arXiv subjects

Kuan Xu

Publications and source records attributed to Kuan Xu.

At least 19 recordsLinked to original sources

arXiv2026

Recycling singular and projection subspaces for pseudospectra computation

Computing matrix pseudospectra over a prescribed region requires evaluating the smallest singular value of $C-zI$ at a large number of grid points, which can be prohibitively expensive for large-scale matrices. We develop a recycling-based framework for accelerating such computations for both dense and sparse matrices. The main idea is to exploit the correlation between singular value problems at neighboring grid points by adaptively recycling singular subspaces computed at previously visited points by an iterative SVD solver. We develop fast Rayleigh-Ritz-SVD procedures for extracting Ritz singular pairs from the recycled singular subspaces, together with fast residual evaluation procedures, with an overall cost that scales linearly with the number of recycled samples. When the iterative SVD solver admits preconditioning, we propose using a two-level preconditioner whose projection subspaces are recycled. Numerical experiments demonstrate that the proposed recycling strategies yield substantial speedups over existing methods while maintaining the accuracy of the computed pseudospectra.

math.NA↗

arXiv2026

Ling and Ring 2.6 Technical Report: Efficient and Instant Agentic Intelligence at Trillion-Parameter Scale

Efficient and scalable agentic intelligence requires models that can deliver both low-latency responses and strong reasoning capabilities while remaining practical to train, serve, and deploy. In this report, we present Ling-2.6 and Ring-2.6, a family of models designed to address this challenge at scale. Ling-2.6 is optimized for instant response generation and high capability per output token, whereas Ring-2.6 is tailored for deeper reasoning and more advanced agentic workflows. Instead of training from scratch, we upgrade the Ling-2.0 base model through architectural migration pre-training and large-scale post-training. This upgrade is guided by a unified co-design of model architecture, optimization objectives, serving systems, and agent training environments, enabling improvements in both model capability and deployment efficiency. At the architectural level, we introduce a hybrid linear attention design that integrates Lightning Attention with MLA, improving the efficiency of long-context training and decoding. To further enhance token efficiency, we optimize capability per output token through Evolutionary Chain-of-Thought, Linguistic Unit Policy Optimization, bidirectional preference alignment, and shortest-correct-response distillation. For agentic capabilities, we propose KPop, a reinforcement learning framework designed to support stable training of Ring-2.6-1T on large-scale environment-grounded data. KPop improves training efficiency through asynchronous scheduling across coding, search, tool use, and workflow execution, enabling scalable learning from complex agent-environment interactions. Together, Ling-2.6 and Ring-2.6 provide a practical pathway toward efficient, scalable, and open agentic systems. We open-source all checkpoints in the 2.6 family to support further research and development in practical agentic intelligence.

cs.CL↗

arXiv2026

Fractional calculus via variable-transform-based spectral approximations

We present a novel and unifying framework for constructing spectral approximations to fractional integral operators. These spectral approximations are based on transplanted Chebyshev polynomials, which are obtained by composing Chebyshev polynomials with a variable transform. When an algebraic transform is used, the framework produces spectral approximations based on Jacobi fractional polynomials. When an exponential transform is used, it yields a versatile spectral approximation that is applicable to a much broader class of fractional calculus problems. The construction of such spectral approximations is both numerically stable and optimal in terms of complexity. These spectral approximations lead to stable and fast spectral methods for fractional calculus. The spectral approximation based on the double-exponential transform is demonstrated through extensive numerical examples that are intractable for existing spectral methods.

math.NA↗

arXiv2026

A Deployable Embodied Vision-Language Navigation System with Hierarchical Cognition and Context-Aware Exploration

