In this poster we study analytically the model of Anderson et al. We explain how the proposed mechanism works. We derive the required conditions to get this invariance. In particular we find that it can only be approximate, that it requires that the neuron firing rate is not too large and that increasing or lowering the contrast too much destroys it. There is also an upper and lower limit for the noise variance. Within these constraints, the mechanism is quite general. Neither the threshold linearity of the transfer function, nor the Gaussianity of the added noise, are crucial.
This is confirmed by a further analytical study which uses an integrate and fire neuron receiving tuned input with added Gaussian noise, and numerical simulations of a conductance based neuron that receives Poissonian synaptic inputs. In these two models we assume that the input is contrast invariant. With an appropriate setting of the noise, this input contrast invariance results in an approximate contrast invariance for the mean voltage as well as the mean firing rate.
We also show that, if this mechanism operates in V1, the spike response, r, and voltage response v of the neurons in V1 should vary with the contrast, C, according to r(C) ~ v(C)a, where a can be estimated from the amount by which the spike tuning curve is sharpened with respect to the voltage tuning curves of the neurons. This prediction does not depends on the details of the model, and can easily be checked experimentally.