Scaling Limits of Constant-Stepsize SGD at Flat Minima

For stochastic gradient descent (SGD) with a constant stepsize $α$, the invariant law of the iterates, centered at a minimizer, describes the behavior of the algorithm over long time horizons. In the strongly convex case, this invariant law has the familiar $\sqrtα$ scaling and a Gaussian limit as $α\downarrow 0$. We show that this behavior changes fundamentally for convex objectives $H$ with flat minima and (sub)quadratic tails. More specifically, we study SGD with Markovian noise generated by a contractive driving chain. For every sufficiently small constant stepsize $α$, we prove existence, uniqueness, and geometric convergence to an augmented invariant law in a Wasserstein distance induced by an $α$-dependent metric. When the minimizer $x_\star$ has local flatness exponent $m\ge2$, meaning that $\nabla^2 H(x)\asymp \lVert x-x_\star\rVert^{m-2} I_d$ as $x\to x_\star$, we obtain a contraction bound with factor $1-cα^{m-1}$, where $c>0$ is a constant. This recovers the factor $1-cα$ in the quadratic case $m=2$. We then analyze the small-stepsize scaling limit. We show that the invariant law concentrates on the scale $α^{1/m}$ and that the rescaled iterates converge weakly to the stationary distribution of the stochastic differential equation $$ dY_t=-h_0(Y_t)\,dt+Σ^{1/2}\,dB_t , $$ where $h_0$ is the limiting drift at the minimizer and $Σ$ denotes the asymptotic covariance. This recovers the Gaussian limit when $m=2$ and gives generally non-Gaussian stationary limits in the flat case $m>2$. Finally, we give corresponding results for coordinate-separable objectives with unequal flatness exponents.

MobileSAM2: Lightweight Segment Anything for Spatial Intelligence

The recent large video foundation model, SAM2, enables segment anything in both images and videos, serving as a powerful base model for various applications. However, many of such use cases require to operate on resource-constrained devices like mobile phones and laptops. In this work, we aim to make SAM2 more mobile-friendly by distilling the heavyweight SAM2 into a lightweight model, facilitating segment anything in both images and videos on mobile devices. To this end, we propose Hypergraphical Knowledge Distill (HyperKD), which introduces the idea of hypergraph into knowledge distillation, aiming to effectively model and transfer SAM2's generalizable and comprehensive knowledge. HyperKD consists of Temporal HyperKD and Granularity HyperKD that construct hypergraphs to explicitly model and extract the generalizable temporal knowledge and the comprehensive multi-granularity knowledge from SAM2 respectively, which are then distilled into the lightweight student model by aligning it with the constructed hypergraphs. Besides, we present MobileSAM2, a new family of lightweight SAM2 that balances efficiency and effectiveness via searching the best model architectures with HyperKD during model size reduction. Extensive experiments validate MobileSAM2 across multiple benchmarks and show promising generalization performance on embodied AI tasks.

IB-Flow: Information Bottleneck-Guided CFG Distillation for Few-Step Text-to-Image Generation

While large-scale text-to-image generative models have achieved unprecedented visual performance, their inherent reliance on multi-step iterative solvers incurs severe inference latency. Few-step distillation targeting the Classifier-Free Guidance (CFG) trajectory has emerged as the prevalent dual-dimensional compression paradigm. However, existing frameworks remain subjugated by a coarse-grained blind injection paradigm that perpetually enforces a globally static guidance strength while indiscriminately sampling the supervisor timestep. This state-agnostic design completely disregards the intrinsic nature of image generation as a dynamic evolutionary process characterized by progressive entropy reduction, which not only restricts the performance boundary of few-step compression but also precipitates severe CFG over-conditioning artifacts. To transcend these limitations, we re-examine the distillation procedure through the theoretical lens of Information Theory, formally modeling it as a dynamic mutual information game constrained by the Information Bottleneck (IB) principle. Specifically, we dismantle traditional blind assumptions via a dual-track adaptive framework. To determine the injection target, we propose an instance-aware selection mechanism that transmutes the intractable KL divergence constraint into a zero-overhead closed-form solution predicated on the local vector field norm. To regulate the injection strength, we introduce an entropy-aware schedule that dynamically decays alongside the SNR, applying maximal thrust for initial structural anchoring before smoothly reverting to the natural manifold to refine micro-details. Extensive empirical evaluations corroborate that our framework fundamentally eradicates over-conditioning artifacts, shattering the performance ceiling to achieve SOTA generative fidelity under extremely stringent 2-step configurations.