Bridging the gap between embodied intelligence and embedded deployment remains a key challenge in intelligent robotic systems, where perception, reasoning, and planning must operate under strict constraints on computation, memory, energy, and real-time execution. In vision-and-language navigation (VLN), existing approaches often face a trade-off between reasoning capability and deployment efficiency on real-world platforms. In this paper, we present a deployable embodied VLN system that achieves both high efficiency and strong high-level reasoning on real-world robots. The system is decomposed into a fast perception-action layer and a deep reasoning layer running asynchronously at different time scales, with a shared memory layer enabling efficient interaction between them. To support long-horizon reasoning, we incrementally construct a compact memory graph and progressively feed decomposed subgraphs into a vision-language model (VLM). Furthermore, we formulate exploration as a Weighted Traveling Repairman Problem (WTRP) by jointly considering reasoning outcomes and the spatial distribution of candidate regions. Extensive experiments in simulation and real-world environments demonstrate improved navigation success and efficiency over existing VLN approaches while maintaining real-time performance on resource-constrained hardware. Code and additional real-world experiments are available at https://github.com/xukuanHIT/HiCo-Nav.

cs.RO↗

arXiv2026

Beyond Imitation: Reinforcement Learning Fine-Tuning for Adaptive Diffusion Navigation Policies

Diffusion-based robot navigation policies trained on large-scale imitation learning datasets, can generate multi-modal trajectories directly from the robot's visual observations, bypassing the traditional localization-mapping-planning pipeline and achieving strong zero-shot generalization. However, their performance remains constrained by the coverage of offline datasets, and when deployed in unseen settings, distribution shift often leads to accumulated trajectory errors and safety-critical failures. Adapting diffusion policies with reinforcement learning is challenging because their iterative denoising structure hinders effective gradient backpropagation, while also making the training of an additional value network computationally expensive and less stable. To address these issues, we propose a reinforcement learning fine-tuning framework tailored for diffusion-based navigation. The method leverages the inherent multi-trajectory sampling mechanism of diffusion models and adopts Group Relative Policy Optimization (GRPO), which estimates relative advantages across sampled trajectories without requiring a separate value network. To preserve pretrained representations while enabling adaptation, we freeze the visual encoder and selectively update the higher decoder layers and action head, enhancing safety-aware behaviors through online environmental feedback. On the PointGoal task in Isaac Sim, our approach improves the Success Rate from 52.0% to 58.7% and SPL from 0.49 to 0.54 on unseen scenes, while reducing collision frequency. Additional experiments show that the fine-tuned policy transfers zero-shot to a real quadruped platform and maintains stable performance in geometrically out-of-distribution environments, suggesting improved adaptability and safe generalization to new domains.

cs.RO↗

arXiv2026

LST-SLAM: A Stereo Thermal SLAM System for Kilometer-Scale Dynamic Environments

Thermal cameras offer strong potential for robot perception under challenging illumination and weather conditions. However, thermal Simultaneous Localization and Mapping (SLAM) remains difficult due to unreliable feature extraction, unstable motion tracking, and inconsistent global pose and map construction, particularly in dynamic large-scale outdoor environments. To address these challenges, we propose LST-SLAM, a novel large-scale stereo thermal SLAM system that achieves robust performance in complex, dynamic scenes. Our approach combines self-supervised thermal feature learning, stereo dual-level motion tracking, and geometric pose optimization. We also introduce a semantic-geometric hybrid constraint that suppresses potentially dynamic features lacking strong inter-frame geometric consistency. Furthermore, we develop an online incremental bag-of-words model for loop closure detection, coupled with global pose optimization to mitigate accumulated drift. Extensive experiments on kilometer-scale dynamic thermal datasets show that LST-SLAM significantly outperforms recent representative SLAM systems, including AirSLAM and DROID-SLAM, in both robustness and accuracy.

cs.RO↗

arXiv2025

Every Step Evolves: Scaling Reinforcement Learning for Trillion-Scale Thinking Model

