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Rui Du

Publications and source records attributed to Rui Du.

At least 19 recordsLinked to original sources

The Diminishing Returns of Early-Exit Decoding in Modern LLMs

In Large Language Model (LLM) inference, early-exit refers to stopping computation at an intermediate layer once the prediction is sufficiently confident, thereby reducing latency and cost. However, recent LLMs adopt improved pretraining recipes and architectures that reduce layer redundancy, potentially limiting early-exit opportunities. We re-evaluate layer-wise early-exit in modern LLMs and analyze how intermediate representations evolve during training. We introduce a metric to quantify a model's intrinsic suitability for early-exit and propose a benchmark for researchers to explore the potential early-exit benefits on different models and workloads. Our results show a diminishing trend in early-exit effectiveness across newer model generations. We further find that dense transformers generally offer greater early-exit potential than Mixture-of-Experts and State Space Models. In addition, larger models, particularly those with more than 20 billion parameters, and base pretrained models without specialized tuning tend to exhibit higher early-exit potential.

cs.CL

Optimal Error Estimates of a Linearized Backward Euler Localized Orthogonal Decomposition for the Landau-Lifshitz Equation

We introduce a novel spatial discretization technique for the reliable and efficient simulation of magnetization dynamics governed by the Landau-Lifshitz (LL) equation. The overall discretization error is systematically decomposed into temporal and spatial components. The spatial error analysis is conducted by formulating the LL equation within the framework of the Localized Orthogonal Decomposition (LOD) method. Numerical examples are presented to validate the accuracy and approximation properties of the proposed scheme.

math.NA

Numerical Homogenization of Landau-Lifshitz Equation with Rough Coefficients

In this work, we develop a numerical homogenization approach for the fully nonlinear Landau-Lifshitz equation with rough coefficients, including non-periodicity and nonseparable scales. Direct numerical resolution of such multiscale problems on fine meshes incurs prohibitive computational costs. To address this challenge, we propose an efficient coarse scale approximation through localized basis functions derived from energy minimization within the Generalized Rough Polyharmonic Splines (GRPS) framework. These basis functions preserve critical multiscale features while operating on a computationally tractable coarse mesh. The nonlinear, vectorial, and non-symmetric nature of the Landau-Lifshitz equation necessitates careful design of variational formulations for basis construction. We introduce several such formulations, each tailored to specific structural aspects of the problem. Through systematic numerical experiments, we demonstrate that our approach achieves significant computational savings without compromising accuracy, offering a robust framework for simulating multiscale magnetic systems with complex microstructures.

math.NA

Equilibrium-distribution-function based mesoscopic finite-difference methods for partial differential equations: Modeling and Analysis

In this paper, based on the idea of direct discrete modeling (DDM) with equilibrium distribution functions (EDFs), we develop a general framework of the mesoscopic numerical method (MesoNM) for macroscopic partial differential equations (PDEs), including but not limited to the nonlinear convection-diffusion equation (NCDE) and the Navier-Stokes equations (NSEs). Unlike the mesoscopic lattice Boltzmann method, this kind of MesoNM is an EDF-based mesoscopic finite-difference (MesoFD) method, and by taking the moments of the MesoFD scheme, its macroscopic version, called MMFD method, can be derived directly. Both MesoFD scheme and MMFD schemes are multi-level FD methods, MesoFD scheme being mesoscopic, and MMFD scheme being its macroscopic form which has the form of the central FD scheme. They are unified FD schemes for PDEs and can be in implicit or explicit forms as needed. The macroscopic moment equations (MEs) can be derived from the MesoFD or MMFD scheme through the Taylor expansion method, and the common PDEs can be recovered from the MEs by using the direct Taylor expansion method. Moreover, the stability of the MMFD scheme is analyzed for linear CDE and liner wave equation with anisotropic diffusion, and the stability conditions of a two-level explicit MMFD scheme, a two-level $\theta$-MMFD scheme (hybrid explicit and implicit MMFD scheme), and a three-level MMFD scheme are obtained, respectively. Finally, we note that some existing lattice Boltzmann (LB) based macroscopic FD models for the NSEs and NCDE are the special cases of present MMFD, which can be considered as a unified framework of FD schemes for PDEs, from this point of view.

