Nonlinear scaling of resource allocation in sensory bottlenecks

In many sensory systems, information transmission is constrained by a bottleneck, where the number of output neurons is vastly smaller than the number of input neurons. Efficient coding theory predicts that in these scenarios the brain should allocate its limited resources by removing redundant information. Previous work has typically assumed that receptors are uniformly distributed across the sensory sheet, when in reality these vary in density, often by an order of magnitude. How, then, should the brain efficiently allocate output neurons when the density of input neurons is nonuniform? Here, we show analytically and numerically that resource allocation scales nonlinearly in efficient coding models that maximize information transfer, when inputs arise from separate regions with different receptor densities.