  We reveal that a synthetic photonic lattice based on coupled optical loops
can be utilized as a neural network for processing of optical pulse sequences
in time domain. As a proof-of-concept, we train the optical system to restore
an initial shape of the pulse train from the signal distorted due to linear
dispersion in a fiber-optic link. We also show efficient training of the
optical network with an intrinsic Kerr-type nonlinearity for the realization of
target nonlinear transmission functions and inference functionality for the
discrimination of different pulse sequences. The theoretical modeling is
performed under practical conditions and can guide future experimental
realizations.
