Embeddings in machine learning are low-dimensional representations of complex\ninput patterns, with the property that simple geometric operations like\nEuclidean distances and dot products can be used for classification and\ncomparison tasks. The proposed meta-embeddings are special embeddings that live\nin more general inner product spaces. They are designed to propagate\nuncertainty to the final output in speaker recognition and similar\napplications. The familiar Gaussian PLDA model (GPLDA) can be re-formulated as\nan extractor for Gaussian meta-embeddings (GMEs), such that likelihood ratio\nscores are given by Hilbert space inner products between Gaussian likelihood\nfunctions. GMEs extracted by the GPLDA model have fixed precisions and do not\npropagate uncertainty. We show that a generalization to heavy-tailed PLDA gives\nGMEs with variable precisions, which do propagate uncertainty. Experiments on\nNIST SRE 2010 and 2016 show that the proposed method applied to i-vectors\nwithout length normalization is up to 20% more accurate than GPLDA applied to\nlength-normalized ivectors.\n