Abstract: We study the problem of verifying when two disjoint closed convex sets remain separable after the application of a quantised random embedding, as a means to ensure exact classification from the signatures produced by this non-linear dimensionality reduction. An analysis of the interplay between the embedding, its quantiser resolution and the sets’ separation is presented in the form of a convex problem; this is completed by its numerical exploration in a special case, for which the phase transition corresponding to exact classification is easily computed.