arXiv subjects

Wenchao Wu

Publications and source records attributed to Wenchao Wu.

14 recordsLinked to original sources

arXiv2026

Irreducible noncommutative quadrics

In this paper, we study irreducible noncommutative quadrics $S/(f)$ via noncommutative graded matrix factorizations. We show that the line modules over $S/(f)$ are described by the rulings arising from indecomposable noncommutative linear matrix factorizations of $f$ of rank $2$. We study when Zhang twists of a standard smooth irreducible noncommutative quadric are standard. Finally, by identifying all singular central Sklyanin quadrics, we prove that every smooth central Sklyanin quadric is standard.

math.RA↗

arXiv2026

The Logarithmic Asymptotic Phenomenon for Generalized Markov-Hurwitz Equations

The purpose of this paper is twofold. First, we introduce a family of generalized Markov-Hurwitz equations, extending classical Markov-Hurwitz equations with additional degree n-1 interaction terms, Gyoda and Matsushita's generalized Markov equations from 3 variables to n variables. Second, we prove a logarithmic asymptotic phenomenon for the positive integer solutions of these equations.

math.NT↗

arXiv2026

Safety-aware Goal-oriented Semantic Sensing, Communication, and Control for Robotics

Wirelessly-connected robotic systems empower robots with real-time intelligence by leveraging remote computing resources for decision-making. However, the data exchange between robots and edge servers often overwhelms communication links, introducing latency that degrades task performance. To tackle this, goal-oriented semantic communication (GSC) has been introduced for wirelessly-connected robotic systems to extract and transmit only goal-relevant semantic representations. While this improves task effectiveness, it generally overlooks practical safety requirements. Meanwhile, existing robotics research often treats safety primarily as a control-level problem, without systematically considering safety across sensing, communication, and control in a closed-loop manner. To bridge this gap, we investigate how to enable safety-aware goal-oriented semantic (SA-GS) sensing, communication, and control co-design in wirelessly-connected robotic systems, aiming to maximize the robotic task effectiveness subject to practical safety requirements. We first introduce {an} architecture {for} wirelessly-connected robotic systems and representative use cases. We then summarize general safety requirements and effectiveness metrics across the use cases. Next, we systematically analyze the unique safety and effectiveness challenges in sensing, communication, and control. Based on these, we further present potential SA-GS research directions. Finally, an Unmanned Aerial Vehicle (UAV) target tracking case study validates that one of the presented SA-GS research directions, i.e., semantic-based C\&C packet execution, could significantly improve safety rate and tracking success rate by more than 2 times and 4.5 times, respectively.

cs.RO↗

arXiv2026

Point varieties and point-exactness of Koszul algebras

In this paper, we introduce the point-exact condition for a Koszul algebra $A$, which is useful for characterizing the (G1) condition of $A$ in the sense of Mori. Let $B = A/(f)$, where $f \in A_2$ is a regular normal element. We show that if $A$ satisfies the (G1) condition and is point-exact up to degree $\ell \geq 2$, then $B$ also satisfies the (G1) condition and is point-exact up to degree $\ell$. Moreover, we show that skew polynomial algebras satisfy the point-exact condition.

math.RA↗

arXiv2026

Guaranteed Image Classification via Goal-oriented Joint Semantic Source and Channel Coding

To enable critical applications such as remote diagnostics, image classification must be guaranteed under bandwidth constraints and unreliable wireless channels through joint source and channel coding (JSCC) design. However, most existing JSCC methods focus on minimizing image distortion, implicitly assuming that all image regions contribute equally to classification performance, thereby overlooking their varying importance for the task. In this paper, we propose a goal-oriented joint semantic source and channel coding (G-JSSCC) framework that applies \emph{various} levels of source coding compression and channel coding protection across image regions based on their semantic importance. Specifically, we design a semantic information extraction method that identifies and ranks various image regions based on their contributions to classification, where the contribution is measured by the shapely value from explainable artificial intelligence (AI). Based on that, we design a semantic source coding and a semantic channel coding method, which allocates higher-quality compression and stronger error protection to image regions of great semantic importance. In addition, we define a new metric, termed coding efficiency, to evaluate the effectiveness of the source and channel coding in the classification task. Simulations show that our proposed G-JSSCC framework improves classification probability by 2.70 times, reduces transmission cost by 38%, and enhances coding efficiency by 5.91 times, compared to the benchmark scheme using uniform compression and an idealized channel code to uniformly protect the whole image.