CoDMD: Copula-aware Distribution Matching Distillation for Fast Video Generation

Few-step distillation for video diffusion models has attracted significant attention, driven by the urgent demand for efficient deployment in real-world scenarios. However, Distribution Matching Distillation (DMD), a leading paradigm, tends to degrade under limited NFE budgets, manifesting in video generation as layout instability, oversaturation, and broken motion dynamics. We trace this failure to a structural limitation: standard DMD is an intra-sample distribution-matching objective with coordinate-wise gradients, and thus imposes no explicit constraint on the relational geometry across batch elements or temporal frames, leaving the underlying copula largely unregulated. Combined with the mode-seeking tendency of its reverse-KL objective, this absence of relational guidance makes DMD prone to collapsing into local optima in the few-step regime. Motivated by this insight, we propose Copula-aware DMD (CoDMD), a lightweight relational regularizer that reuses score estimates already produced by the frozen teacher and the online fake model to construct pairwise relation matrices across samples and frames. These are matched through a supplementary distributional objective that requires no additional networks, datasets, or sampling trajectories. On the Wan-2.1-T2V model series at 1.3B & 14B scales, CoDMD distills 50-step teachers into 4-step students, achieving an approximate 25$\times$ speed-up while attaining VBench scores of 84.46 & 84.87, outperforming prior trajectory-based (rCM 82.81 & 84.05) and distribution-based (DMD 83.38 & 83.81) methods.

OpenClaw-Skill: Collective Skill Tree Search for Agentic Large Language Models

Equipping Large Language Model (LLM) agents with effective skills is crucial for solving complex tasks in real-world systems like OpenClaw. In this work, we aim to develop a framework that automatically constructs such reusable skills to enhance LLMs in tool use, multi-step reasoning, and dynamic environment interaction. To this end, we propose Collective Skill Tree Search (CSTS), a novel tree-search-based skill construction framework that constructs structured, diverse and generalizable tree of skills. The core idea of CSTS is to leverage collective intelligence to jointly search, identify and compose effective skills via two iterative phases: Collective Skill Node Generation (CSN-Gen) and Collective Skill Node Assessment (CSN-Assess). CSN-Gen exploits collective knowledge from multiple models to explore diverse candidate skills for each subtask, enabling comprehensive skill exploration. CSN-Assess employs multiple models as judges to evaluate and select skill nodes with two scoring mechanisms: (1) collective quality scoring that aggregates independent evaluations to produce a robust estimate of skill effectiveness, and (2) collective transferability scoring that explicitly verifies whether a skill generalizes well across different models. With CSTS, we construct a set of comprehensive tree of skills along with skill-augmented training data, enabling models to effectively learn and utilize skills. Besides, we introduce Collective Skill Reinforcement Learning, which actively selects multiple relevant skills from the tree to broaden solution-space exploration, avoid being trapped by a single skill and its resulting homogeneous or suboptimal solutions. As a result, our trained model, OpenClaw-Skill, exhibits outstanding agentic capabilities in long-horizon planning, tool use and generalization over challenging benchmarks.

Wan-Image: Pushing the Boundaries of Generative Visual Intelligence

We present Wan-Image, a unified visual generation system explicitly engineered to paradigm-shift image generation models from casual synthesizers into professional-grade productivity tools. While contemporary diffusion models excel at aesthetic generation, they frequently encounter critical bottlenecks in rigorous design workflows that demand absolute controllability, complex typography rendering, and strict identity preservation. To address these challenges, Wan-Image features a natively unified multi-modal architecture by synergizing the cognitive capabilities of large language models with the high-fidelity pixel synthesis of diffusion transformers, which seamlessly translates highly nuanced user intents into precise visual outputs. It is fundamentally powered by large-scale multi-modal data scaling, a systematic fine-grained annotation engine, and curated reinforcement learning data to surpass basic instruction following and unlock expert-level professional capabilities. These include ultra-long complex text rendering, hyper-diverse portrait generation, palette-guided generation, multi-subject identity preservation, coherent sequential visual generation, precise multi-modal interactive editing, native alpha-channel generation, and high-efficiency 4K synthesis. Across diverse human evaluations, Wan-Image exceeds Seedream 5.0 Lite and GPT Image 1.5 in overall performance, reaching parity with Nano Banana Pro in challenging tasks. Ultimately, Wan-Image revolutionizes visual content creation across e-commerce, entertainment, education, and personal productivity, redefining the boundaries of professional visual synthesis.