math.NA

Finite volume element method for Landau-Lifshitz equation

The Landau-Lifshitz equation describes the dynamics of magnetization in ferromagnetic materials. Due to the essential nonlinearity and nonconvex constraint, it is typically solved numerically. In this paper, we developed a finite volume element method (FVEM) with the Gauss-Seidel projection method (GSPM) for the micromagnetics simulations. We provide the approximation error in space and depict the energy law when the FVEM is adopted. Owing to the GSPM for time-marching, the discrete system is decoupled component by component, making the computational complexity comparable to that of solving the scalar heat equation implicitly. This significantly accelerates real simulations. We present several numerical experiments to validate the theoretical analysis and the efficiency gain. Additionally, we study the blow-up solution and efficiently simulate the 2D magnetic textures using the proposed method.

math.NA

Error Analysis of the Deep Mixed Residual Method for High-order Elliptic Equations

This paper presents an a priori error analysis of the Deep Mixed Residual method (MIM) for solving high-order elliptic equations with non-homogeneous boundary conditions, including Dirichlet, Neumann, and Robin conditions. We examine MIM with two types of loss functions, referred to as first-order and second-order least squares systems. By providing boundedness and coercivity analysis, we leverage C\'{e}a's Lemma to decompose the total error into the approximation, generalization, and optimization errors. Utilizing the Barron space theory and Rademacher complexity, an a priori error is derived regarding the training samples and network size that are exempt from the curse of dimensionality. Our results reveal that MIM significantly reduces the regularity requirements for activation functions compared to the deep Ritz method, implying the effectiveness of MIM in solving high-order equations.

math.NA

OPTIMA: Optimized Policy for Intelligent Multi-Agent Systems Enables Coordination-Aware Autonomous Vehicles

Coordination among connected and autonomous vehicles (CAVs) is advancing due to developments in control and communication technologies. However, much of the current work is based on oversimplified and unrealistic task-specific assumptions, which may introduce vulnerabilities. This is critical because CAVs not only interact with their environment but are also integral parts of it. Insufficient exploration can result in policies that carry latent risks, highlighting the need for methods that explore the environment both extensively and efficiently. This work introduces OPTIMA, a novel distributed reinforcement learning framework for cooperative autonomous vehicle tasks. OPTIMA alternates between thorough data sampling from environmental interactions and multi-agent reinforcement learning algorithms to optimize CAV cooperation, emphasizing both safety and efficiency. Our goal is to improve the generality and performance of CAVs in highly complex and crowded scenarios. Furthermore, the industrial-scale distributed training system easily adapts to different algorithms, reward functions, and strategies.

cs.MA

A Third-order Implicit-Explicit Runge-Kutta Method for Landau-Lifshitz Equation with Arbitrary Damping Parameters

A third-order accurate implicit-explicit Runge-Kutta time marching numerical scheme is proposed and implemented for the Landau-Lifshitz-Gilbert equation, which models magnetization dynamics in ferromagnetic materials, with arbitrary damping parameters. This method has three remarkable advantages:~(1) only a linear system with constant coefficients needs to be solved at each Runge-Kutta stage, which greatly reduces the time cost and improves the efficiency; (2) the optimal rate convergence analysis does not impose any restriction on the magnitude of damping parameter, which is consistent with the third-order accuracy in time for 1-D and 3-D numerical examples; (3) its unconditional stability with respect to the damping parameter has been verified by a detailed numerical study. In comparison with many existing methods, the proposed method indicates a better performance on accuracy and efficiency, and thus provides a better option for micromagnetics simulations.

math.NA

A simple and fast finite difference method for the integral fractional Laplacian of variable order

For the fractional Laplacian of variable order, an efficient and accurate numerical evaluation in multi-dimension is a challenge for the nature of a singular integral. We propose a simple and easy-to-implement finite difference scheme for the multi-dimensional variable-order fractional Laplacian defined by a hypersingular integral. We prove that the scheme is of second-order convergence and apply the developed finite difference scheme to solve various equations with the variable-order fractional Laplacian. We present a fast solver with quasi-linear complexity of the scheme for computing variable-order fractional Laplacian and corresponding PDEs. Several numerical examples demonstrate the accuracy and efficiency of our algorithm and verify our theory.

math.NA

The NeurIPS 2022 Neural MMO Challenge: A Massively Multiagent Competition with Specialization and Trade

