Figure 4.

Modularity improves robustness to perturbation and increases state-dependency for a fixed size of the hidden layer. (A) Robustness of the network averaged over the effects of activating each hidden neuron as a function of the hidden layer size, R and varying levels of modularity, μ. Here, robustness $\mathcal{A}(\mu )$ is defined as the numbers of behaviors that are not affected upon forcefully activating a neuron in the network. (B) Average mutual information (defined as in Equation 9) between the input and output distributions after forced activation of each hidden neuron as a function of the size of the hidden layer R, and varying levels of modularity, μ. To highlight the effects of increasing modularity, we show the results relative to the lowest modularity. The figure for the absolute values is reported in Supplementary Figure 5. The mutual information turns out to be $\mathcal{A}(\mu )\times \frac{1}{M}{\mathrm{\text{log}}}_2(N)$ due to the absence of stereotypy. (A,B) N = M = 100 and results are means over 5 iterations with the error bars corresponding to the standard deviation. Stars correspond to the R_c value for each value of modularity.