In this article,two new algorithms are presented that convert a given data tensor train into either a Tucker decomposition with orthogonal matrix factors or a multi-scale entanglement renormalization ansatz(MERA).The ...In this article,two new algorithms are presented that convert a given data tensor train into either a Tucker decomposition with orthogonal matrix factors or a multi-scale entanglement renormalization ansatz(MERA).The Tucker core tensor is never explicitly computed but stored as a tensor train instead,resulting in both computationally and storage efficient algorithms.Both the multilinear Tucker-ranks as well as the MERA-ranks are automatically determined by the algorithm for a given upper bound on the relative approximation error.In addition,an iterative algorithm with low computational complexity based on solving an orthogonal Procrustes problem is proposed for the first time to retrieve optimal rank-lowering disentangler tensors,which are a crucial component in the construction of a low-rank MERA.Numerical experiments demonstrate the effectiveness of the proposed algorithms together with the potential storage benefit of a low-rank MERA over a tensor train.展开更多
近年来,基于张量补全的频谱制图得到了广泛研究.目前用于频谱制图的张量补全算法大多隐含地假设张量具有平衡特性,而对于非平衡张量,难以利用其低秩性估计完整的张量信息,导致补全算法性能受损.本文提出基于重叠Ket增强(Overlapping Ket...近年来,基于张量补全的频谱制图得到了广泛研究.目前用于频谱制图的张量补全算法大多隐含地假设张量具有平衡特性,而对于非平衡张量,难以利用其低秩性估计完整的张量信息,导致补全算法性能受损.本文提出基于重叠Ket增强(Overlapping Ket Augmentation,OKA)和张量列车(Tensor Train,TT)的非平衡频谱制图算法,以解决非平衡张量在应用传统张量补全算法时性能下降的问题.首先使用OKA将低阶高维张量表示为高阶低维张量,在无信息损耗的情况下解决非平衡张量无法利用其低秩性进行张量补全的问题;然后使用TT矩阵化得到较平衡的矩阵,在维度较平衡条件下提高补全算法的精确度;最后利用高阶低维张量的低秩性,使用并行矩阵分解或基于F范数的无奇异值分解(Singular Value Decomposition Free,SVDFree)算法完成张量补全.仿真结果表明,针对非平衡张量,所提方案与现有的张量补全算法相比,可以获得更精确的无线电地图,同时所提SVDFree算法具有更低的计算复杂度.展开更多
Dynamic mode decomposition(DMD),as a data-driven method,has been frequently used to construct reduced-order models(ROMs)due to its good performance in time extrapolation.However,existing DMD-based ROMs suffer from hig...Dynamic mode decomposition(DMD),as a data-driven method,has been frequently used to construct reduced-order models(ROMs)due to its good performance in time extrapolation.However,existing DMD-based ROMs suffer from high storage and computational costs for high-dimensional problems.To mitigate this problem,we develop a new DMD-based ROM,i.e.,TDMD-GPR,by combining tensor train decomposition(TTD)and Gaussian process regression(GPR),where TTD is used to decompose the high-dimensional tensor into multiple factors,including parameterdependent and time-dependent factors.Parameter-dependent factor is fed into GPR to build the map between parameter value and factor vector.For any parameter value,multiplying the corresponding parameter-dependent factor vector and the timedependent factor matrix,the result describes the temporal behavior of the spatial basis for this parameter value and is then used to train the DMD model.In addition,incremental singular value decomposition is adopted to acquire a collection of important instants,which can further reduce the computational and storage costs of TDMD-GPR.The comparison TDMD and standard DMD in terms of computational and storage complexities shows that TDMD is more advantageous.The performance of the TDMD and TDMD-GPR is assessed through several cases,and the numerical results confirm the effectiveness of them.展开更多
Reinforcement Learning(RL)serves as a fundamental learning paradigm in the field of artificial intelligence,enabling decision-making policies through interactions with environments.However,traditional RL methods encou...Reinforcement Learning(RL)serves as a fundamental learning paradigm in the field of artificial intelligence,enabling decision-making policies through interactions with environments.However,traditional RL methods encounter challenges when dealing with large-scale or continuous state spaces due to the curse of dimensionality.Although Deep Reinforcement Learning(DRL)can handle complex environments,its lack of transparency and interpretability hinders its applicability due to the black box nature.Moreover,centralized data collection and processing methods pose privacy security risks.Federated learning offers a distributed approach that ensures privacy preservation while co-training models.However,existing federated reinforcement learning approaches have not adequately addressed communication and computation overhead issues.To address these challenges,this study proposes a tensor train decomposition-based federated reinforcement learning method that enhances efficiency and provides interpretability.By leveraging tensor to model state-action values and employing tensor decomposition techniques for dimensionality reduction,this method effectively reduces model parameters and communication overhead while maintaining strong interpretability,accelerates algorithm convergence speed.Experimental results validate the advantages of our proposed algorithm in terms of efficiency and reliability.展开更多
基金the Ministry of Education and Science of the Russian Federation(grant 14.756.31.0001).
