检索结果-内蒙古大学图书馆

Desingularization of bounded-rank tensor sets

学校读者我要写书评

暂无评论

arXiv 2024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

Low-rank tensors appear to be prosperous in many applications. However, the sets of bounded-rank tensors are non-smooth and non-convex algebraic varieties, rendering the low-rank optimization problems to be challenging. To this end, we delve into the geometry of bounded-rank tensor sets, including Tucker and tensor train formats. We propose a desingularization approach for bounded-rank tensor sets by introducing slack variables, resulting in a low-dimensional smooth manifold embedded in a higher-dimensional space while preserving the structure of low-rank tensor formats. Subsequently, optimization on tensor varieties can be reformulated to optimization on smooth manifolds, where the methods and convergence are well explored. We reveal the relationship between the landscape of optimization on varieties and that of optimization on manifolds. Numerical experiments on tensor completion illustrate that the proposed methods are in favor of others under different rank *** Codes 15A69, 65K05, 65F30, 90C30 Copyright © 2024, The Authors. All rights reserved.

关键词： Tensors

Taking Myopic Best Response Against the Hedge Algorithm 42

学校读者我要写书评

暂无评论

Taking Myopic Best Response Against the Hedge Algorithm

42nd Chinese Control Conference, CCC 2023

作者： Guo, Xinxiang Mu, Yifen School of Mathematical Sciences University of Chinese Academy of Sciences Beijing China Academy of Mathematics and Systems Science The State Key Laboratory of Scientific and Engineering Computing Chinese Academy of Sciences Beijing China Academy of Mathematics and Systems Science The Key Laboratory of Systems and Control Chinese Academy of Sciences Beijing China

ISBN: (纸本)9789887581543

With the rapid development of artificial intelligence (AI), the game between the human and machine/AI becomes more and more common. The related theoretical analysis becomes significant and necessary, which however is still rare. This problem involves evolution analysis and optimal control of dynamic game systems driven by learning algorithms. In this paper, we consider a finitely repeated two-player zero-sum game. We study the dynamic evolution process of the game system, in which one player employs the Hedge algorithm and the other player takes the myopic best response. By the updating formula of the Hedge algorithm, we define a quantity called the state and construct the State Transition Triangle Graph (STTG). Then, we prove that the game system is periodic after o(T) stages. © 2023 Technical Committee on Control Theory, Chinese Association of Automation.

关键词： Artificial intelligence

Precise Analysis of Covariance Identifiability for Activity Detection in Grant-Free Random Access

学校读者我要写书评

暂无评论

arXiv 2024年

作者： Luo, Shengsong Ma, Junjie Xu, Chongbin Wang, Xin the Department of Communication Science and Engineering Fudan University Shanghai200433 China The 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 Beijing100190 China

We consider the identifiability issue of maximum-likelihood based activity detection in massive MIMO-based grant-free random access. An intriguing observation by Chen et al. [1] indicates that the identifiability undergoes a phase transition for commonly-used random user signatures as L2, N and K tend to infinity with fixed ratios, where L, N and K denote the user signature length, the total number of users, and the number of active users, respectively. In this letter, we provide a precise analytical characterization of the phase transition based on a spectral universality conjecture. Numerical results demonstrate excellent agreement between our theoretical predictions and the empirical phase transitions. Copyright © 2024, The Authors. All rights reserved.

关键词： Maximum likelihood

Adaptive energy-preserving algorithms for guiding center system

学校读者我要写书评

暂无评论

Plasma Science and Technology 2023年第4期25卷 11-22页

作者：朱贝贝刘健张嘉炜祝爱卿唐贻发 Department of Applied Mathematics School of Mathematics and PhysicsUniversity of Science and Technology BeijingBeijing 100083Peopleʼs Republic of China School of Nuclear Science and Technology University of Science and Technology of ChinaHefei 230026Peopleʼs Republic of China Advanced algorithm Joint Lab Shandong Computer Science CenterQilu University of TechnologyJinan 250014Peopleʼs Republic of China The State Key Laboratory of Scientific and Engineering Computing The Institute of Computational Mathematics and Scientific/Engineering ComputingAcademy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100190Peopleʼs Republic of China School of Mathematical Sciences University of Chinese Academy of SciencesBeijing 100049Peopleʼs Republic of China

We develop two types of adaptive energy preserving algorithms based on the averaged vector field for the guiding center dynamics,which plays a key role in magnetized *** adaptive scheme is applied to the Gauss Legendre’s quadrature rules and time stepsize respectively to overcome the energy drift problem in traditional energy-preserving *** new adaptive algorithms are second order,and their algebraic order is carefully *** results show that the global energy errors are bounded to the machine precision over long time using these adaptive algorithms without massive extra computation cost.

