A mechanism is proposed by which feedback pathways model spatial patterns of feedforward activity in cortical maps. The mechanism can be viewed equivalently as readout of a content-addressable memory or as decoding of a population code. The model is based on the evidence that cortical receptive fields can often be described as a separable product of functions along several dimensions, each represented in a spatially ordered map. Given this, it is shown that for an N-dimensional map, accurate modeling and decoding of xN feedforward activity patterns can be done with Nx fibers, N of which must be active at any one time. The proposed mechanism explains several known properties of the cortex and pyramidal neurons: (1) the integration of signals by dendrites with a narrow tangential distribution, that is, apical dendrites; (2) the presence of fast-conducting feedback projections with broad tangential distributions; (3) the multiplicative effects of attention on receptive field profiles; and (4) the existence of multiplicative interactions between subthreshold feedforward inputs to basal dendrites and inputs to apical dendrites.