  We propose a neural network for both forward and inverse continuous nonlinear
Fourier transforms, NFT and INFT respectively. We demonstrate the network's
capability to perform NFT and INFT for a random mix of NFDM-QAM signals. The
network transformations (NFT and INFT) exhibit true characteristics of these
transformations; they are significantly different for low and high-power input
pulses. The network shows adequate accuracy with an RMSE of 5e-3 for forward
and 3e-2 for inverse transforms. We further show that the trained network can
be used to perform general nonlinear Fourier transforms on arbitrary pulses
beyond the training pulse types.
