Extended Data Fig. 3: Abrupt changes in encoding parameters arise from bifurcations in error landscapes.
a,b, Encoding nonlinearies (left panels; shown in Fig. 4d,e) show abrupt changes for small variations in the system’s posterior belief P(high) = \({P}_{t}^{H}\). These changes arise from variations in the underlying error landscapes (right panels) in which a single minimum bifurcates into two minima or vice-versa (a, upper row; global minima marked by red x’s), or when one of multiple local minima becomes the global minimum (a, lower row; b, both rows). In the case of variance adaptation, the error landscape is symmetric to positive versus negative variations in the offset of the encoding nonlinearity (x0), and thus bifurcations in the error landscape lead to two symmetric solutions (a, upper row). In such scenarios, we chose the solution corresponding to the lower value of x0 (marked by circles), because it produces lower spike counts on average.
