(A) Normalized root mean square error (NRMSE) between neural and head angular velocity, for gain-1 networks that subsequently have been rewired to learn different gains. To compute the NRMSE, we first estimate from PI performance plots (examples in (B), (C), and (D)) the root mean square error (RMSE) between the neural and head angular velocity, but only within the range of head angular velocities that each network can handle. This range is restricted because there is a maximum neural angular velocity (e.g. blue dot-dashed line in C; see also Appendix 1—figure 1A); thus the range of head angular velocity is given by this maximum neural angular velocity divided by the gain . Then, to obtain the NRMSE we divide the RMSE by that range. For instance, in (C), and deg/s. Then the head angular velocity range we test is determined by the x-coordinate for which the Gain-10 line (gray, dashed) meets the neural velocity limit line (blue, dot-dash); hence in this extreme example we only test for the range [-115, 115] deg/s. We find that rewiring performance is excellent for gains between 0.25 and 4.5, for which NRMSE is less than 0.15. Note that the more a new gain differs from original gain 1, the longer it takes for the network to rewire. (B), (C) PI performance plots for a small () and a large () gain. The NRMSE is 0.31 and 0.46, respectively. Performance is impaired because the flat area for small angular velocities gets enlarged in (B), whereas the network struggles to keep up with the desired gain in (C). (D) PI performance plot for a network that has been instructed to reverse its gain (from +1 to -1), i.e. when the visual and self-motion inputs are signaling movement in opposite directions. Performance is excellent, indicating that there is nothing special about negative gains; albeit learning takes considerably more time. (E), (F) Weight history for HR-to-HD and for recurrent connections, respectively, for the network trained to reverse its gain. The directionality of the asymmetric HR-to-HD connections in (E) reverses only after ∼20 hours, while the recurrent weights in (F) remain largely unaltered.