This paper provides a theoretical framework for interpreting acoustic contiguous embeddings, which are representations of variable-width audio or textual speech content in a fixed-dimensional embedding space. Based on a common quantitative definition of phonetic similarity between words, a probabilistic interpretation of the distance between embeddings is proposed. This provides a framework for understanding and applying embedding in a principled way. Theoretical and empirical evidence is presented to support a uniform clusterwise isotropic approximation, which reduces the distance to a simple Euclidean distance. We describe four experiments that validate the framework and demonstrate how it can be applied to a variety of problems. Nearest neighbor search between audio and text embeddings yields isolated word classification accuracy comparable to finite state transducer (FST) for vocabularies as large as 500k. Embedding distance provides a 0.5 percentage point difference in accuracy compared to telephone edit distance in recovering out-of-lexical words and produces a clustering hierarchy that is identical to that obtained from human listening experiments in English dialect clustering. The theoretical framework also allows us to use embeddings to predict the expected disruption of device wake-up words. All source code and pre-trained models are provided.