In this paper, we present the results of the NeurIPS-2022 Neural MMO Challenge, which attracted 500 participants and received over 1,600 submissions. Like the previous IJCAI-2022 Neural MMO Challenge, it involved agents from 16 populations surviving in procedurally generated worlds by collecting resources and defeating opponents. This year's competition runs on the latest v1.6 Neural MMO, which introduces new equipment, combat, trading, and a better scoring system. These elements combine to pose additional robustness and generalization challenges not present in previous competitions. This paper summarizes the design and results of the challenge, explores the potential of this environment as a benchmark for learning methods, and presents some practical reinforcement learning training approaches for complex tasks with sparse rewards. Additionally, we have open-sourced our baselines, including environment wrappers, benchmarks, and visualization tools for future research.

cs.AI

An Overview on IEEE 802.11bf: WLAN Sensing

With recent advancements, the wireless local area network (WLAN) or wireless fidelity (Wi-Fi) technology has been successfully utilized to realize sensing functionalities such as detection, localization, and recognition. However, the WLANs standards are developed mainly for the purpose of communication, and thus may not be able to meet the stringent requirements for emerging sensing applications. To resolve this issue, a new Task Group (TG), namely IEEE 802.11bf, has been established by the IEEE 802.11 working group, with the objective of creating a new amendment to the WLAN standard to meet advanced sensing requirements while minimizing the effect on communications. This paper provides a comprehensive overview on the up-to-date efforts in the IEEE 802.11bf TG. First, we introduce the definition of the 802.11bf amendment and its formation and standardization timeline. Next, we discuss the WLAN sensing use cases with the corresponding key performance indicator (KPI) requirements. After reviewing previous WLAN sensing research based on communication-oriented WLAN standards, we identify their limitations and underscore the practical need for the new sensing-oriented amendment in 802.11bf. Furthermore, we discuss the WLAN sensing framework and procedure used for measurement acquisition, by considering both sensing at sub-7GHz and directional multi-gigabit (DMG) sensing at 60 GHz, respectively, and address their shared features, similarities, and differences. In addition, we present various candidate technical features for IEEE 802.11bf, including waveform/sequence design, feedback types, as well as quantization and compression techniques. We also describe the methodologies and the channel modeling used by the IEEE 802.11bf TG for evaluation. Finally, we discuss the challenges and future research directions to motivate more research endeavors towards this field in details.

eess.SP

Benchmarking Robustness and Generalization in Multi-Agent Systems: A Case Study on Neural MMO

We present the results of the second Neural MMO challenge, hosted at IJCAI 2022, which received 1600+ submissions. This competition targets robustness and generalization in multi-agent systems: participants train teams of agents to complete a multi-task objective against opponents not seen during training. The competition combines relatively complex environment design with large numbers of agents in the environment. The top submissions demonstrate strong success on this task using mostly standard reinforcement learning (RL) methods combined with domain-specific engineering. We summarize the competition design and results and suggest that, as an academic community, competitions may be a powerful approach to solving hard problems and establishing a solid benchmark for algorithms. We will open-source our benchmark including the environment wrapper, baselines, a visualization tool, and selected policies for further research.

cs.AI

Micromagnetics simulations and phase transitions of ferromagnetics with Dzyaloshinskii-Moriya interaction

Magnetic skyrmions widely exist in a diverse range of magnetic systems, including chiral magnets with a non-centrosymmetric structure characterized by Dzyaloshinkii-Moriya interaction~(DMI). In this study, we propose a generalized semi-implicit backward differentiation formula projection method, enabling the simulations of the Landau-Lifshitz~(LL) equation in chiral magnets in a typical time step-size of $1$ ps, markedly exceeding the limit subjected by existing numerical methods of typically $0.1$ ps. Using micromagnetics simulations, we show that the LL equation with DMI reveals an intriguing dynamic instability in magnetization configurations as the damping varies. Both the isolated skyrmionium and skyrmionium clusters can be consequently produced using a simple initialization strategy and a specific damping parameter. Assisted by the string method, the transition path between skyrmion and skyrmionium, along with the escape of a skyrmion from the skyrmion clusters, are then thoroughly examined. The numerical methods developed in this work not only provide a reliable paradigm to investigate the skyrmion-based textures and their transition paths, but also facilitate the understandings for magnetization dynamics in complex magnetic systems.

math.NA

Capacity-CRB Tradeoff in OFDM Integrated Sensing and Communication Systems

Integrated sensing and communication (ISAC) has emerged as a key technology for future communication systems. In this paper, we provide a general framework to reveal the fundamental tradeoff between sensing and communication in OFDM systems, where a unified ISAC waveform is exploited to perform both tasks. In particular, we define the Capacity-Bayesian Cramer Rao Bound (BCRB) region in the asymptotically case when the number of subcarriers is large. Specifically, we show that the asymptotically optimal input distribution that achieves the Pareto boundary point of the Capacity-BCRB region is Gaussian and the entire Pareto boundary can be obtained by solving a convex power allocation problem. Moreover, we characterize the structure of the sensing-optimal power allocation in the asymptotically case. Finally, numerical simulations are conducted to verify the theoretical analysis and provide useful insights.

