Figure 2

Signal to solution maps and their statistical properties. (a) Output signals of reservoirs, shown in red, are mapped to (i) binary sequences by thresholding signal amplitude (i.e., neural activity) at regular time intervals (top), or to permutations by ordering these signal amplitudes. (b–e) Statistical representation bias of signal to solution maps, showing that a few solutions are represented by many signals, while most solutions are represented by only a few signals. (b, d) Number of different solutions as a function of the number of sampled solutions. Samples are drawn uniformly in signal space (blue; see “Materials and methods” for details), or in solution space (red). While uniform sampling in solution space saturates exponentially, uniform sampling in signal space leads to a different saturation curve as an effect of some solutions being sampled many times while others are sampled less or not at all. (c, e) Number of different solutions (types, y axis) with a given sampled frequency (token frequency, x axis), mirroring representation bias.