关键词： guiding center system energy-preserving methods adaptive energy conservation

STk: A Scalable Module for Solving Top-k Problems 38

学校读者我要写书评

暂无评论

STk: A Scalable Module for Solving Top-k Problems

38th Conference on Neural Information Processing Systems, NeurIPS 2024

作者： Xia, Hanchen Liu, Weidong Mao, Xiaojun School of Mathematical Sciences Shanghai Jiao Tong University Shanghai China Ministry of Education Key Lab of Artificial Intelligence Shanghai Jiao Tong University Shanghai China Ministry of Education Key Laboratory of Scientific and Engineering Computing Shanghai Jiao Tong University Shanghai China RoyalFlush AI Research Institute Hangzhou China

The cost of ranking becomes significant in the new stage of deep learning. We propose STk, a fully differentiable module with a single trainable parameter, designed to solve the Top-k problem without requiring additional time or GPU memory. Due to its fully differentiable nature, STk can be embedded end-to-end into neural networks and optimize the Top-k problems within a unified computational graph. We apply STk to the Average Top-k Loss (ATk), which inherently faces a Top-k problem. The proposed STk Loss outperforms ATk Loss and achieves the best average performance on multiple benchmarks, with the lowest standard deviation. With the assistance of STk Loss, we surpass the state-of-the-art (SOTA) on both CIFAR-100-LT and Places-LT leaderboards. © 2024 Neural information processing systems foundation. All rights reserved.

关键词：

MODERATE DEVIATION PRINCIPLES FOR A REACTION DIFFUSION MODEL IN NON-EQUILIBRIUM

学校读者我要写书评

暂无评论

arXiv 2024年

作者： Zhao, Linjie School of Mathematics and Statistics Hubei Key Laboratory of Engineering Modeling and Scientific Computing Huazhong University of Science and Technology Wuhan430074 China

We study moderate deviations from hydrodynamic limits of a reaction diffusion model. The process is defined as the superposition of the symmetric exclusion process with a Glauber dynamics. When the process starts from a product measure with a constant density, which is a non-equilibrium measure for the process, we prove that the re-scaled density fluctuation field satisfies the moderate deviation principle. Our proof relies on the so-called main lemma developed by Jara and Menezes [5, 6]. © 2024, CC BY.

关键词： Equilibrium constants

HPE Transformer: Learning to Optimize Multi-Group Multicast Beamforming Under Nonconvex QoS Constraints

学校读者我要写书评

暂无评论

arXiv 2024年

作者： Li, Yang Liu, Ya-Feng The Shenzhen Research Institute of Big Data Shenzhen518172 China The 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 Beijing100190 China

This paper studies the quality-of-service (QoS) constrained multi-group multicast beamforming design problem, where each multicast group is composed of a number of users requiring the same content. Due to the nonconvex QoS constraints, this problem is nonconvex and NP-hard. While existing optimization-based iterative algorithms can obtain a suboptimal solution, their iterative nature results in large computational complexity and delay. To facilitate real-time implementations, this paper proposes a deep learning-based approach, which consists of a beamforming structure assisted problem transformation and a customized neural network architecture named hierarchical permutation equivariance (HPE) transformer. The proposed HPE transformer is proved to be permutation equivariant with respect to the users within each multicast group, and also permutation equivariant with respect to different multicast groups. Simulation results demonstrate that the proposed HPE transformer outperforms state-of-the-art optimization-based and deep learning-based approaches for multi-group multicast beamforming design in terms of the total transmit power, the constraint violation, and the computational time. In addition, the proposed HPE transformer achieves pretty good generalization performance on different numbers of users, different numbers of multicast groups, and different signal-to-interference-plus-noise ratio targets. Copyright © 2024, The Authors. All rights reserved.

关键词： Beamforming

OPTIMIZATION ON PRODUCT MANIFOLDS UNDER A PRECONDITIONED METRIC

学校读者我要写书评

暂无评论

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 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 China

Since optimization on Riemannian manifolds relies on the chosen metric, it is appealing to know that how the performance of a Riemannian optimization method varies with different metrics and how to exquisitely construct a metric such that a method can be accelerated. To this end, we propose a general framework for optimization problems on product manifolds endowed with a preconditioned metric, and we develop Riemannian methods under this metric. Generally, the metric is constructed by an operator that aims to approximate the diagonal blocks of the Riemannian Hessian of the cost function. We propose three specific approaches to design the operator: exact block diagonal preconditioning, left and right preconditioning, and Gauss–Newton type preconditioning. Specifically, we tailor new preconditioned metrics and adapt the proposed Riemannian methods to the canonical correlation analysis and the truncated singular value decomposition problems, which provably accelerate the Riemannian methods. Additionally, we adopt the Gauss–Newton type preconditioning to solve the tensor ring completion problem. Numerical results among these applications verify that a delicate metric does accelerate the Riemannian optimization *** Codes 15A69, 65K05, 65F30, 90C30 Copyright © 2023, The Authors. All rights reserved.

关键词： Cost functions

GLOBAL STRONG SOLUTION FOR THE STOCHASTIC TAMED CHEMOTAXIS-NAVIER-STOKES SYSTEM IN R3

学校读者我要写书评

暂无评论

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 work, we consider the 3D Cauchy problem for a coupled system arising from the biomathematics, which consists of a chemotaxis model with cubic logistic source and the stochastic tamed Navier-Stokes equations (STCNS, for short). Our main goal is to establish the existence and uniqueness of global strong solution (strong in both the probabilistic and PDE senses) for the 3D STCNS system with large initial data. To achieve this, we first introduce a triple approximation scheme by virtue of the Friedrichs mollifier, frequency truncation operators and cut-off functions, which makes it possible for constructing sufficiently smooth approximation solutions, and facilitating the effective use of stochastic entropy-energy estimates. Then, building on the entropy-energy estimates, we further derive some higher-order energy estimates, which together with the stochastic compactness method permits us to construct the strong solution for the STCNS system. Copyright © 2024, The Authors. All rights reserved.

关键词： Navier Stokes equations