cs.IT

Fundamental Limits and Optimization of Multiband Sensing

Multiband sensing is a promising technology that utilizes multiple non-contiguous frequency bands to achieve high-resolution target sensing. In this paper, we investigate the fundamental limits and optimization of multiband sensing, focusing on the fundamental limits associated with time delay. We first derive a Fisher information matrix (FIM) with a compact form using the Dirichlet kernel and then derive a closed-form expression of the Cramer-Rao bound (CRB) for the delay separation in a simplified case to reveal useful insights. Then, a metric called the statistical resolution limit (SRL) that provides a resolution limit is employed to investigate the fundamental limits of delay resolution. The fundamental limits of delay estimation are also investigated based on the CRB and Ziv-Zakai bound (ZZB). Based on the above derived fundamental limits, numerical results are presented to analyze the effect of frequency band apertures and phase distortions on the performance limits of the multiband sensing systems. We formulate an optimization problem to find the optimal system configuration in multiband sensing systems with the objective of minimizing the delay SRL. To solve this non-convex constrained problem, we propose an efficient alternating optimization (AO) algorithm which iteratively optimizes the variables using successive convex approximation (SCA) and one-dimensional search. Simulation results demonstrate the effectiveness of the proposed algorithm.

eess.SP

An Overview on IEEE 802.11bf: WLAN Sensing

With recent advancements, the wireless local area network (WLAN) or wireless fidelity (Wi-Fi) technology has been successfully utilized to realize sensing functionalities such as detection, localization, and recognition. However, the WLANs standards are developed mainly for the purpose of communication, and thus may not be able to meet the stringent sensing requirements in emerging applications. To resolve this issue, a new Task Group (TG), namely IEEE 802.11bf, has been established by the IEEE 802.11 working group, with the objective of creating a new amendment to the WLAN standard to provide advanced sensing requirements while minimizing the effect on communications. This paper provides a comprehensive overview on the up-to-date efforts in the IEEE 802.11bf TG. First, we introduce the definition of the 802.11bf amendment and its standardization timeline. Then, we discuss the WLAN sensing procedure and framework used for measurement acquisition, by considering both conventional sensing at sub-7 GHz and directional multi-gigabit (DMG) sensing at 60 GHz, respectively. Next, we present various candidate technical features for IEEE 802.11bf, including waveform/sequence design, feedback types, quantization, as well as security and privacy. Finally, we describe the methodologies used by the IEEE 802.11bf TG to evaluate the alternative performance. It is desired that this overview paper provide useful insights on IEEE 802.11 WLAN sensing to people with great interests and promote the IEEE 802.11bf standard to be widely deployed.

cs.NI

Networked Sensing in 6G Cellular Networks: Opportunities and Challenges

Radar and wireless communication are widely acknowledged as the two most successful applications of the radio technology over the past decades. Recently, there is a trend in both academia and industry to achieve integrated sensing and communication (ISAC) in one system via utilizing a common radio spectrum and the same hardware platform. This article will discuss about the possibility of exploiting the future sixth-generation (6G) cellular network to realize ISAC. Our vision is that the cellular base stations (BSs) deployed all over the world can be transformed into a powerful sensor to provide highresolution localization services. Specifically, motivated by the joint encoding/decoding gain in multi-cell coordinated communication, we advocate the adoption of the networked sensing technique in 6G network to achieve the above goal, where the BSs can share the sensing information with each other for jointly estimating the locations and velocities of the targets. Several opportunities and challenges to realize networked sensing in the 6G era will be revealed in this article. Moreover, the future research directions for this promising trend will be outlined as well.

eess.SP

Mapping evolving population geography in China

China's demographic changes have important global economic and geopolitical implications. Yet, our understanding of such transitions at the micro-spatial scale remains limited due to spatial inconsistency of the census data caused by administrative boundary adjustments. To fill this gap, we manually collected and built a population census panel from 2010 to 2020 at both the county and prefectural-city levels. We show that the massive internal migration drives China's increasing population concentration and regional disparity, resulting in severe population aging in shrinking cities and increasing gender imbalance in growing cities.

econ.GN