[R] Neural networks vs The Game of Life

I think I see what you're saying, but... The way the paper reads, the problem tackled is: "Given sample trajectories from Game of Life but no access to / knowledge of the source code, create a model that perfectly predicts the game's dynamic." However, by using n to set the problem difficulty (by using a terminal loss instead of a trajectory loss), the actual problem being tackled is: "Given sample state pairs {y[0], y[n]} spaced n steps apart... create a model that perfectly predicts the game's dynamic." The latter is clearly a much more difficult problem. I can agree that a narrow network may have difficulties with it (perhaps related to the lottery hypothesis).