We present a new Deep Neural Network (DNN) architecture capable of approximating functions up to machine accuracy. Termed Chebyshev Feature Neural Network (CFNN), the new structure employs Chebyshev functions with learnable frequencies as the first hidden layer, followed by the standard fully connected hidden layers. The learnable frequencies of the Chebyshev layer are initialized with exponential distributions to cover a wide range of frequencies. Combined with a multi-stage training strategy, we demonstrate that this CFNN structure can achieve machine accuracy during training. A comprehensive set of numerical examples for dimensions up to $20$ are provided to demonstrate the effectiveness and scalability of the method.

翻译：本文提出一种能够以机器精度逼近函数的新型深度神经网络架构。该结构被称为切比雪夫特征神经网络，其首层隐藏层采用具有可学习频率的切比雪夫函数，后续连接标准的全连接隐藏层。切比雪夫层的可学习频率采用指数分布初始化，以覆盖广泛的频率范围。结合多阶段训练策略，我们证明该CFNN结构在训练过程中能够达到机器精度。本文提供了维度高达$20$的全面数值算例，以验证该方法的有效性和可扩展性。