Chebyshev Feature Neural Network for Accurate Function Approximation

• URL: http://arxiv.org/abs/2409.19135v1
• Date: Fri, 27 Sep 2024 20:41:17 GMT
• Title: Chebyshev Feature Neural Network for Accurate Function Approximation
• Authors: Zhongshu Xu, Yuan Chen, Dongbin Xiu,
• Abstract summary: We present a new Deep Neural Network 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.
• Score: 3.8769921482808116
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

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