文摘In this article,two new algorithms are presented that convert a given data tensor train into either a Tucker decomposition with orthogonal matrix factors or a multi-scale entanglement renormalization ansatz(MERA).The Tucker core tensor is never explicitly computed but stored as a tensor train instead,resulting in both computationally and storage efficient algorithms.Both the multilinear Tucker-ranks as well as the MERA-ranks are automatically determined by the algorithm for a given upper bound on the relative approximation error.In addition,an iterative algorithm with low computational complexity based on solving an orthogonal Procrustes problem is proposed for the first time to retrieve optimal rank-lowering disentangler tensors,which are a crucial component in the construction of a low-rank MERA.Numerical experiments demonstrate the effectiveness of the proposed algorithms together with the potential storage benefit of a low-rank MERA over a tensor train.
文摘近年来,基于张量补全的频谱制图得到了广泛研究.目前用于频谱制图的张量补全算法大多隐含地假设张量具有平衡特性,而对于非平衡张量,难以利用其低秩性估计完整的张量信息,导致补全算法性能受损.本文提出基于重叠Ket增强(Overlapping Ket Augmentation,OKA)和张量列车(Tensor Train,TT)的非平衡频谱制图算法,以解决非平衡张量在应用传统张量补全算法时性能下降的问题.首先使用OKA将低阶高维张量表示为高阶低维张量,在无信息损耗的情况下解决非平衡张量无法利用其低秩性进行张量补全的问题;然后使用TT矩阵化得到较平衡的矩阵,在维度较平衡条件下提高补全算法的精确度;最后利用高阶低维张量的低秩性,使用并行矩阵分解或基于F范数的无奇异值分解(Singular Value Decomposition Free,SVDFree)算法完成张量补全.仿真结果表明,针对非平衡张量,所提方案与现有的张量补全算法相比,可以获得更精确的无线电地图,同时所提SVDFree算法具有更低的计算复杂度.
基金supported by the Taishan Scholars Program(tsqn202211059)the National Natural Science Foundation of China(12201592)+1 种基金the Shandong Provincial Natural Science Foundation(ZR2022QA006)Laoshan Laboratory(LSKJ202202302)。
文摘Dynamic mode decomposition(DMD),as a data-driven method,has been frequently used to construct reduced-order models(ROMs)due to its good performance in time extrapolation.However,existing DMD-based ROMs suffer from high storage and computational costs for high-dimensional problems.To mitigate this problem,we develop a new DMD-based ROM,i.e.,TDMD-GPR,by combining tensor train decomposition(TTD)and Gaussian process regression(GPR),where TTD is used to decompose the high-dimensional tensor into multiple factors,including parameterdependent and time-dependent factors.Parameter-dependent factor is fed into GPR to build the map between parameter value and factor vector.For any parameter value,multiplying the corresponding parameter-dependent factor vector and the timedependent factor matrix,the result describes the temporal behavior of the spatial basis for this parameter value and is then used to train the DMD model.In addition,incremental singular value decomposition is adopted to acquire a collection of important instants,which can further reduce the computational and storage costs of TDMD-GPR.The comparison TDMD and standard DMD in terms of computational and storage complexities shows that TDMD is more advantageous.The performance of the TDMD and TDMD-GPR is assessed through several cases,and the numerical results confirm the effectiveness of them.
基金supported by the National Natural Science Foundation of China(Nos.U23A20300 and 62207033)the Fundamental Research Funds for the Central Universities of South-Central Minzu University(No.CSZ23013).
文摘Reinforcement Learning(RL)serves as a fundamental learning paradigm in the field of artificial intelligence,enabling decision-making policies through interactions with environments.However,traditional RL methods encounter challenges when dealing with large-scale or continuous state spaces due to the curse of dimensionality.Although Deep Reinforcement Learning(DRL)can handle complex environments,its lack of transparency and interpretability hinders its applicability due to the black box nature.Moreover,centralized data collection and processing methods pose privacy security risks.Federated learning offers a distributed approach that ensures privacy preservation while co-training models.However,existing federated reinforcement learning approaches have not adequately addressed communication and computation overhead issues.To address these challenges,this study proposes a tensor train decomposition-based federated reinforcement learning method that enhances efficiency and provides interpretability.By leveraging tensor to model state-action values and employing tensor decomposition techniques for dimensionality reduction,this method effectively reduces model parameters and communication overhead while maintaining strong interpretability,accelerates algorithm convergence speed.Experimental results validate the advantages of our proposed algorithm in terms of efficiency and reliability.
