Before revision:  Among all the possible hierarchically local tasks in vision, text and speech we explore a few of them experimentally by studying how they are affected by disrupting locality in the input images . We also discuss a taxonomy of tasks ranging from local, to hierarchically local, to global and make predictions about the type of networks required to perform efficiently on these different types of tasks .
After revision:  To evaluate this, we consider a set of visual tasks where we disrupt the URLanization of images via "deterministic scrambling" to later perform a visual task on these images structurally-altered in the same way for training and testing. For object recognition we find, as expected, that scrambling does not affect the performance of shallow or deep fully connected networks contrary to the out-performance of convolutional networks. Not all tasks involving images are however affected. Texture perception and global color estimation are much less sensitive to deterministic scrambling showing that the underlying functions corresponding to these tasks are not hierarchically local; and also counter-intuitively showing that these tasks are better approximated by networks that are not deep (texture) nor convolutional (color). Altogether, these results shed light into the importance of matching a network architecture with its embedded prior of the task to be learned .