eess.IV↗

arXiv2026

Classification of noncommutative central conics

Classification of noncommutative quadric hypersurfaces is one of the major projects in noncommutative algebraic geometry. In recent years, we are dedicated to complete the classification of noncommutative central conics. To achieve this goal, we and other authors develop some theories to study and classify some classes of noncommutative quadric hypersurfaces in a series of papers. Finally, in this paper, we completely classify noncommutative central conics by developing the general theory of homogenization and dehomogenization for noncommutative algebras and by previous results. As a main result, we show that there are bijections among the following sets of objects (i) the set of isomorphism classes of $4$-dimensional Frobenius algebras, (ii) the set of isomorphism classes of noncommutative affine pencils of conics, and (iii) the set of isomorphism classes of noncommutative central conics.

math.RA↗

arXiv2025

GFS: A Preemption-aware Scheduling Framework for GPU Clusters with Predictive Spot Instance Management

The surge in large language models (LLMs) has fundamentally reshaped the landscape of GPU usage patterns, creating an urgent need for more efficient management strategies. While cloud providers employ spot instances to reduce costs for low-priority (LP) tasks, existing schedulers still grapple with high eviction rates and lengthy queuing times. To address these limitations, we present GFS, a novel preemptive scheduling framework that enhances service-level objective (SLO) compliance for high-priority (HP) tasks while minimizing preemptions to LP tasks. Firstly, GFS utilizes a lightweight forecasting model that predicts GPU demand among different tenants, enabling proactive resource management. Secondly, GFS employs a dynamic allocation mechanism to adjust the spot quota for LP tasks with guaranteed durations. Lastly, GFS incorporates a preemptive scheduling policy that prioritizes HP tasks while minimizing the impact on LP tasks. We demonstrate the effectiveness of GFS through both real-world implementation and simulations. The results show that GFS reduces eviction rates by 33.0\%, and cuts queuing delays by 44.1\% for LP tasks. Furthermore, GFS enhances the GPU allocation rate by up to 22.8\% in real production clusters. In a production cluster of more than 10,000 GPUs, GFS yields roughly \$459,715 in monthly benefits.

cs.DC↗

arXiv2025

Noncommutative affine pencils of conics

This paper is one of the series of papers which are dedicated to the complete classification of noncommutative conics. In this paper, we define and study noncommutative affine pencils of conics, and give a complete classification result. We also fully classify $4$-dimensional Frobenius algebras. It turns out that the classification of noncommutative affine pencils of conics is the same as the classification of $4$-dimensional Frobenius algebras.

math.RA↗

arXiv2025

Noncommutative Knörrer periodicity via equivariantization

We establish noncommutative Knörrer periodicity for projective-module factorizations over an arbitrary ring, using the equivariantization theory with respect to various actions by a cyclic group of order two. We obtain an explicit quasi-inverse of the periodicity. We compare the periodicity with a certain tensor functor between big singularity categories.

math.RA↗

arXiv2024

Goal-oriented Semantic Communications for Robotic Waypoint Transmission: The Value and Age of Information Approach

The ultra-reliable and low-latency communication (URLLC) service of the fifth-generation (5G) mobile communication network struggles to support safe robot operation. Nowadays, the sixth-generation (6G) mobile communication network is proposed to provide hyper-reliable and low-latency communication to enable safer control for robots. However, current 5G/ 6G research mainly focused on improving communication performance, while the robotics community mostly assumed communication to be ideal. To jointly consider communication and robotic control with a focus on the specific robotic task, we propose goal-oriented semantic communication in robotic control (GSRC) to exploit the context of data and its importance in achieving the task at both transmitter and receiver. At the transmitter, we propose a deep reinforcement learning algorithm to generate optimal control and command (C&C) data and a proactive repetition scheme (DeepPro) to increase the successful transmission probability. At the receiver, we design the value of information (VoI) and age of information (AoI) based queue ordering mechanism (VA-QOM) to rank the queue based on the semantic information extracted from AoI and VoI. The simulation results validate that our proposed GSRC framework achieves a 91.5% improvement in the mean square error compared to the traditional unmanned aerial vehicle control framework.

cs.RO↗

arXiv2024

FALCON: Pinpointing and Mitigating Stragglers for Large-Scale Hybrid-Parallel Training

