In the early sensory and motor areas of the cortex, individual neurons transmit information about specific sensory features via a peaked response. This concept has been crystallized as `labeled lines,' to denote that axons communicate the specific properties of their sensory or motor parent cell. Such cells also can be characterized as being polarized, that is, as representing a signed quantity that is either positive or negative. We show in a model simulation that there are two important consequences when learning receptive fields using such signed codings in circuits that subtract different inputs. The first is that, in feedback circuits using labeled lines, such arithmetic operations need to be distributed across multiple distinct pathways. The second consequence is that such pathways must be necessarily dynamic, i.e. that synapses can grow and retract when forming receptive fields. The model monitors the breaking and growing of new circuit connections when their synapses need to change polarities and predicts that the rate of such changes should be inversely correlated with the progress of receptive field formation.