The capability of multilayer perceptrons(MLPs)for approximating continuous functions with arbitrary accuracy has been demonstrated in the past decades.Back propagation(BP)algorithm is the most popular learning algorit...The capability of multilayer perceptrons(MLPs)for approximating continuous functions with arbitrary accuracy has been demonstrated in the past decades.Back propagation(BP)algorithm is the most popular learning algorithm for training of MLPs.In this paper,a simple iteration formula is used to select the leaming rate for each cycle of training procedure,and a convergence result is presented for the BP algo- rithm for training MLP with a hidden layer and a linear output unit.The monotonicity of the error function is also guaranteed during the training iteration.展开更多
基金This research was supported by the National Natural Science Foundation of China (10471017).
文摘The capability of multilayer perceptrons(MLPs)for approximating continuous functions with arbitrary accuracy has been demonstrated in the past decades.Back propagation(BP)algorithm is the most popular learning algorithm for training of MLPs.In this paper,a simple iteration formula is used to select the leaming rate for each cycle of training procedure,and a convergence result is presented for the BP algo- rithm for training MLP with a hidden layer and a linear output unit.The monotonicity of the error function is also guaranteed during the training iteration.
文摘由于超大规模MIMO(Extremely Large-scale MIMO,XL-MIMO)系统中空间非平稳性的存在,使得部分天线对系统性能贡献较小,从而增加了系统能耗。通过天线选择并结合波束成形从而优化系统性能。以最小化基站发射功率为目标建模,在满足信干噪比和基站激活天线数的约束下,优化基站处的波束成形矩阵。由于该优化问题是典型的混合整数非线性规划问题,传统方法使用连续近似来求解,然而获得的解都是次优解。鉴于此,首先提出采用分支定界算法(Branch and Bound,BAB)求解上述优化问题,从而保证解的最优性。然而,BAB算法在处理大规模问题,特别是基站天线数大于128时,计算复杂度往往过高。为了解决这一问题,提出了一种基于图神经网络和多层感知机(Graph Neural Network and Multilayer Perceptron,GNN+MLP)的方法,通过利用GNN在BAB树的根节点提取一次全局特征,并在每个子节点利用MLP提取局部特征,通过结合全局特征和局部特征来训练一个二进制的节点分类器,以判断当前节点是否需要进一步分支,从而加速计算的过程。仿真结果表明,在天线数等于512时,GNN+MLP比BAB减少了54.2%的计算时间。