Muon+: Towards Better Muon via One Additional Normalization Step

The Muon optimizer has demonstrated promising performance in pre-training large language models through gradient (or momentum) orthogonalization. In this work, we propose a simple yet effective enhancement to Muon, namely Muon+, which introduces an additional normalization step after orthogonalization. We demonstrate the effectiveness of Muon+ through extensive pre-training experiments across a wide range of model scales and architectures. Our evaluation includes GPT-style models ranging from 130M to 774M parameters and LLaMA-style models ranging from 60M to 1B parameters. We comprehensively evaluate the effectiveness of Muon+ in the compute-optimal training regime and further extend the token-to-parameter (T2P) ratio to an industrial level of $\approx 200$. Experimental results show that Muon+ provides a consistent boost on training and validation perplexity over Muon. We provide our code here: https://github.com/K1seki221/MuonPlus.

Decoupling Vision and Language: Codebook Anchored Visual Adaptation

Large Vision-Language Models (LVLMs) use their vision encoders to translate images into representations for downstream reasoning, but the encoders often underperform in domain-specific visual tasks such as medical image diagnosis or fine-grained classification, where representation errors can cascade through the language model, leading to incorrect responses. Existing adaptation methods modify the continuous feature interface between encoder and language model through projector tuning or other parameter-efficient updates, which still couples the two components and requires re-alignment whenever the encoder changes. We introduce CRAFT (Codebook RegulAted Fine-Tuning), a lightweight method that fine-tunes the encoder using a discrete codebook that anchors visual representations to a stable token space, achieving domain adaptation without modifying other parts of the model. This decoupled design allows the adapted encoder to seamlessly boost the performance of LVLMs with different language architectures, as long as they share the same codebook. Empirically, CRAFT achieves an average gain of 13.51% across 10 domain-specific benchmarks such as VQARAD and PlantVillage, while preserving the LLM's linguistic capabilities and outperforming peer methods that operate on continuous tokens.

Powering Up Zeroth-Order Training via Subspace Gradient Orthogonalization

Zeroth-order (ZO) optimization provides a gradient-free alternative to first-order (FO) methods by estimating gradients via finite differences of function evaluations, and has recently emerged as a memory-efficient paradigm for fine-tuning large-scale models by avoiding backpropagation. However, ZO optimization has a fundamental tension between accuracy and query efficiency. In this work, we show that ZO optimization can be substantially improved by unifying two complementary principles: (i) a projection-based subspace view that reduces gradient estimation variance by exploiting the intrinsic low-rank structure of model updates, and (ii) Muon-style spectral optimization that applies gradient orthogonalization to extract informative spectral structure from noisy ZO gradients. These findings form a unified framework of subspace gradient orthogonalization, which we instantiate in a new method, ZO-Muon, admitting a natural interpretation as a low-rank Muon optimizer in the ZO setting. Extensive experiments on large language models (LLMs) and vision transformers (ViTs) demonstrate that ZO-Muon significantly accelerates convergence and achieves a win-win improvement in accuracy and query/runtime efficiency. Notably, compared to the popular MeZO baseline, ZO-Muon requires only 24.7% of the queries to reach the same SST-2 performance for LLM fine-tuning, and improves accuracy by 25.1% on ViT-B fine-tuning on CIFAR-100.

MirrorLA: Reflecting Feature Map for Vision Linear Attention

Linear attention significantly reduces the computational complexity of Transformers from quadratic to linear, yet it consistently lags behind softmax-based attention in performance. We identify the root cause of this degradation as the non-negativity constraint imposed on kernel feature maps: standard projections like ReLU act as "passive truncation" operators, indiscriminately discarding semantic information residing in the negative domain. We propose MirrorLA, a geometric framework that substitutes passive truncation with active reorientation. By leveraging learnable Householder reflections, MirrorLA rotates the feature geometry into the non-negative orthant to maximize information retention. Our approach restores representational density through a cohesive, multi-scale design: it first optimizes local discriminability via block-wise isometries, stabilizes long-context dynamics using variance-aware modulation to diversify activations, and finally, integrates dispersed subspaces via cross-head reflections to induce global covariance mixing. MirrorLA achieves state-of-the-art performance across standard benchmarks, demonstrating that strictly linear efficiency can be achieved without compromising representational fidelity.

Causal Graph Spatial-Temporal Autoencoder for Reliable and Interpretable Process Monitoring

To improve the reliability and interpretability of industrial process monitoring, this article proposes a Causal Graph Spatial-Temporal Autoencoder (CGSTAE). The network architecture of CGSTAE combines two components: a correlation graph structure learning module based on spatial self-attention mechanism (SSAM) and a spatial-temporal encoder-decoder module utilizing graph convolutional long-short term memory (GCLSTM). The SSAM learns correlation graphs by capturing dynamic relationships between variables, while a novel three-step causal graph structure learning algorithm is introduced to derive a causal graph from these correlation graphs. The algorithm leverages a reverse perspective of causal invariance principle to uncover the invariant causal graph from varying correlations. The spatial-temporal encoder-decoder, built with GCLSTM units, reconstructs time-series process data within a sequence-to-sequence framework. The proposed CGSTAE enables effective process monitoring and fault detection through two statistics in the feature space and residual space. Finally, we validate the effectiveness of CGSTAE in process monitoring through the Tennessee Eastman process and a real-world air separation process.

