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arXiv 2024年

作者： Xu, Fan Zhang, Lei Liu, Bin School of Mathematics and Statistics Hubei Key Laboratory of Engineering Modeling and Scientific Computing Huazhong University of Science and Technology Hubei Wuhan430074 China

In this paper, we study the initial-boundary value problem for the stochastic Landau-Lifshitz-Baryakhtar (SLLBar) equation with Stratonovich-type noise in bounded domains O ⊂ Rd, d = 1, 2, 3. Our main results can be briefly described as follows: (1) for d = 1, 2, 3 and any u0 ∈ H1, the SLLBar equation admits a unique local-in-time pathwise weak solution;(2) for d = 1 and small-data u0 ∈ H1, the SLLBar equation has a unique global-in-time pathwise weak solution and at least one invariant measure;(3) for d = 1, 2 and small-data u0 ∈ L2, the SLLBar equation possesses a unique global-in-time pathwise very weak solution and at least one invariant measure, while for d = 3 only the existence of martingale solution is obtained due to the loss of pathwise uniqueness. Copyright © 2024, The Authors. All rights reserved.

关键词： Stochastic systems

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Expert with Outlier Exposure for Continual Learning of New Diseases

Expert with Outlier Exposure for Continual Learning of New D...

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2022 IEEE International Conference on Bioinformatics and Biomedicine, BIBM 2022

作者： Xu, Zhengjing Chen, Kanghao Zheng, Wei-Shi Tan, Zhijun Yang, Xiaobo Wang, Ruixuan Sun Yat-sen University School of Computer Science and Engineering Guangzhou China Key Laboratory of Machine Intelligence and Advanced Computing MOE China State Key Laboratory of Dampness Syndrome of Chinese Medicine Guangzhou China Peng Cheng Laboratory Department of Network Intelligence Shenzhen China

ISBN: (纸本)9781665468190

Current intelligent diagnosis systems struggle to continually learn to diagnose more and more diseases due to catastrophic forgetting of old knowledge when learning new knowledge. Although storing small old data for subsequent continual learning can effectively help alleviate the forgetting issue, the heavy data imbalance between old classes and to-be-learned new classes in classifier training often causes biased prediction towards the new classes just learned by the updated classifier. In this study, an outlier detection technique is novelly applied to train an additional expert classifier for new classes to help alleviate the class imbalance issue and discriminate the learned new classes from old classes during inference (instead of the training phase). Specially, the stored small data of old classes are considered as outliers during training the expert classifier, such that the output probability distributions from the expert classifier are expected to be obviously different between test data of the old classes and those of the new classes. Such difference between old classes and new classes can be used to fine-tune the original output from the updated classifier which is responsible for prediction of all learned (old and new) classes. During inference, a novel ensemble strategy is proposed to combine the predictions from the updated classifier, the expert classifier, and the previously learned old classifier. The proposed learning and inference framework can be easily combined with existing continual learning strategies. Empirical evaluations on three medical image datasets and one natural image dataset show that the proposed framework can effectively improve continual learning performance. © 2022 IEEE.

关键词： Forecasting

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Instance-adaptive Zero-shot Chain-of-Thought Prompting 38

Instance-adaptive Zero-shot Chain-of-Thought Prompting

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38th Conference on Neural Information Processing Systems, NeurIPS 2024

作者： Yuan, Xiaosong Shen, Chen Yan, Shaotian Zhang, Xiaofeng Xie, Liang Wang, Wenxiao Guan, Renchu Wang, Ying Ye, Jieping College of Computer Science and Technology Jilin University China Key Laboratory of Symbolic Computation and Knowledge Engineering MoE Jilin University China Alibaba Cloud Computing China Shanghai Jiao Tong University China College of Computer Science and Technology Zhejiang University of Technology China College of Software Zhejiang University China