HyperLiDAR: Adaptive Post-Deployment LiDAR Segmentation via Hyperdimensional Computing

LiDAR semantic segmentation plays a pivotal role in 3D scene understanding for edge applications such as autonomous driving. However, significant challenges remain for real-world deployments, particularly for on-device post-deployment adaptation. Real-world environments can shift as the system navigates through different locations, leading to substantial performance degradation without effective and timely model adaptation. Furthermore, edge systems operate under strict computational and energy constraints, making it infeasible to adapt conventional segmentation models (based on large neural networks) directly on-device. To address the above challenges, we introduce HyperLiDAR, the first lightweight, post-deployment LiDAR segmentation framework based on Hyperdimensional Computing (HDC). The design of HyperLiDAR fully leverages the fast learning and high efficiency of HDC, inspired by how the human brain processes information. To further improve the adaptation efficiency, we identify the high data volume per scan as a key bottleneck and introduce a buffer selection strategy that focuses learning on the most informative points. We conduct extensive evaluations on two state-of-the-art LiDAR segmentation benchmarks and two representative devices. Our results show that HyperLiDAR outperforms or achieves comparable adaptation performance to state-of-the-art segmentation methods, while achieving up to a 13.8x speedup in retraining.

Reinforcing Structured Chain-of-Thought for Video Understanding

Multi-modal Large Language Models (MLLMs) show promise in video understanding. However, their reasoning often suffers from thinking drift and weak temporal comprehension, even when enhanced by Reinforcement Learning (RL) techniques like Group Relative Policy Optimization (GRPO). Moreover, existing RL methods usually depend on Supervised Fine-Tuning (SFT), which requires costly Chain-of-Thought (CoT) annotation and multi-stage training, and enforces fixed reasoning paths, limiting MLLMs' ability to generalize and potentially inducing bias. To overcome these limitations, we introduce Summary-Driven Reinforcement Learning (SDRL), a novel single-stage RL framework that obviates the need for SFT by utilizing a Structured CoT format: Summarize -> Think -> Answer. SDRL introduces two self-supervised mechanisms integrated into the GRPO objective: 1) Consistency of Vision Knowledge (CVK) enforces factual grounding by reducing KL divergence among generated summaries; and 2) Dynamic Variety of Reasoning (DVR) promotes exploration by dynamically modulating thinking diversity based on group accuracy. This novel integration effectively balances alignment and exploration, supervising both the final answer and the reasoning process. Our method achieves state-of-the-art performance on seven public VideoQA datasets.

KLDrive: Fine-Grained 3D Scene Reasoning for Autonomous Driving based on Knowledge Graph

Autonomous driving requires reliable reasoning over fine-grained 3D scene facts. Fine-grained question answering over multi-modal driving observations provides a natural way to evaluate this capability, yet existing perception pipelines and driving-oriented large language model (LLM) methods still suffer from unreliable scene facts, hallucinations, opaque reasoning, and heavy reliance on task-specific training. We present KLDrive, the first knowledge-graph-augmented LLM reasoning framework for fine-grained question answering in autonomous driving. KLDrive addresses this problem through designing two tightly coupled components: an energy-based scene fact construction module that consolidates multi-source evidence into a reliable scene knowledge graph, and an LLM agent that performs fact-grounded reasoning over a constrained action space under explicit structural constraints. By combining structured prompting with few-shot in-context exemplars, the framework adapts to diverse reasoning tasks without heavy task-specific fine-tuning. Experiments on two large-scale autonomous-driving QA benchmarks show that KLDrive outperforms prior state-of-the-art methods, achieving the best overall accuracy of 65.04% on NuScenes-QA and the best SPICE score of 42.45 on GVQA. On counting, the most challenging factual reasoning task, it improves over the strongest baseline by 46.01 percentage points, demonstrating substantially reduced hallucinations and the benefit of coupling reliable scene fact construction with explicit reasoning.

SRRM: Improving Recursive Transport Surrogates in the Small-Discrepancy Regime

Recursive partitioning methods provide computationally efficient surrogates for the Wasserstein distance, yet their statistical behavior and their resolution in the small-discrepancy regime remain insufficiently understood. We study Recursive Rank Matching (RRM) as a representative instance of this class under a population-anchored reference. In this setting, we establish consistency and an explicit convergence rate for the anchored empirical RRM under the quadratic cost. We then identify a dominant mismatch mechanism responsible for the loss of resolution in the small-discrepancy regime. Based on this analysis, we introduce Selective Recursive Rank Matching (SRRM), which suppresses the resulting dominant mismatches and yields a higher-fidelity practical surrogate for the Wasserstein distance at moderate additional computational cost.