How Do Efficient Coding Strategies Depend on Origins of Noise in Neural Circuits?
Fig 2
Optimal nonlinearities when one noise source dominates, found by minimizing the mean squared error (MSE) of a linear estimator.
Each row shows three separate cases in which a single source of noise dominates. The dominant noise source is indicated by the highlighted source in the circuit schematics left of each row. The overall level of noise is quantified by the signal-to-noise ratio (SNR), which is fixed in each column. The SNR is largest in the leftmost column and smallest in the rightmost column; i.e., the strength of the noise increases toward the right. The shape of the optimal nonlinearity changes markedly depending on which noise source dominates the circuit, even when the overall signal-to-noise ratio of model responses is the same. Analytical results (dashed colored lines) and simulations with sigmoidal nonlinearities (solid lines) are shown. The stimulus distribution (dashed gray curve) is also shown for reference. Shaded regions encompass nonlinearities that perform within 1% of the minimum mean squared error of the optimal sigmoidal nonlinearity. The SNR is computed as the variance of the signal (the variance, across all inputs, of the average response to a given input) divided by the variance of the noise (the average variance in responses to a given input); see Methods.