We present Ring-1T, the first open-source, state-of-the-art thinking model with a trillion-scale parameter. It features 1 trillion total parameters and activates approximately 50 billion per token. Training such models at a trillion-parameter scale introduces unprecedented challenges, including train-inference misalignment, inefficiencies in rollout processing, and bottlenecks in the RL system. To address these, we pioneer three interconnected innovations: (1) IcePop stabilizes RL training via token-level discrepancy masking and clipping, resolving instability from training-inference mismatches; (2) C3PO++ improves resource utilization for long rollouts under a token budget by dynamically partitioning them, thereby obtaining high time efficiency; and (3) ASystem, a high-performance RL framework designed to overcome the systemic bottlenecks that impede trillion-parameter model training. Ring-1T delivers breakthrough results across critical benchmarks: 93.4 on AIME-2025, 86.72 on HMMT-2025, 2088 on CodeForces, and 55.94 on ARC-AGI-1. Notably, it attains a silver medal-level result on the IMO-2025, underscoring its exceptional reasoning capabilities. By releasing the complete 1T parameter MoE model to the community, we provide the research community with direct access to cutting-edge reasoning capabilities. This contribution marks a significant milestone in democratizing large-scale reasoning intelligence and establishes a new baseline for open-source model performance.

cs.CL↗

arXiv2025

A Fast and Light-weight Non-Iterative Visual Odometry with RGB-D Cameras

In this paper, we introduce a novel approach for efficiently estimating the 6-Degree-of-Freedom (DoF) robot pose with a decoupled, non-iterative method that capitalizes on overlapping planar elements. Conventional RGB-D visual odometry(RGBD-VO) often relies on iterative optimization solvers to estimate pose and involves a process of feature extraction and matching. This results in significant computational burden and time delays. To address this, our innovative method for RGBD-VO separates the estimation of rotation and translation. Initially, we exploit the overlaid planar characteristics within the scene to calculate the rotation matrix. Following this, we utilize a kernel cross-correlator (KCC) to ascertain the translation. By sidestepping the resource-intensive iterative optimization and feature extraction and alignment procedures, our methodology offers improved computational efficacy, achieving a performance of 71Hz on a lower-end i5 CPU. When the RGBD-VO does not rely on feature points, our technique exhibits enhanced performance in low-texture degenerative environments compared to state-of-the-art methods.

cs.RO↗

arXiv2025

Spectral Approximation to Fractional Integral Operators

We propose a fast and stable method for constructing matrix approximations to fractional integral operators applied to series in the Chebyshev fractional polynomials. This method utilizes a recurrence relation satisfied by the fractional integrals of mapped Chebyshev polynomials and significantly outperforms existing methods. Through numerical examples, we highlight the broad applicability of these matrix approximations, including the solution of boundary value problems for fractional integral and differential equations. Additional applications include fractional differential equation initial value problems and fractional eigenvalue problems.

math.NA↗

arXiv2025

Ring-lite: Scalable Reasoning via C3PO-Stabilized Reinforcement Learning for LLMs

We present Ring-lite, a Mixture-of-Experts (MoE)-based large language model optimized via reinforcement learning (RL) to achieve efficient and robust reasoning capabilities. Built upon the publicly available Ling-lite model, a 16.8 billion parameter model with 2.75 billion activated parameters, our approach matches the performance of state-of-the-art (SOTA) small-scale reasoning models on challenging benchmarks (e.g., AIME, LiveCodeBench, GPQA-Diamond) while activating only one-third of the parameters required by comparable models. To accomplish this, we introduce a joint training pipeline integrating distillation with RL, revealing undocumented challenges in MoE RL training. First, we identify optimization instability during RL training, and we propose Constrained Contextual Computation Policy Optimization(C3PO), a novel approach that enhances training stability and improves computational throughput via algorithm-system co-design methodology. Second, we empirically demonstrate that selecting distillation checkpoints based on entropy loss for RL training, rather than validation metrics, yields superior performance-efficiency trade-offs in subsequent RL training. Finally, we develop a two-stage training paradigm to harmonize multi-domain data integration, addressing domain conflicts that arise in training with mixed dataset. We will release the model, dataset, and code.

