The interesting part is that this trivial toy problem is hard to learn for a standard CNN.
They probably engineered the toy problem to be that simple, looking for the simplest problem that still displays the phenomenon.
They probably engineered the toy problem to be that simple, looking for the simplest problem that still displays the phenomenon.
"For any problem involving pixels or spatial representations, common intuition holds that convolutional neural networks may be appropriate. In this paper we show a striking counterexample to this intuition via the seemingly trivial coordinate transform problem, which simply requires learning a mapping between coordinates in (x,y) Cartesian space and one-hot pixel space. Although convolutional networks would seem appropriate for this task, we show that they fail spectacularly. We demonstrate and carefully analyze the failure first on a toy problem, at which point a simple fix becomes obvious."