In extreme learning machines (ELM) the hidden-layer coefficients are randomly set and fixed, while the output-layer coefficients of the neural network are computed by a least squares method. The randomly-assigned coefficients in ELM are known to influence its performance and accuracy significantly. In this paper we present a modified batch intrinsic plasticity (modBIP) method for pre-training the random coefficients in the ELM neural networks. The current method is devised based on the same principle as the batch intrinsic plasticity (BIP) method, namely, by enhancing the information transmission in every node of the neural network. It differs from BIP in two prominent aspects. First, modBIP does not involve the activation function in its algorithm, and it can be applied with any activation function in the neural network. In contrast, BIP employs the inverse of the activation function in its construction, and requires the activation function to be invertible (or monotonic). The modBIP method can work with the often-used non-monotonic activation functions (e.g. Gaussian, swish, Gaussian error linear unit, and radial-basis type functions), with which BIP breaks down. Second, modBIP generates target samples on random intervals with a minimum size, which leads to highly accurate computation results when combined with ELM. The combined ELM/modBIP method is markedly more accurate than ELM/BIP in numerical simulations. Ample numerical experiments are presented with shallow and deep neural networks for function approximation and boundary/initial value problems with partial differential equations. They demonstrate that the combined ELM/modBIP method produces highly accurate simulation results, and that its accuracy is insensitive to the random-coefficient initializations in the neural network. This is in sharp contrast with the ELM results without pre-training of the random coefficients.

在极限学习机（ELM）中，隐藏层系数是随机设置和固定的，而神经网络的输出层系数是通过最小二乘法计算的。众所周知，ELM 中随机分配的系数会显着影响其性能和准确性。在本文中，我们提出了一种改进的批量固有可塑性 (modBIP) 方法，用于预训练 ELM 神经网络中的随机系数。当前的方法是基于与批量固有可塑性（BIP）方法相同的原理设计的，即通过增强神经网络每个节点的信息传递。它在两个显着方面不同于 BIP。首先，modBIP 在其算法中不涉及激活函数，它可以与神经网络中的任何激活函数一起应用。相比之下，BIP 在其构造中使用激活函数的逆，并要求激活函数是可逆的（或单调的）。modBIP 方法可以与常用的非单调激活函数（例如 Gaussian、swish、高斯误差线性单元和径向基类型函数）一起使用，BIP 会因这些函数而失效。其次，modBIP 以最小的随机间隔生成目标样本，当与 ELM 结合时，这会导致高度准确的计算结果。在数值模拟中，ELM/modBIP 组合方法明显比 ELM/BIP 更准确。针对函数逼近和偏微分方程的边界/初值问题，使用浅层和深层神经网络提供了大量数值实验。他们证明了组合 ELM/modBIP 方法可产生高度准确的模拟结果，并且其准确性对神经网络中的随机系数初始化不敏感。这与没有预训练随机系数的 ELM 结果形成鲜明对比。