Nonlinear dendrites increase the robustness of associative memory retrieval against noise, optimally at an intermediate number of branches. (A) Overlap m of the network state with a retrieval pattern for linear dendrites (black) and increasing strengths of the dendritic nonlinearity (gray, yellow, red). The critical temperature TC at which the overlap becomes zero increases with increasing nonlinearity. Analytical and numerical results are given by continuous curves and circles, respectively. (B) Overlap vs. temperature-curves for different numbers of dendritic branches, increasing branch numbers are color-coded from black to red. The critical temperature depends non-monotonically on the number of branches and assumes a maximum at an intermediate value (C).