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For questions about artificial networks, such as MLPs, CNNs, RNNs, LSTM, and GRU networks, their variants or any other AI system components that qualify as a neural networks in that they are, in part, inspired by biological neural networks.
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What makes the approximation capabilities of neural networks different than something like, ...
It's worth noting that the Fourier series analogy was used in early explorations of universal approximation theorems https://ieeexplore.ieee.org/document/23903.