  Given the success of the deep convolutional neural networks (DCNNs) in
applications of visual recognition and classification, it would be tantalizing
to test if DCNNs can also learn spatial concepts, such as straightness,
convexity, left/right, front/back, relative size, aspect ratio, polygons, etc.,
from varied visual examples of these concepts that are simple and yet vital for
spatial reasoning. Much to our dismay, extensive experiments of the type of
cognitive psychology demonstrate that the data-driven deep learning (DL) cannot
see through superficial variations in visual representations and grasp the
spatial concept in abstraction. The root cause of failure turns out to be the
learning methodology, not the computational model of the neural network itself.
By incorporating task-specific convolutional kernels, we are able to construct
DCNNs for spatial cognition tasks that can generalize to input images not drawn
from the same distribution of the training set. This work raises a precaution
that without manually-incorporated priors or features DCCNs may fail spatial
cognitive tasks at rudimentary level.