Zero-shot Chain-of-Thought (CoT) prompting emerges as a simple and effective strategy for enhancing the performance of large language models (LLMs) in real-world reasoning tasks. Nonetheless, the efficacy of a singular, task-level prompt uniformly applied across the whole of instances is inherently limited since one prompt cannot be a good partner for all, a more appropriate approach should consider the interaction between the prompt and each instance meticulously. This work introduces an instance-adaptive prompting algorithm as an alternative zero-shot CoT reasoning scheme by adaptively differentiating good and bad prompts. Concretely, we first employ analysis on LLMs through the lens of information flow to detect the mechanism under zero-shot CoT reasoning, in which we discover that information flows from question to prompt and question to rationale jointly influence the reasoning results most. We notice that a better zero-shot CoT reasoning needs the prompt to obtain semantic information from the question, and then the rationale aggregates sufficient information from the question directly and via the prompt indirectly. On the contrary, lacking any of those would probably lead to a bad one. Stem from that, we further propose an instance-adaptive prompting strategy (IAP) for zero-shot CoT reasoning. Experiments conducted with LLaMA-2, LLaMA-3, and Qwen on math, logic, and commonsense reasoning tasks (e.g., GSM8k, MMLU, Causal Judgement) obtain consistent improvement, demonstrating that the instance-adaptive zero-shot CoT prompting performs better than other task-level methods with some curated prompts or sophisticated procedures, showing the significance of our findings in the zero-shot CoT reasoning mechanism. © 2024 Neural information processing systems foundation. All rights reserved.

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Statistical Multiplexing Gain Analysis of Centralized Open Radio Access Networks with Limited Cells and Heterogeneous Traffics

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IEEE Transactions on Vehicular Technology 2025年

作者： Wang, Lu Zhou, Yiqing Liu, Ya-Feng Liu, Ling Shi, Ningzhe Tian, Lin Shi, Jinglin National Key Laboratory of Transient Impact Beijing102202 China 208 Research Institute of China Ordnance Industries Beijing102202 China Chinese Academy of Sciences State Key Lab of Processors Institute of Computing Technology Beijing100190 China University of Chinese Academy of Sciences Beijing100049 China Beijing Key Laboratory of Mobile Computing and Pervasive Device Beijing100190 China Chinese Academy of Sciences State Key Laboratory of Scientific and Engineering Computing Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Beijing100190 China Chinese Academy of Sciences Institute of Computing Technology Beijing100190 China Nanjing Institute of InforSuperBahn Nanjing211100 China

Centralized open radio access networks (O-RANs) aggregate computing resources of multiple cells to improve resource utilization and achieve statistical multiplexing gain (SMG), i.e., the ratio of the number of deployed resources (DepR) for distributed radio access network (D-RAN) to that for O-RAN. SMG of O-RAN has been investigated with infinite number of cells with homogeneous bursty-temporal traffic features. However, in practice, the number of cells is limited, and in the era of Internet of Things (IoT), cells with heterogeneous bursty-temporal traffics (het-traffics), should be considered. This paper analyzes the SMG of O-RAN with limited het-traffic cells. First of all, given traffic models of het-traffic cells following different bursty lognormal distribution and periodic time-varying features, required resources (ReqR) for D-RAN can be derived. Then, to obtain the distribution of ReqR for O-RAN with limited het-traffic cells, a Gaussian mixture model (GMM) based resource distribution approximation (GMM-RDA) is proposed. Thus SMG can be obtained for any given service rate. In simulations, the effectiveness of GMM-RDA is verified by Kolmogorov-Smirnov (K-S) test, and the accuracy of achieved SMG can be up to 99.7%, which is about 33% higher than that obtained by the law of large numbers (LLN) for infinite cells. Moreover, het-traffic cells resulting from service diversification can enhance SMG in O-RAN by 34.7%. © 1967-2012 IEEE.

关键词： Radio access networks

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A riemannian exponential augmented lagrangian method for computing the projection robust Wasserstein distance 23

A riemannian exponential augmented lagrangian method for com...

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Proceedings of the 37th International Conference on Neural Information Processing Systems

作者： Bo Jiang Ya-Feng Liu Ministry of Education Key Laboratory of NSLSCS School of Mathematical Sciences Nanjing Normal University Nanjing China State Key Laboratory of Scientific and Engineering Computing Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing China

Projection robust Wasserstein (PRW) distance is recently proposed to efficiently mitigate the curse of dimensionality in the classical Wasserstein distance. In this paper, by equivalently reformulating the computation of the PRW distance as an optimization problem over the Cartesian product of the Stiefel manifold and the Euclidean space with additional nonlinear inequality constraints, we propose a Riemannian exponential augmented Lagrangian method (REALM) for solving this problem. Compared with the existing Riemannian exponential penalty-based approaches, REALM can potentially avoid too small penalty parameters and exhibit more stable numerical performance. To solve the subproblems in REALM efficiently, we design an inexact Riemannian Barzilai-Borwein method with Sinkhorn iteration (iRBBS), which selects the stepsizes adaptively rather than tuning the step-sizes in efforts as done in the existing methods. We show that iRBBS can return an ε-stationary point of the original PRW distance problem within O(ε-3) iterations, which matches the best known iteration complexity result. Extensive numerical results demonstrate that our proposed methods outperform the state-of-the-art solvers for computing the PRW distance.