Fail-slows, or stragglers, are common but largely unheeded problems in large-scale hybrid-parallel training that spans thousands of GPU servers and runs for weeks to months. Yet, these problems are not well studied, nor can they be quickly detected and effectively mitigated. In this paper, we first present a characterization study on a shared production cluster with over 10,000 GPUs1. We find that fail-slows are caused by various CPU/GPU computation and cross-node networking issues, lasting from tens of seconds to nearly ten hours, and collectively delaying the average job completion time by 1.34%. The current practice is to manually detect these fail-slows and simply treat them as fail-stops using a checkpoint-and-restart failover approach, which are labor-intensive and time-consuming. In this paper, we propose FALCON, a framework that rapidly identifies fail-slowed GPUs and/or communication links, and effectively tackles them with a novel multi-level mitigation mechanism, all without human intervention. We have applied FALCON to detect human-labeled fail-slows in a production cluster with over 99% accuracy. Cluster deployment further demonstrates that FALCON effectively handles manually injected fail-slows, mitigating the training slowdown by 60.1%.

cs.DC↗

arXiv2024

Goal-Oriented UAV Communication Design and Optimization for Target Tracking: A MachineLearning Approach

To accomplish various tasks, safe and smooth control of unmanned aerial vehicles (UAVs) needs to be guaranteed, which cannot be met by existing ultra-reliable low latency communications (URLLC). This has attracted the attention of the communication field, where most existing work mainly focused on optimizing communication performance (i.e., delay) and ignored the performance of the task (i.e., tracking accuracy). To explore the effectiveness of communication in completing a task, in this letter, we propose a goal-oriented communication framework adopting a deep reinforcement learning (DRL) algorithm with a proactive repetition scheme (DeepP) to optimize C&C data selection and the maximum number of repetitions in a real-time target tracking task, where a base station (BS) controls a UAV to track a mobile target. The effectiveness of our proposed approach is validated by comparing it with the traditional proportional integral derivative (PID) algorithm.

eess.SY↗

arXiv2024

Intelligent Chemical Purification Technique Based on Machine Learning

We present an innovative of artificial intelligence with column chromatography, aiming to resolve inefficiencies and standardize data collection in chemical separation and purification domain. By developing an automated platform for precise data acquisition and employing advanced machine learning algorithms, we constructed predictive models to forecast key separation parameters, thereby enhancing the efficiency and quality of chromatographic processes. The application of transfer learning allows the model to adapt across various column specifications, broadening its utility. A novel metric, separation probability ($S_p$), quantifies the likelihood of effective compound separation, validated through experimental verification. This study signifies a significant step forward int the application of AI in chemical research, offering a scalable solution to traditional chromatography challenges and providing a foundation for future technological advancements in chemical analysis and purification.

cs.LG↗

arXiv2021

Review of Learning-based Longitudinal Motion Planning for Autonomous Vehicles: Research Gaps between Self-driving and Traffic Congestion

Self-driving technology companies and the research community are accelerating their pace to use machine learning longitudinal motion planning (mMP) for autonomous vehicles (AVs). This paper reviews the current state of the art in mMP, with an exclusive focus on its impact on traffic congestion. We identify the availability of congestion scenarios in current datasets, and summarize the required features for training mMP. For learning methods, we survey the major methods in both imitation learning and non-imitation learning. We also highlight the emerging technologies adopted by some leading AV companies, e.g. Tesla, Waymo, and Comma.ai. We find that: i) the AV industry has been mostly focusing on the long tail problem related to safety and overlooked the impact on traffic congestion, ii) the current public self-driving datasets have not included enough congestion scenarios, and mostly lack the necessary input features/output labels to train mMP, and iii) albeit reinforcement learning (RL) approach can integrate congestion mitigation into the learning goal, the major mMP method adopted by industry is still behavior cloning (BC), whose capability to learn a congestion-mitigating mMP remains to be seen. Based on the review, the study identifies the research gaps in current mMP development. Some suggestions towards congestion mitigation for future mMP studies are proposed: i) enrich data collection to facilitate the congestion learning, ii) incorporate non-imitation learning methods to combine traffic efficiency into a safety-oriented technical route, and iii) integrate domain knowledge from the traditional car following (CF) theory to improve the string stability of mMP.

eess.SP↗