Deep Learning without Global Optimization by Random Fourier Neural Networks

• URL: http://arxiv.org/abs/2407.11894v1
• Date: Tue, 16 Jul 2024 16:23:40 GMT
• Title: Deep Learning without Global Optimization by Random Fourier Neural Networks
• Authors: Owen Davis, Gianluca Geraci, Mohammad Motamed,
• Abstract summary: We introduce a new training algorithm for variety of deep neural networks that utilize random complex exponential activation functions. Our approach employs a Markov Chain Monte Carlo sampling procedure to iteratively train network layers. It consistently attains the theoretical approximation rate for residual networks with complex exponential activation functions.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We introduce a new training algorithm for variety of deep neural networks that utilize random complex exponential activation functions. Our approach employs a Markov Chain Monte Carlo sampling procedure to iteratively train network layers, avoiding global and gradient-based optimization while maintaining error control. It consistently attains the theoretical approximation rate for residual networks with complex exponential activation functions, determined by network complexity. Additionally, it enables efficient learning of multiscale and high-frequency features, producing interpretable parameter distributions. Despite using sinusoidal basis functions, we do not observe Gibbs phenomena in approximating discontinuous target functions.

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