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Low-rank optimization on Tucker tensor varieties

arXiv

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arXiv 2023年

作者： Gao, Bin Peng, Renfeng Yuan, Ya-Xiang State Key Laboratory of Scientific and Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing China State Key Laboratory of Scientific and Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences University of Chinese Academy of Sciences Beijing China

In the realm of tensor optimization, the low-rank Tucker decomposition is crucial for reducing the number of parameters and for saving storage. We explore the geometry of Tucker tensor varieties—the set of tensors with bounded Tucker rank—which is notably more intricate than the well-explored matrix varieties. We give an explicit parametrization of the tangent cone of Tucker tensor varieties and leverage its geometry to develop provable gradient-related line-search methods for optimization on Tucker tensor varieties. To the best of our knowledge, this is the first work concerning geometry and optimization on Tucker tensor varieties. In practice, low-rank tensor optimization suffers from the difficulty of choosing a reliable rank parameter. To this end, we incorporate the established geometry and propose a Tucker rank-adaptive method that aims to identify an appropriate rank with guaranteed convergence. Numerical experiments on tensor completion reveal that the proposed methods are in favor of recovering performance over other state-of-the-art methods. The rank-adaptive method performs the best across various rank parameter selections and is indeed able to find an appropriate *** Codes 15A69, 65K05, 65F30, 90C30 Copyright © 2023, The Authors. All rights reserved.

关键词： Tensors

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Heterogeneity-aware Personalized Federated Learning via Adaptive Dual-Agent Reinforcement Learning

arXiv

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arXiv 2025年

作者： Chen, Xi Li, Qin Cai, Haibin Wang, Ting MoE Engineering Research Center of Software/Hardware Co-design Technology and Application Shanghai Key Laboratory of Trustworthy Computing East China Normal University Shanghai200062 China

Federated Learning (FL) empowers multiple clients to collaboratively train machine learning models without sharing local data, making it highly applicable in heterogeneous Internet of Things (IoT) environments. However, intrinsic heterogeneity in clients’ model architectures and computing capabilities often results in model accuracy loss and the intractable straggler problem, which significantly impairs training effectiveness. To tackle these challenges, this paper proposes a novel Heterogeneity-aware Personalized Federated Learning method, named HAPFL, via multi-level Reinforcement Learning (RL) mechanisms. HAPFL optimizes the training process by incorporating three strategic components: 1) An RL-based heterogeneous model allocation mechanism. The parameter server employs a Proximal Policy Optimization (PPO)-based RL agent to adaptively allocate appropriately sized, differentiated models to clients based on their performance, effectively mitigating performance disparities. 2) An RL-based training intensity adjustment scheme. The parameter server leverages another PPO-based RL agent to dynamically fine-tune the training intensity for each client to further enhance training efficiency and reduce straggling latency. 3) A knowledge distillation-based mutual learning mechanism. Each client deploys both a heterogeneous local model and a homogeneous lightweight model named LiteModel, where these models undergo mutual learning through knowledge distillation. This uniform LiteModel plays a pivotal role in aggregating and sharing global knowledge, significantly enhancing the effectiveness of personalized local training. Experimental results across multiple benchmark datasets demonstrate that HAPFL not only achieves high accuracy but also substantially reduces the overall training time by 20.9%-40.4% and decreases straggling latency by 19.0%-48.0% compared to existing solutions. © 2025, CC BY.

关键词： Federated learning

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QoS-Based Beamforming and Compression Design for Cooperative Cellular Networks via Lagrangian Duality

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IEEE Transactions on Signal Processing 2025年

作者： Fan, Xilai Liu, Ya-Feng Liu, Liang Chang, Tsung-Hui Chinese Academy of Sciences State Key Laboratory of Scientific and Engineering Computing Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Beijing100190 China The Hong Kong Polytechnic University Department of Electronic and Information Engineering Hong Kong Hong Kong The Chinese University of HongKong School of Science and Engineering Shenzhen Shenzhen China Shenzhen Research Institute of Big Data China