cs.CL↗

arXiv2025

Learning to Search for Vehicle Routing with Multiple Time Windows

In this study, we propose a reinforcement learning-based adaptive variable neighborhood search (RL-AVNS) method designed for effectively solving the Vehicle Routing Problem with Multiple Time Windows (VRPMTW). Unlike traditional adaptive approaches that rely solely on historical operator performance, our method integrates a reinforcement learning framework to dynamically select neighborhood operators based on real-time solution states and learned experience. We introduce a fitness metric that quantifies customers' temporal flexibility to improve the shaking phase, and employ a transformer-based neural policy network to intelligently guide operator selection during the local search. Extensive computational experiments are conducted on realistic scenarios derived from the replenishment of unmanned vending machines, characterized by multiple clustered replenishment windows. Results demonstrate that RL-AVNS significantly outperforms traditional variable neighborhood search (VNS), adaptive VNS (AVNS), and state-of-the-art learning-based heuristics, achieving substantial improvements in solution quality and computational efficiency across various instance scales and time window complexities. Particularly notable is the algorithm's capability to generalize effectively to problem instances not encountered during training, underscoring its practical utility for complex logistics scenarios.

cs.LG↗

arXiv2025

AirSwarm: Enabling Cost-Effective Multi-UAV Research with COTS drones

Traditional unmanned aerial vehicle (UAV) swarm missions rely heavily on expensive custom-made drones with onboard perception or external positioning systems, limiting their widespread adoption in research and education. To address this issue, we propose AirSwarm. AirSwarm democratizes multi-drone coordination using low-cost commercially available drones such as Tello or Anafi, enabling affordable swarm aerial robotics research and education. Key innovations include a hierarchical control architecture for reliable multi-UAV coordination, an infrastructure-free visual SLAM system for precise localization without external motion capture, and a ROS-based software framework for simplified swarm development. Experiments demonstrate cm-level tracking accuracy, low-latency control, communication failure resistance, formation flight, and trajectory tracking. By reducing financial and technical barriers, AirSwarm makes multi-robot education and research more accessible. The complete instructions and open source code will be available at

cs.RO↗

arXiv2025

Every FLOP Counts: Scaling a 300B Mixture-of-Experts LING LLM without Premium GPUs

In this technical report, we tackle the challenges of training large-scale Mixture of Experts (MoE) models, focusing on overcoming cost inefficiency and resource limitations prevalent in such systems. To address these issues, we present two differently sized MoE large language models (LLMs), namely Ling-Lite and Ling-Plus (referred to as "Bailing" in Chinese, spelled B\v{a}il\'ing in Pinyin). Ling-Lite contains 16.8 billion parameters with 2.75 billion activated parameters, while Ling-Plus boasts 290 billion parameters with 28.8 billion activated parameters. Both models exhibit comparable performance to leading industry benchmarks. This report offers actionable insights to improve the efficiency and accessibility of AI development in resource-constrained settings, promoting more scalable and sustainable technologies. Specifically, to reduce training costs for large-scale MoE models, we propose innovative methods for (1) optimization of model architecture and training processes, (2) refinement of training anomaly handling, and (3) enhancement of model evaluation efficiency. Additionally, leveraging high-quality data generated from knowledge graphs, our models demonstrate superior capabilities in tool use compared to other models. Ultimately, our experimental findings demonstrate that a 300B MoE LLM can be effectively trained on lower-performance devices while achieving comparable performance to models of a similar scale, including dense and MoE models. Compared to high-performance devices, utilizing a lower-specification hardware system during the pre-training phase demonstrates significant cost savings, reducing computing costs by approximately 20%. The models can be accessed at https://huggingface.co/inclusionAI.

cs.LG↗

arXiv2025

A new banded Petrov--Galerkin spectral method

We propose a Petrov--Galerkin spectral method for ODEs with variable coefficients. When the variable coefficients are smooth, the new method yields a strictly banded linear system, which can be efficiently constructed and solved in linear complexity. The performance advantage of our method is demonstrated through benchmarking against Mortensen's Galerkin method and the ultraspherical spectral method. Furthermore, we introduce a systematic approach for designing the recombined basis and establish that our new method serves as a unifying framework that encompasses all existing banded Galerkin spectral methods. This significantly addresses the ongoing challenge of developing recombined bases and sparse Galerkin spectral method. Additionally, the accelerating techniques presented in this paper can also enhance the performance of the ultraspherical spectral method.

