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What happens if we have complex-valued neural networks? A Thought Experiment

  • Exploring complex-valued neural networks reveals hidden periodic alter-egos of activation functions.
  • Transitioning neural networks to complex numbers introduces challenges with activation function differentiability.
  • Complex-Valued Neural Networks (CVNNs) show promise in wave-related fields but face activation function limitations.
  • Traditional activation functions like tanh become singular and non-differentiable in the complex plane.
  • There is a trade-off between boundedness and differentiability leading to need for specialized functions.

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