Figure 1.

Schematic diagram illustrating bases for the proposed measure of degeneracy. (A) We consider a system X, composed of individual elements (gray circles, n = 8) that are interconnected (arrows) among each other [with a connection matrix CON(X)] and that also have connections to a set of output units O [with a connection matrix CON(X;O)]. (B) A subset (shaded in gray) of the system X is perturbed by injecting (large Vs at the top) a fixed amount of variance (uncorrelated noise) into each of its constituent units. This perturbation activates numerous connections within the system (thick arrows) and produces changes in the variance of a number of units within X and O. The resulting mutual information under perturbation MI^P(X^k_j;O) is computed (see Eq. 1). This procedure is repeated for all subsets of sizes 1 ≤ k ≤ n of the system X.