  Embeddings in machine learning are low-dimensional representations of complex
input patterns, with the property that simple geometric operations like
Euclidean distances and dot products can be used for classification and
comparison tasks. The proposed meta-embeddings are special embeddings that live
in more general inner product spaces. They are designed to propagate
uncertainty to the final output in speaker recognition and similar
applications. The familiar Gaussian PLDA model (GPLDA) can be re-formulated as
an extractor for Gaussian meta-embeddings (GMEs), such that likelihood ratio
scores are given by Hilbert space inner products between Gaussian likelihood
functions. GMEs extracted by the GPLDA model have fixed precisions and do not
propagate uncertainty. We show that a generalization to heavy-tailed PLDA gives
GMEs with variable precisions, which do propagate uncertainty. Experiments on
NIST SRE 2010 and 2016 show that the proposed method applied to i-vectors
without length normalization is up to 20% more accurate than GPLDA applied to
length-normalized ivectors.
