based on this, we propose Embedding Duality Theory, where the parameterized embedding layer essentially provides a linear estimation of the non-linear time series dynamics. This theory enables us to bypass the parameterized embedding layer and directly employ physical reconstruction techniques to acquire a data embedding representation. Utilizing physical priors results in a 10X reduction in parameters, a 3X increase in speed, and maximum performance boosts of 18% in expert, 22% in few-shot, and 53\% in zero-shot tasks without any hyper-parameter tuning. All methods are encapsulated as a plug-and-play module

TwinS: Revisiting Non-Stationarity in Multivariate Time Series Forecasting

Recently, multivariate time series forecasting tasks have garnered increasing attention due to their significant practical applications, leading to the emergence of various deep forecasting models. However, real-world time series exhibit pronounced non-stationary distribution characteristics. These characteristics are not solely limited to time-varying statistical properties highlighted by non-stationary Transformer but also encompass three key aspects: nested periodicity, absence of periodic distributions, and hysteresis among time variables. In this paper, we begin by validating this theory through wavelet analysis and propose the Transformer-based TwinS model, which consists of three modules to address the non-stationary periodic distributions: Wavelet Convolution, Period-Aware Attention, and Channel-Temporal Mixed MLP. Specifically, The Wavelet Convolution models nested periods by scaling the convolution kernel size like wavelet transform. The Period-Aware Attention guides attention computation by generating period relevance scores through a convolutional sub-network. The Channel-Temporal Mixed MLP captures the overall relationships between time series through channel-time mixing learning. TwinS achieves SOTA performance compared to mainstream TS models, with a maximum improvement in MSE of 25.8\% over PatchTST.

Time-SSM: Simplifying and Unifying State Space Models for Time Series Forecasting

State Space Models (SSMs) have emerged as a potent tool in sequence modeling tasks in recent years. These models approximate continuous systems using a set of basis functions and discretize them to handle input data, making them well-suited for modeling time series data collected at specific frequencies from continuous systems. Despite its potential, the application of SSMs in time series forecasting remains underexplored, with most existing models treating SSMs as a black box for capturing temporal or channel dependencies. To address this gap, this paper proposes a novel theoretical framework termed Dynamic Spectral Operator, offering more intuitive and general guidance on applying SSMs to time series data. Building upon our theory, we introduce Time-SSM, a novel SSM-based foundation model with only one-seventh of the parameters compared to Mamba. Various experiments validate both our theoretical framework and the superior performance of Time-SSM.

BiVRec: Bidirectional View-based Multimodal Sequential Recommendation

The integration of multimodal information into sequential recommender systems has attracted significant attention in recent research. In the initial stages of multimodal sequential recommendation models, the mainstream paradigm was ID-dominant recommendations, wherein multimodal information was fused as side information. However, due to their limitations in terms of transferability and information intrusion, another paradigm emerged, wherein multimodal features were employed directly for recommendation, enabling recommendation across datasets. Nonetheless, it overlooked user ID information, resulting in low information utilization and high training costs. To this end, we propose an innovative framework, BivRec, that jointly trains the recommendation tasks in both ID and multimodal views, leveraging their synergistic relationship to enhance recommendation performance bidirectionally. To tackle the information heterogeneity issue, we first construct structured user interest representations and then learn the synergistic relationship between them. Specifically, BivRec comprises three modules: Multi-scale Interest Embedding, comprehensively modeling user interests by expanding user interaction sequences with multi-scale patching; Intra-View Interest Decomposition, constructing highly structured interest representations using carefully designed Gaussian attention and Cluster attention; and Cross-View Interest Learning, learning the synergistic relationship between the two recommendation views through coarse-grained overall semantic similarity and fine-grained interest allocation similarity BiVRec achieves state-of-the-art performance on five datasets and showcases various practical advantages.