Smooth random manifolds provide a flexible way of generating synthetic spike-timing data sets. (a) Four one-dimensional example manifolds for different smoothness parameters $α$ in a three-dimensional embedding space. From each manifold, we plotted 1000 random data points. (b) Same as in panel a, but keeping $α=3$ fixed while changing the manifold-dimension $D$ and the number of random manifolds (different colors). By sampling different random manifolds, it is straight-forward to build synthetic multiway classification tasks. (c) Spike raster plots corresponding to 12 samples along the intrinsic manifold coordinate $x$ of a one-dimensional smooth random manifold (⁠$α=3$⁠) whereby we interpreted the embedding space coordinates as firing times of the individual neurons.