math.NA↗

arXiv2025

ChorusCVR: Chorus Supervision for Entire Space Post-Click Conversion Rate Modeling

Post-click conversion rate (CVR) estimation is a vital task in many recommender systems of revenue businesses, e.g., e-commerce and advertising. In a perspective of sample, a typical CVR positive sample usually goes through a funnel of exposure to click to conversion. For lack of post-event labels for un-clicked samples, CVR learning task commonly only utilizes clicked samples, rather than all exposed samples as for click-through rate (CTR) learning task. However, during online inference, CVR and CTR are estimated on the same assumed exposure space, which leads to a inconsistency of sample space between training and inference, i.e., sample selection bias (SSB). To alleviate SSB, previous wisdom proposes to design novel auxiliary tasks to enable the CVR learning on un-click training samples, such as CTCVR and counterfactual CVR, etc. Although alleviating SSB to some extent, none of them pay attention to the discrimination between ambiguous negative samples (un-clicked) and factual negative samples (clicked but un-converted) during modelling, which makes CVR model lacks robustness. To full this gap, we propose a novel ChorusCVR model to realize debiased CVR learning in entire-space.

cs.IR↗

arXiv2024

Enhancing Scene Coordinate Regression with Efficient Keypoint Detection and Sequential Information

Scene Coordinate Regression (SCR) is a visual localization technique that utilizes deep neural networks (DNN) to directly regress 2D-3D correspondences for camera pose estimation. However, current SCR methods often face challenges in handling repetitive textures and meaningless areas due to their reliance on implicit triangulation. In this paper, we propose an efficient and accurate SCR system. Compared to existing SCR methods, we propose a unified architecture for both scene encoding and salient keypoint detection, allowing our system to prioritize the encoding of informative regions. This design significantly improves computational efficiency. Additionally, we introduce a mechanism that utilizes sequential information during both mapping and relocalization. The proposed method enhances the implicit triangulation, especially in environments with repetitive textures. Comprehensive experiments conducted across indoor and outdoor datasets demonstrate that the proposed system outperforms state-of-the-art (SOTA) SCR methods. Our single-frame relocalization mode improves the recall rate of our baseline by 6.4% and increases the running speed from 56Hz to 90Hz. Furthermore, our sequence-based mode increases the recall rate by 11% while maintaining the original efficiency.

cs.RO↗

arXiv2024

AirSLAM: An Efficient and Illumination-Robust Point-Line Visual SLAM System

In this paper, we present an efficient visual SLAM system designed to tackle both short-term and long-term illumination challenges. Our system adopts a hybrid approach that combines deep learning techniques for feature detection and matching with traditional backend optimization methods. Specifically, we propose a unified convolutional neural network (CNN) that simultaneously extracts keypoints and structural lines. These features are then associated, matched, triangulated, and optimized in a coupled manner. Additionally, we introduce a lightweight relocalization pipeline that reuses the built map, where keypoints, lines, and a structure graph are used to match the query frame with the map. To enhance the applicability of the proposed system to real-world robots, we deploy and accelerate the feature detection and matching networks using C++ and NVIDIA TensorRT. Extensive experiments conducted on various datasets demonstrate that our system outperforms other state-of-the-art visual SLAM systems in illumination-challenging environments. Efficiency evaluations show that our system can run at a rate of 73Hz on a PC and 40Hz on an embedded platform. Our implementation is open-sourced: https://github.com/sair-lab/AirSLAM.

cs.RO↗

arXiv2024

Understanding the ultraspherical spectral method

The ultraspherical spectral method features high accuracy and fast solution. In this article, we determine the sources of error arising from the ultraspherical spectral method and derive its effective condition number, which explains why its backward error is consistent with a numerical method with bounded condition number. In addition, we show the cause for the Cauchy error to go below the machine epsilon and decay eventually to exact zero, revealing the fact that the Cauchy error can be misleading when used as an indicator of convergence and accuracy. The analysis in this work can be readily extended to other spectral methods, when applicable, and to the solution of PDEs.

math.NA↗