Figure 3

(a) Recurrent Darwinian neurodynamics over a 1D array of reservoirs solving the travelling salesman problem (TSP). Shorter paths in solution space correspond to higher fitness in signal space. Top: Highest-fitness signals of their generation. Bottom: Corresponding solutions, permutations representing a path over major Hungarian cities. (b) Phylogenies of neural firing patterns. A 1D array of reservoirs is shown horizontally; time evolution proceeds vertically downwards. Color corresponds to the fitness of signals outputted by their reservoirs, evaluated over an NK landscape with \(N=20\) and \(K=5\). Signals with higher fitness spread over local connections between reservoirs. Reservoirs differ in their ability to learn, in extreme cases, they form defects or local walls. (c) Phylogeny of firing patterns over a 2D sheet of reservoirs. Cross sections (right) illustrate local spread of high fitness firing patterns, leading to competing homogeneous islands. Sporadic reservoirs with diminished ability to learn do not hinder the process significantly, as opposed to the 1D case. (d) Evolutionary information gain \(I_f\) over time. In all cases, the population of firing patterns adapts to an NK landscape with \(N=20\) (hence the maximum of \(I_f\) is 20) and \(K=5\). We display three levels of between-run variability here. (i) dimensionality of the arrangement of reservoirs (columns); (ii) two realizations of an NK landscape with \(N=20\) and \(K=5\) (top & bottom); (iii) two different initial populations of firing patterns (rows in each block). Although there is a high level of between-run variability across all dimensions, the population of firing patterns keeps finding better and better solutions in all cases, suggesting the feasibility of this process as an efficient computational module.