  Pulse shaping for coherent optical fiber communication has been an active
area of research for the past decade. Most of the early schemes are based on
classic Nyquist pulse shaping that was originally intended for linear channels.
The best known classic scheme, the split digital back-propagation (DBP), uses
joint pre-distortion and post equalization and hence, a nonlinear transmitter
(TX); it, however, suffers from spectral broadening on the fiber due to the
Kerr-effect. With the advent of deep learning in communications, it has been
realized that an Autoencoder can learn to communicate efficiently over the
optical fiber channel, jointly optimizing geometric constellations and pulse
shaping - while also taking into account linear and nonlinear impairments such
as chromatic dispersion and Kerr-nonlinearity. E.g., arXiv:2006.15027 shows how
an Autoencoder can learn to mitigate spectral broadening due to the Kerr-effect
using a trainable linear TX. In this paper, we extend this linear architectural
template to a scalable nonlinear pulse shaping consisting of a Convolutional
Neural Network at both transmitter and receiver. By introducing a novel
$\gamma$-lifting training procedure tailored to the nonlinear optical fiber
channel, we achieve stable Autoencoder convergence to pulse shapes reaching
information rates outperforming the classic split DBP reference at high input
powers.
