Is the U-Net Directional-Relationship Aware?

CNNs are often assumed to be capable of using contextual information about distinct objects (such as their directional relations) inside their receptive field. However, the nature and limits of this capacity has never been explored in full. We explore a specific type of relationship~-- directional~-- using a standard U-Net trained to optimize a cross-entropy loss function for segmentation. We train this network on a pretext segmentation task requiring directional relation reasoning for success and state that, with enough data and a sufficiently large receptive field, it succeeds to learn the proposed task. We further explore what the network has learned by analysing scenarios where the directional relationships are perturbed, and show that the network has learned to reason using these relationships.