Fig. 2
From: Input–output maps are strongly biased towards simple outputs
Variable complexity matrix map. The complexity of the 20 × 20 circulant matrix map can be varied by changing the complexity \(\tilde K(\mathrm{row})\) of the first row that defines the map. \(\tilde K_o{\mathrm{/}}\tilde K_i\) measures the ratio of the mean complexity of all individual outputs of a given map, divided by the mean complexity of outputs generated by random sampling over all inputs. In this plot, made with 2.5 × 104 matrices, the distribution of ratios \(\tilde K_o{\mathrm{/}}\tilde K_i\) is shown in a standard violin plot format. The horizontal dark blue lines denote the mean \(\tilde K_o{\mathrm{/}}\tilde K_i\) for each value of \(\tilde K(\mathrm{row})\). Only relatively simple matrix maps (with smaller K̃(row)) exhibit simplicity bias, as indicated by \(\tilde K_o{\mathrm{/}}\tilde K_i\) being significantly >1
