Us chemists use retrosynthesis to disconnect the target cpd into accessible fragments of appropiate polarity that can be conveniently joined (that's three issues in one), and consider electron flow (i.e. arrow pushing) to think about what reactions would proceed smoothly.

Manipulation of 2D-connectivity, as seen in the paper is new and not for humans.

For predicting of reactions using computers, there are several methods out there, some of which use physical (quantum mechanics) calculations. Each reaction can take a long time to run, which is why we've turned to machine learning.

We chose to use fingerprints, i.e. a vector representation of the graphical features of a molecule, for the inputs of our reactions, which is often used when machine learning properties of molecules, or for classifying the entire reaction as David pointed mentioned before. There's one paper from the Baldi group that uses inputs that are more like orbitals, and tries to predict the mechanisms of reactions directly : http://pubs.acs.org/doi/abs/10.1021/ci3003039