This paper considers the quality-of-service (QoS)-based joint beamforming and compression design problem in the downlink cooperative cellular network, where multiple relay-like base stations (BSs), connected to the central processor via ratelimited fronthaul links, cooperatively transmit messages to the users. The problem of interest is formulated as the minimization of the total transmit power of the BSs, subject to all users' signal-to-interference-plus-noise ratio (SINR) constraints and all BSs' fronthaul rate constraints. In this paper, we first show that there is no duality gap between the considered joint optimization problem and its Lagrangian dual by showing the tightness of its semidefinite relaxation (SDR). Then, we propose an efficient algorithm based on the above duality result for solving the considered problem. The proposed algorithm judiciously exploits the special structure of an enhanced Karush-Kuhn-Tucker (KKT) conditions of the considered problem and approaches the solution that satisfies the enhanced KKT conditions via two fixed point iterations. Two key features of the proposed algorithm are: (1) it is able to detect whether the considered problem is feasible or not and find its globally optimal solution when it is feasible;(2) it is highly efficient because both of the fixed point iterations in the proposed algorithm are linearly convergent and function evaluations in the fixed point iterations are computationally cheap. Numerical results show the global optimality and efficiency of the proposed algorithm. © 1991-2012 IEEE.

关键词： Lagrange multipliers

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Energy Stable Nodal DG Methods for Maxwell’s Equations of Mixed-Order Form in Nonlinear Optical Media

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Communications on Applied Mathematics and Computation 2024年第1期6卷 30-63页

作者： Maohui Lyu Vrushali A.Bokil Yingda Cheng Fengyan Li State Key Laboratory of Scientific and Engineering Computing(LSEC) Academy of Mathematics and System SciencesChinese Academy of SciencesBeijing100190China Department of Mathematics College of ScienceOregon State UniversityCorvallisOR97331USA Department of Mathematics Michigan State UniversityEast LansingMI48824USA Department of Computational Mathematics Science and EngineeringMichigan State UniversityEast LansingMI48824USA Department of Mathematical Sciences Rensselaer Polytechnic InstituteTroyNY12180USA

In this work,we develop energy stable numerical methods to simulate electromagnetic waves propagating in optical media where the media responses include the linear Lorentz dispersion,the instantaneous nonlinear cubic Kerr response,and the nonlinear delayed Raman molecular vibrational *** the first-order PDE-ODE governing equations considered previously in Bokil et al.(J Comput Phys 350:420–452,2017)and Lyu et al.(J Sci Comput 89:1–42,2021),a model of mixed-order form is adopted here that consists of the first-order PDE part for Maxwell’s equations coupled with the second-order ODE part(i.e.,the auxiliary differential equations)modeling the linear and nonlinear dispersion in the *** main contribution is a new numerical strategy to treat the Kerr and Raman nonlinearities to achieve provable energy stability property within a second-order temporal discretization.A nodal discontinuous Galerkin(DG)method is further applied in space for efficiently handling nonlinear terms at the algebraic level,while preserving the energy stability and achieving high-order *** with d_(E)as the number of the components of the electric field,only a d_(E)×d_(E)nonlinear algebraic system needs to be solved at each interpolation node,and more importantly,all these small nonlinear systems are completely decoupled over one time step,rendering very high parallel *** evaluate the proposed schemes by comparing them with the methods in Bokil et al.(2017)and Lyu et al.(2021)(implemented in nodal form)regarding the accuracy,computational efficiency,and energy stability,by a parallel scalability study,and also through the simulations of the soliton-like wave propagation in one dimension,as well as the spatial-soliton propagation and two-beam interactions modeled by the two-dimensional transverse electric(TE)mode of the equations.

关键词： Maxwell’s equations Kerr and Raman Discontinuous Galerkin method Energy stability

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On the convergence of stochastic gradient descent with bandwidth-based step size

The Journal of Machine Learning Research

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The Journal of Machine Learning Research 2023年第1期24卷 1990-2038页

作者： Xiaoyu Wang Ya-xiang Yuan Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing China and University of Chinese Academy of Sciences Beijing China State Key Laboratory of Scientific/Engineering Computing Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing China

We first propose a general step-size framework for the stochastic gradient descent(SGD) method: bandwidth-based step sizes that are allowed to vary within a banded region. The framework provides efficient and flexible step size selection in optimization, including cyclical and non-monotonic step sizes (e.g., triangular policy and cosine with restart), for which theoretical guarantees are rare. We provide state-of-the-art convergence guarantees for SGD under mild conditions and allow a large constant step size at the beginning of training. Moreover, we investigate the error bounds of SGD under the bandwidth step size where the boundary functions are in the same order and different orders, respectively. Finally, we propose a 1/t up-down policy and design novel non-monotonic step sizes. Numerical experiments demonstrate these bandwidth-based step sizes' efficiency and significant potential in training regularized logistic regression and several large-scale neural network tasks.

关键词： stochastic gradient descent bandwidth-based step size non-asymptotic convergence non-monotonic step size machine learning

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