Efficient sensory coding of multidimensional stimuli
Fig 2
Parameterizing hetereogeneous neuronal populations.
A) A uniform population of neurons approximately tiles the stimulus space (s) with identical, equally spaced Gaussian tuning curves. B) The Fisher information of this population is roughly uniform (blue line), matching the approximation in Eq (16) (red line). C) A displacement field that is smooth and slowly varying relative to the tuning curves. These displacement values apply to the stimulus space, arrows below illustrate the direction and magnitude of shifts in the resulting tuning curves defined over s (which corresponds to the inverse of the displacement field). D) After the displacement field is applied, the neuronal population now has heterogeneous tuning curves. Displacements that stretch the stimulus space result in denser, narrower tunings. Displacements that compress the stimulus space result in sparser, wider tunings. E) A gain function that is smooth relative to the tuning curves can also allow neurons to have different response magnitudes. F) Following the application of both the displacement field and the gain function, we have a transformed heterogeneous population with variable tuning curves. G) The Fisher information in the hetereogenous population is no longer uniform, as illustrated by the measured (blue) and approximated (red) lines. S1 Fig illustrates the consequences when the displacement field and gain function are not smooth and slowly varying with respect to the tuning curves.