Interpreting and Controlling LLM Reasoning through Integrated Policy Gradient

Large language models (LLMs) demonstrate strong reasoning abilities in solving complex real-world problems. Yet, the internal mechanisms driving these complex reasoning behaviors remain opaque. Existing interpretability approaches targeting reasoning either identify components (e.g., neurons) correlated with special textual patterns, or rely on human-annotated contrastive pairs to derive control vectors. Consequently, current methods struggle to precisely localize complex reasoning mechanisms or capture sequential influence from model internal workings to the reasoning outputs. In this paper, built on outcome-oriented and sequential-influence-aware principles, we focus on identifying components that have sequential contribution to reasoning behavior where outcomes are cumulated by long-range effects. We propose Integrated Policy Gradient (IPG), a novel framework that attributes reasoning behaviors to model's inner components by propagating compound outcome-based signals such as post reasoning accuracy backward through model inference trajectories. Empirical evaluations demonstrate that our approach achieves more precise localization and enables reliable modulation of reasoning behaviors (e.g., reasoning capability, reasoning strength) across diverse reasoning models.

STILL: Selecting Tokens for Intra-Layer Hybrid Attention to Linearize LLMs

Linearizing pretrained large language models (LLMs) primarily relies on intra-layer hybrid attention mechanisms to alleviate the quadratic complexity of standard softmax attention. Existing methods perform token routing based on sliding-window partitions, resulting in position-based selection and fails to capture token-specific global importance. Meanwhile, linear attention further suffers from distribution shift caused by learnable feature maps that distort pretrained feature magnitudes. Motivated by these limitations, we propose STILL, an intra-layer hybrid linearization framework for efficiently linearizing LLMs. STILL introduces a Self-Saliency Score with strong local-global consistency, enabling accurate token selection using sliding-window computation, and retains salient tokens for sparse softmax attention while summarizing the remaining context via linear attention. To preserve pretrained representations, we design a Norm-Preserved Feature Map (NP-Map) that decouples feature direction from magnitude and reinjects pretrained norms. We further adopt a unified training-inference architecture with chunk-wise parallelization and delayed selection to improve hardware efficiency. Experiments show that STILL matches or surpasses the original pretrained model on commonsense and general reasoning tasks, and achieves up to a 86.2% relative improvement over prior linearized attention methods on long-context benchmarks.

Grad2Reward: From Sparse Judgment to Dense Rewards for Improving Open-Ended LLM Reasoning

Reinforcement Learning with Verifiable Rewards (RLVR) has catalyzed significant breakthroughs in complex LLM reasoning within verifiable domains, such as mathematics and programming. Recent efforts have sought to extend this paradigm to open-ended tasks by employing LLMs-as-a-Judge to provide sequence-level rewards for policy optimization. However, these rewards are inherently sparse, failing to provide the fine-grained supervision necessary for generating complex, long-form trajectories. Furthermore, current work treats the Judge as a black-box oracle, discarding the rich intermediate feedback signals encoded in it. To address these limitations, we introduce Grad2Reward, a novel framework that extracts dense process rewards directly from the Judge's model inference process via a single backward pass. By leveraging gradient-based attribution, Grad2Reward enables precise token-level credit assignment, substantially enhancing training efficiency and reasoning quality. Additionally, Grad2Reward introduces a self-judging mechanism, allowing the policy to improve through its own evaluative signals without training specialized reward models or reliance on superior external Judges. The experiments demonstrate that policies optimized with Grad2Reward achieve outstanding performance across diverse open-ended tasks, affirming its effectiveness and broad generalizability.

One Size, Many Fits: Aligning Diverse Group-Wise Click Preferences in Large-Scale Advertising Image Generation

Advertising image generation has increasingly focused on online metrics like Click-Through Rate (CTR), yet existing approaches adopt a ``one-size-fits-all" strategy that optimizes for overall CTR while neglecting preference diversity among user groups. This leads to suboptimal performance for specific groups, limiting targeted marketing effectiveness. To bridge this gap, we present \textit{One Size, Many Fits} (OSMF), a unified framework that aligns diverse group-wise click preferences in large-scale advertising image generation. OSMF begins with product-aware adaptive grouping, which dynamically organizes users based on their attributes and product characteristics, representing each group with rich collective preference features. Building on these groups, preference-conditioned image generation employs a Group-aware Multimodal Large Language Model (G-MLLM) to generate tailored images for each group. The G-MLLM is pre-trained to simultaneously comprehend group features and generate advertising images. Subsequently, we fine-tune the G-MLLM using our proposed Group-DPO for group-wise preference alignment, which effectively enhances each group's CTR on the generated images. To further advance this field, we introduce the Grouped Advertising Image Preference Dataset (GAIP), the first large-scale public dataset of group-wise image preferences, including around 600K groups built from 40M users. Extensive experiments demonstrate that our framework achieves the state-of-the-art performance in both offline and online settings. Our code and datasets will be released at https://github.com/JD-GenX/OSMF.

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.