研究人员开发了一种新算法，用于优化随机神经网络（RaNNDy）中的激活函数，以逼近动力系统中的传递算子。该方法保持网络权重和偏置固定，显著降低了训练成本，同时提高了基函数的适用性。另外，一篇综述回顾了神经网络逼近理论的演变，涵盖了经典的密度结果、逼近误差的定量界限，以及深度和宽度等架构特征的影响。它还强调了近期对Kolmogorov-Arnold Networks (KANs) 作为一种替代架构范式的关注。 AI
影响 神经网络逼近理论和优化方法的进步可能导致更高效、更强大的AI模型用于复杂系统分析。
排序理由 两篇arXiv论文讨论了神经网络理论和优化技术。
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arXiv:2605.23689v1 Announce Type: new Abstract: RaNNDy is a randomized neural network architecture for the data-driven approximation of transfer operators associated with complex dynamical systems. The weights and biases of the hidden layers of the network are randomly initialize…
RaNNDy is a randomized neural network architecture for the data-driven approximation of transfer operators associated with complex dynamical systems. The weights and biases of the hidden layers of the network are randomly initialized and kept fixed, only the output layer is train…
arXiv:2605.21451v1 Announce Type: cross Abstract: Universal approximation theorems provide a mathematical explanation for the expressive power of neural networks. They assert that, under mild conditions on the activation function, feedforward neural networks are dense in broad fu…
Universal approximation theorems provide a mathematical explanation for the expressive power of neural networks. They assert that, under mild conditions on the activation function, feedforward neural networks are dense in broad function classes, such as continuous functions on co…